WEBVTT 00:00:00.000 --> 00:00:01.973 align:middle line:90% [SQUEAKING] 00:00:01.973 --> 00:00:03.446 align:middle line:90% [RUSTLING] 00:00:03.446 --> 00:00:05.901 align:middle line:90% [CLICKING] 00:00:05.901 --> 00:00:10.140 align:middle line:90% 00:00:10.140 --> 00:00:15.600 align:middle line:84% HAZHIR RAHMANDAD: OK, so for today, 00:00:15.600 --> 00:00:19.880 align:middle line:84% we can actually do a quick recap on SEIRb. 00:00:19.880 --> 00:00:24.120 align:middle line:84% So as we discussed, I think we covered pretty much everything. 00:00:24.120 --> 00:00:28.800 align:middle line:84% There were a couple of items that when I decided, OK, maybe I 00:00:28.800 --> 00:00:34.400 align:middle line:84% should build a solution-ish model to share with you, 00:00:34.400 --> 00:00:37.100 align:middle line:84% I noted that we didn't discuss it as closely, 00:00:37.100 --> 00:00:40.940 align:middle line:84% so I wanted to bring up those couple of items. 00:00:40.940 --> 00:00:44.860 align:middle line:84% And then we can switch to our main work. 00:00:44.860 --> 00:00:50.040 align:middle line:84% So last week, Alexander asked the question about, 00:00:50.040 --> 00:00:54.600 align:middle line:84% how do we handle the waning of immunity due to natural 00:00:54.600 --> 00:00:58.920 align:middle line:90% versus vaccine-based immunity? 00:00:58.920 --> 00:01:01.780 align:middle line:84% And the challenge is that if you have somebody 00:01:01.780 --> 00:01:07.660 align:middle line:84% who had gotten vaccinated and then later they got the disease, 00:01:07.660 --> 00:01:11.780 align:middle line:84% they have both natural immunity and vaccine-driven immunity. 00:01:11.780 --> 00:01:14.360 align:middle line:84% And you need to decide how do you route them. 00:01:14.360 --> 00:01:17.420 align:middle line:84% Do you send them back to the group that 00:01:17.420 --> 00:01:21.280 align:middle line:84% is susceptible but vaccinated-- that is, 00:01:21.280 --> 00:01:27.640 align:middle line:84% keep their vaccine immunity, but wane their natural immunity? 00:01:27.640 --> 00:01:33.940 align:middle line:84% Or send them to the group that is susceptible and completely 00:01:33.940 --> 00:01:37.440 align:middle line:84% unprotected-- that is wane both of them at the same time? 00:01:37.440 --> 00:01:41.980 align:middle line:84% Or even send them to the group of recovered 00:01:41.980 --> 00:01:44.420 align:middle line:84% but without vaccine immunity-- that 00:01:44.420 --> 00:01:48.560 align:middle line:84% is wane the vaccine immunity, but not the natural immunity? 00:01:48.560 --> 00:01:51.360 align:middle line:84% And then later, the natural immunity waning happens. 00:01:51.360 --> 00:01:53.440 align:middle line:90% And we didn't really discuss it. 00:01:53.440 --> 00:01:57.640 align:middle line:84% And I gave a quick answer that wasn't quite going 00:01:57.640 --> 00:01:59.180 align:middle line:90% through the details of it. 00:01:59.180 --> 00:02:02.500 align:middle line:84% So I wanted to highlight how to deal with that situation, 00:02:02.500 --> 00:02:05.020 align:middle line:84% because it's a fairly common situation, actually, 00:02:05.020 --> 00:02:10.080 align:middle line:84% when you have these multiple stages and different movements 00:02:10.080 --> 00:02:11.840 align:middle line:84% across different multiple stages-- that 00:02:11.840 --> 00:02:17.440 align:middle line:84% is, for example, you can both go right and down, if you are 00:02:17.440 --> 00:02:19.880 align:middle line:90% thinking of the two dimensions. 00:02:19.880 --> 00:02:25.240 align:middle line:84% So here is the model I put together. 00:02:25.240 --> 00:02:28.120 align:middle line:84% And here, we are really talking about what 00:02:28.120 --> 00:02:32.920 align:middle line:84% is happening on the right-hand side 00:02:32.920 --> 00:02:39.400 align:middle line:84% from people who are vaccinated and recovered. 00:02:39.400 --> 00:02:41.880 align:middle line:84% And then what happens to them, basically? 00:02:41.880 --> 00:02:47.840 align:middle line:84% So one possibility for them is to wane their natural immunity 00:02:47.840 --> 00:02:52.720 align:middle line:84% and go into the vaccinated susceptible population. 00:02:52.720 --> 00:02:58.250 align:middle line:84% Another possibility for them is to wane their vaccine immunity 00:02:58.250 --> 00:03:03.210 align:middle line:84% and go up into recovered population 00:03:03.210 --> 00:03:05.810 align:middle line:90% without vaccine protection. 00:03:05.810 --> 00:03:09.130 align:middle line:84% And we also discussed a possibility 00:03:09.130 --> 00:03:12.570 align:middle line:84% of these people waning both types of immunity 00:03:12.570 --> 00:03:16.450 align:middle line:84% and going to unvaccinated susceptible population. 00:03:16.450 --> 00:03:20.530 align:middle line:84% And the critical idea here to keep in mind 00:03:20.530 --> 00:03:24.690 align:middle line:84% is that we usually don't want to have two different state 00:03:24.690 --> 00:03:27.490 align:middle line:84% transitions happening at the same time. 00:03:27.490 --> 00:03:33.450 align:middle line:84% So the long jump from recovered vaccinated all the way 00:03:33.450 --> 00:03:38.310 align:middle line:84% to susceptible and unvaccinated has these double jumps. 00:03:38.310 --> 00:03:41.530 align:middle line:84% That is, you're capturing two different state transitions 00:03:41.530 --> 00:03:42.770 align:middle line:90% at the same time. 00:03:42.770 --> 00:03:46.890 align:middle line:84% And it is hard to do that internally consistently. 00:03:46.890 --> 00:03:52.890 align:middle line:84% So as a good heuristic, avoid doing that, and do one jump. 00:03:52.890 --> 00:03:55.250 align:middle line:84% And then when you do one jump, it is very easy. 00:03:55.250 --> 00:03:57.870 align:middle line:84% Basically, both jumps can happen with 00:03:57.870 --> 00:04:00.110 align:middle line:90% their own independent rates. 00:04:00.110 --> 00:04:02.710 align:middle line:84% Now, there are some underlying assumptions when 00:04:02.710 --> 00:04:06.470 align:middle line:90% you make that type of movement. 00:04:06.470 --> 00:04:09.950 align:middle line:84% That is, you're saying the two types of immunity 00:04:09.950 --> 00:04:11.910 align:middle line:90% are independent of each other. 00:04:11.910 --> 00:04:14.990 align:middle line:84% One can wane with its own rate and the other 00:04:14.990 --> 00:04:19.510 align:middle line:84% can wane with its own rate, and the two don't impact each other. 00:04:19.510 --> 00:04:21.089 align:middle line:90% That is an assumption. 00:04:21.089 --> 00:04:22.970 align:middle line:84% Now, if you want to relax that assumption, 00:04:22.970 --> 00:04:26.810 align:middle line:84% you really have to model how they are interdependent. 00:04:26.810 --> 00:04:31.710 align:middle line:84% That is, when you get vaccine immunity 00:04:31.710 --> 00:04:34.430 align:middle line:84% and then you get the disease, you 00:04:34.430 --> 00:04:37.190 align:middle line:84% go into a different type of a state that changes 00:04:37.190 --> 00:04:42.950 align:middle line:90% your rate of immunity loss. 00:04:42.950 --> 00:04:46.430 align:middle line:84% So that becomes a little bit more complex but doable. 00:04:46.430 --> 00:04:48.550 align:middle line:84% Here, we are keeping the simple assumption 00:04:48.550 --> 00:04:52.570 align:middle line:84% that the two sources of immunity are independent of each other. 00:04:52.570 --> 00:04:56.430 align:middle line:84% And then it becomes the simple formulation that we have here. 00:04:56.430 --> 00:04:58.530 align:middle line:84% It's actually very straightforward, very 00:04:58.530 --> 00:05:01.950 align:middle line:84% parallel with what is happening in the rest of the method. 00:05:01.950 --> 00:05:04.290 align:middle line:84% That is, you have the vaccine waning, 00:05:04.290 --> 00:05:08.750 align:middle line:84% which is with the vaccine efficacy duration. 00:05:08.750 --> 00:05:11.490 align:middle line:84% So this is the same time constant with which 00:05:11.490 --> 00:05:15.610 align:middle line:84% we are waning the immunity of Vaccinated S going back 00:05:15.610 --> 00:05:21.170 align:middle line:84% into Unvaccinated S. So the same time constant works 00:05:21.170 --> 00:05:22.490 align:middle line:90% for both of them. 00:05:22.490 --> 00:05:30.750 align:middle line:84% And similarly, we have the waning of natural immunity, 00:05:30.750 --> 00:05:33.790 align:middle line:84% so vaccinated waning of natural immunity, 00:05:33.790 --> 00:05:37.290 align:middle line:84% that happens with the natural immunity period, which 00:05:37.290 --> 00:05:39.970 align:middle line:84% is the same parameter used to wane 00:05:39.970 --> 00:05:43.810 align:middle line:84% the immunity for the recovered population. 00:05:43.810 --> 00:05:46.770 align:middle line:84% Natural immunity period is also operating here. 00:05:46.770 --> 00:05:51.030 align:middle line:84% So this keeps things fairly simple, fairly clean. 00:05:51.030 --> 00:05:57.890 align:middle line:84% And the things are internally consistent. 00:05:57.890 --> 00:06:02.250 align:middle line:84% And you can actually now do the calculations, 00:06:02.250 --> 00:06:08.550 align:middle line:84% for example, how long a typical person entering the Vaccinated R 00:06:08.550 --> 00:06:13.710 align:middle line:84% state will remain in this state, which 00:06:13.710 --> 00:06:22.070 align:middle line:84% is the harmonic average of the two time constants. 00:06:22.070 --> 00:06:28.470 align:middle line:84% You can calculate what's the probability that they go up 00:06:28.470 --> 00:06:29.730 align:middle line:90% versus they go down. 00:06:29.730 --> 00:06:34.130 align:middle line:84% You can do all of the kind of equilibrium-type of analysis 00:06:34.130 --> 00:06:39.590 align:middle line:84% you may be interested in once you lay this out. 00:06:39.590 --> 00:06:40.930 align:middle line:90% So that's number one. 00:06:40.930 --> 00:06:44.710 align:middle line:84% And in fact, theoretically, you could 00:06:44.710 --> 00:06:50.160 align:middle line:84% have the waning of vaccine immunity 00:06:50.160 --> 00:06:52.980 align:middle line:84% during the period you are vaccinated and infected. 00:06:52.980 --> 00:06:59.520 align:middle line:84% You could actually go up into unvaccinated and infected stock 00:06:59.520 --> 00:07:01.200 align:middle line:84% because your immunity from vaccine 00:07:01.200 --> 00:07:03.680 align:middle line:84% is waning during that short period. 00:07:03.680 --> 00:07:07.320 align:middle line:84% In fact, that is probably a little bit more correct in terms 00:07:07.320 --> 00:07:09.640 align:middle line:90% of the machinery of the model. 00:07:09.640 --> 00:07:11.940 align:middle line:84% But because this is a very short period 00:07:11.940 --> 00:07:15.840 align:middle line:84% and you could kind of assume that during the time 00:07:15.840 --> 00:07:19.840 align:middle line:84% you are getting sick, actually, waning of immunity 00:07:19.840 --> 00:07:21.800 align:middle line:84% stops because your immune system is responding 00:07:21.800 --> 00:07:24.320 align:middle line:84% very heavily and so on, I think it is also 00:07:24.320 --> 00:07:28.240 align:middle line:84% OK not to include that flow variable in this model. 00:07:28.240 --> 00:07:32.120 align:middle line:84% So that's kind of a choice that we are making. 00:07:32.120 --> 00:07:33.740 align:middle line:84% It's not something we are missing. 00:07:33.740 --> 00:07:35.380 align:middle line:90% So that's number one. 00:07:35.380 --> 00:07:37.880 align:middle line:84% Any questions on that conversation 00:07:37.880 --> 00:07:40.260 align:middle line:90% on this part of the model? 00:07:40.260 --> 00:07:45.000 align:middle line:90% 00:07:45.000 --> 00:07:49.000 align:middle line:84% So then one more very minor thing, 00:07:49.000 --> 00:07:52.300 align:middle line:84% but something that is important for accounting. 00:07:52.300 --> 00:07:58.060 align:middle line:84% We talked about the current fraction of population 00:07:58.060 --> 00:08:00.300 align:middle line:90% that is willing to vaccinate. 00:08:00.300 --> 00:08:07.900 align:middle line:84% We said that's an important concept we need for calculating 00:08:07.900 --> 00:08:10.300 align:middle line:90% the vaccination rate. 00:08:10.300 --> 00:08:13.940 align:middle line:84% So the way we formulated vaccination rate up here 00:08:13.940 --> 00:08:19.940 align:middle line:84% is that we said, we need to have the unvaccinated fraction that 00:08:19.940 --> 00:08:22.300 align:middle line:90% is willing to vaccinate. 00:08:22.300 --> 00:08:25.500 align:middle line:84% That unvaccinated fraction that is willing to vaccinate 00:08:25.500 --> 00:08:27.140 align:middle line:84% comes from the current fraction that 00:08:27.140 --> 00:08:30.300 align:middle line:84% is willing to vaccinate of the total population 00:08:30.300 --> 00:08:32.900 align:middle line:90% versus vaccinated fraction. 00:08:32.900 --> 00:08:36.179 align:middle line:84% And vaccinated fraction is all of the vaccinated people divided 00:08:36.179 --> 00:08:40.940 align:middle line:84% by all of the people and current fraction willing to vaccinate. 00:08:40.940 --> 00:08:43.843 align:middle line:84% Normally, you may think of it as a fixed number. 00:08:43.843 --> 00:08:45.260 align:middle line:84% It's just a fraction of population 00:08:45.260 --> 00:08:47.160 align:middle line:90% that is willing to vaccinate. 00:08:47.160 --> 00:08:50.500 align:middle line:84% But if you think about these dynamics, 00:08:50.500 --> 00:08:53.960 align:middle line:84% if you had a disease where vaccine was very protective 00:08:53.960 --> 00:08:57.040 align:middle line:84% and the disease was very deadly, people 00:08:57.040 --> 00:08:59.440 align:middle line:84% who are unwilling to vaccinate are 00:08:59.440 --> 00:09:02.680 align:middle line:84% likely to get the disease very frequently 00:09:02.680 --> 00:09:06.080 align:middle line:90% and die at a much higher rate. 00:09:06.080 --> 00:09:08.520 align:middle line:84% In which case, the fraction of people 00:09:08.520 --> 00:09:11.500 align:middle line:84% who are willing to vaccinate is dynamically changing. 00:09:11.500 --> 00:09:14.720 align:middle line:84% That is, over time that fraction is increasing. 00:09:14.720 --> 00:09:18.240 align:middle line:84% So you need to capture that dynamic explicitly. 00:09:18.240 --> 00:09:22.380 align:middle line:84% So that's another wrinkle that we didn't really talk about. 00:09:22.380 --> 00:09:25.720 align:middle line:84% But for an internally consistent clean model, 00:09:25.720 --> 00:09:27.300 align:middle line:90% we need to capture that. 00:09:27.300 --> 00:09:31.640 align:middle line:84% Now to capture that, you need to accumulate the vaccinated dead. 00:09:31.640 --> 00:09:33.320 align:middle line:84% You need to basically see how many 00:09:33.320 --> 00:09:38.100 align:middle line:84% people who aren't unvaccinated that are dead 00:09:38.100 --> 00:09:41.800 align:middle line:84% and then calculate what fraction of the population 00:09:41.800 --> 00:09:50.820 align:middle line:84% remains that is willing to get vaccinated. 00:09:50.820 --> 00:09:53.480 align:middle line:84% And total population is accounting for those deaths. 00:09:53.480 --> 00:09:57.140 align:middle line:84% So the unvaccinated that is dead is removed 00:09:57.140 --> 00:09:59.520 align:middle line:90% from the total population. 00:09:59.520 --> 00:10:04.100 align:middle line:84% So those two, I think, are kind of two small pieces 00:10:04.100 --> 00:10:07.940 align:middle line:84% from last week that we didn't close the loop on. 00:10:07.940 --> 00:10:10.980 align:middle line:84% We also didn't discuss the equilibrium conditions 00:10:10.980 --> 00:10:12.700 align:middle line:90% explicitly. 00:10:12.700 --> 00:10:15.960 align:middle line:84% And the equilibrium conditions, I think a couple of you-- 00:10:15.960 --> 00:10:19.100 align:middle line:84% so I think you submitted one and Jason submitted one, 00:10:19.100 --> 00:10:20.200 align:middle line:90% so that was nice. 00:10:20.200 --> 00:10:24.340 align:middle line:84% I think those who submitted it for the situation 00:10:24.340 --> 00:10:29.320 align:middle line:84% that we had the waning of natural immunity 00:10:29.320 --> 00:10:32.740 align:middle line:84% but not vaccination and no behavioral response. 00:10:32.740 --> 00:10:37.500 align:middle line:84% So without those, it is a fairly straightforward setup. 00:10:37.500 --> 00:10:39.460 align:middle line:84% You can solve it for the case where 00:10:39.460 --> 00:10:41.940 align:middle line:84% we do have behavioral response, as well, 00:10:41.940 --> 00:10:45.300 align:middle line:84% depending on the formulation you use for behavioral response. 00:10:45.300 --> 00:10:49.000 align:middle line:84% So in the paper that I shared through email, 00:10:49.000 --> 00:10:50.880 align:middle line:84% there is a section that actually I 00:10:50.880 --> 00:10:54.480 align:middle line:84% go through solving of that equilibrium condition 00:10:54.480 --> 00:10:56.560 align:middle line:90% with behavioral response. 00:10:56.560 --> 00:10:57.980 align:middle line:90% So take a look at that. 00:10:57.980 --> 00:11:05.160 align:middle line:84% That might be kind of helpful for thinking through the case 00:11:05.160 --> 00:11:09.240 align:middle line:84% with behavioral response, which is the more realistic one. 00:11:09.240 --> 00:11:13.960 align:middle line:84% And then the vaccination and waning of vaccination, 00:11:13.960 --> 00:11:16.700 align:middle line:84% it is a linear model, so I think it is solvable, 00:11:16.700 --> 00:11:18.540 align:middle line:84% but it becomes a messier problem. 00:11:18.540 --> 00:11:21.520 align:middle line:84% So it's something you can actually 00:11:21.520 --> 00:11:25.560 align:middle line:84% try defining the problem cleanly for ChatGPT 00:11:25.560 --> 00:11:31.560 align:middle line:84% and see if it can solve the equilibrium condition for you. 00:11:31.560 --> 00:11:35.920 align:middle line:84% You should be able to at least define the problem very clearly 00:11:35.920 --> 00:11:36.620 align:middle line:90% for it to work. 00:11:36.620 --> 00:11:43.870 align:middle line:84% So that was kind of the couple of items I had on the SEIRb. 00:11:43.870 --> 00:11:50.330 align:middle line:84% Any questions on SEIRb before we move to our coflows of energy 00:11:50.330 --> 00:11:53.530 align:middle line:90% efficiency? 00:11:53.530 --> 00:11:58.450 align:middle line:84% OK, so the main part of work today 00:11:58.450 --> 00:12:01.450 align:middle line:84% is to look at the models for energy coflows. 00:12:01.450 --> 00:12:05.810 align:middle line:84% And so basically, the coflow structure 00:12:05.810 --> 00:12:09.030 align:middle line:84% is probably something that most of you had seen. 00:12:09.030 --> 00:12:11.230 align:middle line:84% But some of you, it might have been new for you. 00:12:11.230 --> 00:12:13.410 align:middle line:84% So that would be a little bit more 00:12:13.410 --> 00:12:16.850 align:middle line:84% of the work to just learn the basics of the coflows. 00:12:16.850 --> 00:12:19.130 align:middle line:84% And then we were asking for something 00:12:19.130 --> 00:12:22.430 align:middle line:84% that was a little bit more than just plain vanilla coflow. 00:12:22.430 --> 00:12:27.690 align:middle line:84% A coflow structure for tracking energy efficiency requires 00:12:27.690 --> 00:12:31.950 align:middle line:84% capturing vintage effects, capturing retrofits-- that is, 00:12:31.950 --> 00:12:36.770 align:middle line:84% changing of the energy efficiency that has limits-- 00:12:36.770 --> 00:12:44.590 align:middle line:84% and new technology that may be introduced and change the limits 00:12:44.590 --> 00:12:47.190 align:middle line:84% to efficiency gains so it can make 00:12:47.190 --> 00:12:54.390 align:middle line:84% it more feasible to introduce effective, meaningful retrofits. 00:12:54.390 --> 00:12:57.030 align:middle line:84% And ultimately, we are looking for formulations 00:12:57.030 --> 00:13:01.670 align:middle line:84% that are robust for capturing the overall energy 00:13:01.670 --> 00:13:05.630 align:middle line:84% consumption given various types of interventions 00:13:05.630 --> 00:13:07.770 align:middle line:84% in terms of investing in retrofits, 00:13:07.770 --> 00:13:12.490 align:middle line:84% investing in efficiency energy technology introduction, 00:13:12.490 --> 00:13:14.510 align:middle line:84% and changes in the rates of building 00:13:14.510 --> 00:13:16.810 align:middle line:90% coming into the pipeline. 00:13:16.810 --> 00:13:18.810 align:middle line:84% So that was the problem definition. 00:13:18.810 --> 00:13:23.150 align:middle line:84% So let's now go and see the submissions we have. 00:13:23.150 --> 00:13:27.270 align:middle line:84% So a good piece of feedback that you guys provided 00:13:27.270 --> 00:13:32.490 align:middle line:84% last time was maybe focusing on one aspect 00:13:32.490 --> 00:13:35.070 align:middle line:84% and going through multiple models 00:13:35.070 --> 00:13:37.770 align:middle line:84% is easier cognitively rather than going 00:13:37.770 --> 00:13:40.450 align:middle line:84% through multiple models very quickly 00:13:40.450 --> 00:13:43.590 align:middle line:84% and discuss different aspects on all those models. 00:13:43.590 --> 00:13:46.110 align:middle line:90% So let's try that idea today. 00:13:46.110 --> 00:13:50.730 align:middle line:84% So I'll open multiple models that have been submitted. 00:13:50.730 --> 00:13:55.290 align:middle line:84% We can do a quick look at each aspect 00:13:55.290 --> 00:14:00.850 align:middle line:84% or how people are capturing those and see how it goes. 00:14:00.850 --> 00:14:06.350 align:middle line:84% So we'll learn as we go, in terms of how effective it is. 00:14:06.350 --> 00:14:11.610 align:middle line:90% 00:14:11.610 --> 00:14:17.610 align:middle line:84% So I'm opening the available models. 00:14:17.610 --> 00:14:24.630 align:middle line:90% So we have the vintage flows. 00:14:24.630 --> 00:14:26.267 align:middle line:90% So these are the buildings, Ali? 00:14:26.267 --> 00:14:26.850 align:middle line:90% AUDIENCE: Yes. 00:14:26.850 --> 00:14:27.725 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:14:27.725 --> 00:14:31.250 align:middle line:90% So the vintage is the buildings. 00:14:31.250 --> 00:14:33.910 align:middle line:84% And then you have buildings under construction. 00:14:33.910 --> 00:14:37.810 align:middle line:84% That's OK but not really central to our problem. 00:14:37.810 --> 00:14:39.270 align:middle line:90% We could just skip that. 00:14:39.270 --> 00:14:41.470 align:middle line:84% So we have new buildings coming in. 00:14:41.470 --> 00:14:46.590 align:middle line:84% And these buildings have average lifetime. 00:14:46.590 --> 00:14:48.630 align:middle line:84% And then the vintages, probably you 00:14:48.630 --> 00:14:55.810 align:middle line:84% are dividing it to different stages. 00:14:55.810 --> 00:15:00.070 align:middle line:90% 00:15:00.070 --> 00:15:03.750 align:middle line:90% And you have three stages. 00:15:03.750 --> 00:15:05.470 align:middle line:90% But how is it-- 00:15:05.470 --> 00:15:08.110 align:middle line:84% AUDIENCE: I think you have to move it back. 00:15:08.110 --> 00:15:11.830 align:middle line:84% HAZHIR RAHMANDAD: So why is that this last removal time is not 00:15:11.830 --> 00:15:12.590 align:middle line:90% dependent? 00:15:12.590 --> 00:15:14.970 align:middle line:84% Oh, is it dependent on the average lifetime? 00:15:14.970 --> 00:15:16.470 align:middle line:90% OK. 00:15:16.470 --> 00:15:19.070 align:middle line:90% So it's just a 1/3 of that. 00:15:19.070 --> 00:15:20.415 align:middle line:90% AUDIENCE: Yeah, the right group. 00:15:20.415 --> 00:15:21.290 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:15:21.290 --> 00:15:23.890 align:middle line:84% So that's just the stock and flow of buildings. 00:15:23.890 --> 00:15:25.510 align:middle line:90% Fairly straightforward. 00:15:25.510 --> 00:15:28.150 align:middle line:84% Average residence time in each, I assume, 00:15:28.150 --> 00:15:33.870 align:middle line:84% is 1/3 third of the total or something like that, yes. 00:15:33.870 --> 00:15:36.160 align:middle line:84% So for each of these flows, it is 00:15:36.160 --> 00:15:40.240 align:middle line:84% that stock divided by the average lifetime divided 00:15:40.240 --> 00:15:42.640 align:middle line:84% by 3, assuming we have three vintages. 00:15:42.640 --> 00:15:44.800 align:middle line:90% And that's fine. 00:15:44.800 --> 00:15:48.440 align:middle line:84% Then, you have this retrofitted on the top, 00:15:48.440 --> 00:15:49.780 align:middle line:90% which I don't know what it is. 00:15:49.780 --> 00:15:56.680 align:middle line:84% So let me see what you have below here. 00:15:56.680 --> 00:15:59.620 align:middle line:84% And then you have energy consumption of vintage. 00:15:59.620 --> 00:16:03.000 align:middle line:90% 00:16:03.000 --> 00:16:05.340 align:middle line:84% So what is the energy consumption of vintage? 00:16:05.340 --> 00:16:07.960 align:middle line:84% So what's the definition of that variable for you? 00:16:07.960 --> 00:16:11.840 align:middle line:84% AUDIENCE: So we could have gone with two conceptualizations-- 00:16:11.840 --> 00:16:14.200 align:middle line:84% either considering the efficiency of each building 00:16:14.200 --> 00:16:16.272 align:middle line:84% and then multiply it by something 00:16:16.272 --> 00:16:18.480 align:middle line:84% that gives us the energy consumption or the other way 00:16:18.480 --> 00:16:18.980 align:middle line:90% around. 00:16:18.980 --> 00:16:24.160 align:middle line:84% So we can assume a baseline energy consumption. 00:16:24.160 --> 00:16:25.880 align:middle line:84% And the technology on the bottom is 00:16:25.880 --> 00:16:28.420 align:middle line:84% going to reduce energy consumption in that case. 00:16:28.420 --> 00:16:30.640 align:middle line:84% HAZHIR RAHMANDAD: OK, so this is basically 00:16:30.640 --> 00:16:34.760 align:middle line:84% energy consumption of all of the buildings together. 00:16:34.760 --> 00:16:36.590 align:middle line:84% So this is kilowatt hours per year. 00:16:36.590 --> 00:16:37.340 align:middle line:90% AUDIENCE: Exactly. 00:16:37.340 --> 00:16:40.175 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:16:40.175 --> 00:16:45.780 align:middle line:84% And it is basically initialized to be 00:16:45.780 --> 00:16:50.100 align:middle line:84% the vintage multiplied by the initial energy consumption. 00:16:50.100 --> 00:16:51.560 align:middle line:90% So all of that is good. 00:16:51.560 --> 00:16:55.140 align:middle line:90% 00:16:55.140 --> 00:17:02.342 align:middle line:84% Now, how does retrofitting work in this setup? 00:17:02.342 --> 00:17:03.300 align:middle line:90% AUDIENCE: Retrofitting? 00:17:03.300 --> 00:17:05.359 align:middle line:84% Well, I made a very simplistic assumption, 00:17:05.359 --> 00:17:08.287 align:middle line:84% just it happens to the oldest buildings. 00:17:08.287 --> 00:17:10.579 align:middle line:84% HAZHIR RAHMANDAD: Ah, so that's an important assumption 00:17:10.579 --> 00:17:14.579 align:middle line:84% you're making, that retrofits happen to the last vintage 00:17:14.579 --> 00:17:16.119 align:middle line:90% not to other ones. 00:17:16.119 --> 00:17:19.500 align:middle line:84% So let's track what is happening with your last vintage 00:17:19.500 --> 00:17:20.380 align:middle line:90% in this case. 00:17:20.380 --> 00:17:24.180 align:middle line:84% So in the last vintage, you have retrofitted 00:17:24.180 --> 00:17:29.520 align:middle line:84% buildings versus not retrofitted buildings. 00:17:29.520 --> 00:17:40.320 align:middle line:84% So you are basically separating buildings 00:17:40.320 --> 00:17:43.520 align:middle line:84% by whether they are retrofitted or not. 00:17:43.520 --> 00:17:49.240 align:middle line:84% So that's one way to do it, but it's probably not the easiest 00:17:49.240 --> 00:17:49.740 align:middle line:90% way. 00:17:49.740 --> 00:17:54.160 align:middle line:84% There is probably an easier way to do it. 00:17:54.160 --> 00:17:59.440 align:middle line:84% And what you're doing here is that you are taking away 00:17:59.440 --> 00:18:04.560 align:middle line:84% the energy consumption of the vintage 00:18:04.560 --> 00:18:10.140 align:middle line:90% based on retrofitting rate. 00:18:10.140 --> 00:18:17.960 align:middle line:84% So as you retrofit, you're taking away how much? 00:18:17.960 --> 00:18:19.280 align:middle line:90% AUDIENCE: All of the averages. 00:18:19.280 --> 00:18:23.600 align:middle line:84% HAZHIR RAHMANDAD: All of the average consumption 00:18:23.600 --> 00:18:29.990 align:middle line:84% that those retrofitted buildings have. 00:18:29.990 --> 00:18:34.340 align:middle line:84% AUDIENCE: This is our thought process. 00:18:34.340 --> 00:18:35.300 align:middle line:90% HAZHIR RAHMANDAD: Yes? 00:18:35.300 --> 00:18:38.620 align:middle line:84% AUDIENCE: If there is natural demolition rate, 00:18:38.620 --> 00:18:41.023 align:middle line:84% so it's like a regular coflow that you see. 00:18:41.023 --> 00:18:41.940 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:18:41.940 --> 00:18:43.740 align:middle line:84% AUDIENCE: But then we were thinking 00:18:43.740 --> 00:18:46.400 align:middle line:84% that if you are retrofitting some of these buildings, 00:18:46.400 --> 00:18:51.020 align:middle line:84% so a fraction of them will get retrofitted, so in addition 00:18:51.020 --> 00:18:54.720 align:middle line:84% to the natural outflow of the energy consumption, 00:18:54.720 --> 00:18:59.380 align:middle line:84% something additionally should be subtracted from the energy 00:18:59.380 --> 00:19:04.900 align:middle line:84% consumption to account for the decline of the stock of energy 00:19:04.900 --> 00:19:07.520 align:middle line:90% consumption for the buildings. 00:19:07.520 --> 00:19:08.460 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:19:08.460 --> 00:19:11.800 align:middle line:84% So this is important when we are doing coflows. 00:19:11.800 --> 00:19:14.420 align:middle line:84% The first thing is that for the main flow, which 00:19:14.420 --> 00:19:17.520 align:middle line:84% is in this case, buildings, every stock that you have, 00:19:17.520 --> 00:19:24.220 align:middle line:84% you usually need to have equivalent stock for the coflow. 00:19:24.220 --> 00:19:27.320 align:middle line:84% Otherwise it becomes very hard to keep track of things. 00:19:27.320 --> 00:19:29.180 align:middle line:84% It is very easy to make mistakes. 00:19:29.180 --> 00:19:32.120 align:middle line:84% Not impossible to do it right, but I don't recommend it 00:19:32.120 --> 00:19:33.060 align:middle line:90% at the beginning. 00:19:33.060 --> 00:19:36.420 align:middle line:84% So in this case, we have a violation of that heuristic. 00:19:36.420 --> 00:19:39.940 align:middle line:84% That is, we have the vintage tree versus retrofitted tree. 00:19:39.940 --> 00:19:42.760 align:middle line:84% These are different groups of buildings. 00:19:42.760 --> 00:19:47.080 align:middle line:84% But the coflow here, this energy consumption of vintage 00:19:47.080 --> 00:19:50.120 align:middle line:84% is basically capturing the energy consumption 00:19:50.120 --> 00:19:52.300 align:middle line:90% for both of these groups. 00:19:52.300 --> 00:19:54.080 align:middle line:84% AUDIENCE: There's another stock offering 00:19:54.080 --> 00:19:56.860 align:middle line:84% if you go further on in this model. 00:19:56.860 --> 00:19:58.560 align:middle line:90% HAZHIR RAHMANDAD: Ah, OK. 00:19:58.560 --> 00:19:59.840 align:middle line:90% Sorry. 00:19:59.840 --> 00:20:04.020 align:middle line:84% So this is because I didn't look closely. 00:20:04.020 --> 00:20:04.640 align:middle line:90% Thank you. 00:20:04.640 --> 00:20:06.920 align:middle line:84% So this energy consumption of retrofitting tree 00:20:06.920 --> 00:20:10.760 align:middle line:84% is exactly what you are trying to do. 00:20:10.760 --> 00:20:17.120 align:middle line:84% Now, it's much easier to keep it here within the same stock 00:20:17.120 --> 00:20:18.560 align:middle line:90% and flow chain. 00:20:18.560 --> 00:20:25.560 align:middle line:84% And then when you are reducing energy consumption from a group, 00:20:25.560 --> 00:20:28.170 align:middle line:84% you are doing the retrofitting on it. 00:20:28.170 --> 00:20:31.650 align:middle line:84% So I think the confusion for you or the challenge 00:20:31.650 --> 00:20:36.170 align:middle line:84% here is that at one time, you're taking them out, 00:20:36.170 --> 00:20:40.330 align:middle line:84% you are removing all of the retrofitted, all of the energy 00:20:40.330 --> 00:20:43.330 align:middle line:84% consumption that goes with them, and then 00:20:43.330 --> 00:20:49.770 align:middle line:84% you go up there and create this other stock that is having 00:20:49.770 --> 00:20:51.715 align:middle line:90% the retrofitted value for-- 00:20:51.715 --> 00:20:53.090 align:middle line:84% AUDIENCE: New energy consumption. 00:20:53.090 --> 00:20:55.170 align:middle line:84% HAZHIR RAHMANDAD: New energy consumption, yes. 00:20:55.170 --> 00:20:57.450 align:middle line:90% So this actually should work. 00:20:57.450 --> 00:21:00.210 align:middle line:90% That is, it shouldn't be wrong. 00:21:00.210 --> 00:21:03.070 align:middle line:84% It probably does what you want to do. 00:21:03.070 --> 00:21:06.290 align:middle line:84% Basically, you're taking this group, 00:21:06.290 --> 00:21:10.810 align:middle line:84% the action of retrofitting reduces their energy consumption 00:21:10.810 --> 00:21:12.850 align:middle line:90% per building. 00:21:12.850 --> 00:21:15.110 align:middle line:90% So it does what you want to do. 00:21:15.110 --> 00:21:19.810 align:middle line:90% 00:21:19.810 --> 00:21:25.830 align:middle line:84% It is not the simplest kind of formulation for this case. 00:21:25.830 --> 00:21:28.950 align:middle line:84% We'll see how others have done it. 00:21:28.950 --> 00:21:32.770 align:middle line:84% But let's see if the basic logic here is working for other parts. 00:21:32.770 --> 00:21:36.590 align:middle line:84% So once you are in this stock, then when you leave, 00:21:36.590 --> 00:21:40.230 align:middle line:84% you are taking out the retrofitted average, which 00:21:40.230 --> 00:21:42.010 align:middle line:90% is what you should be doing. 00:21:42.010 --> 00:21:42.970 align:middle line:90% So that's good. 00:21:42.970 --> 00:21:47.270 align:middle line:90% 00:21:47.270 --> 00:21:49.710 align:middle line:90% And the average time-- 00:21:49.710 --> 00:21:53.170 align:middle line:84% AUDIENCE: That is also a very simplistic assumption. 00:21:53.170 --> 00:21:55.170 align:middle line:84% So maybe I should have used another average. 00:21:55.170 --> 00:21:56.587 align:middle line:84% HAZHIR RAHMANDAD: So then there is 00:21:56.587 --> 00:21:59.170 align:middle line:84% the question of retrofitting rate, where it is coming from. 00:21:59.170 --> 00:22:08.110 align:middle line:84% And you are using the investment process to drive that decision. 00:22:08.110 --> 00:22:13.350 align:middle line:84% And as long as you are using the investment 00:22:13.350 --> 00:22:17.090 align:middle line:84% process, an independent process to retrofit things, 00:22:17.090 --> 00:22:23.030 align:middle line:84% to move items between Vintage 3 and Retrofitted 3, you are OK. 00:22:23.030 --> 00:22:26.610 align:middle line:84% You don't need to worry about the demolition 00:22:26.610 --> 00:22:28.910 align:middle line:84% rate or the average lifetime thing, 00:22:28.910 --> 00:22:30.530 align:middle line:84% assuming that the lifetime doesn't 00:22:30.530 --> 00:22:33.210 align:middle line:90% change because of retrofitting. 00:22:33.210 --> 00:22:36.090 align:middle line:84% And you can actually change that assumption as well. 00:22:36.090 --> 00:22:37.350 align:middle line:90% That would be OK as well. 00:22:37.350 --> 00:22:42.150 align:middle line:84% But with that assumption, I think this would work fine. 00:22:42.150 --> 00:22:44.830 align:middle line:84% Now, let me take a look at the equations you have here. 00:22:44.830 --> 00:22:52.370 align:middle line:84% So removal rate for Vintage 3 is Vintage 3 divided by this total. 00:22:52.370 --> 00:22:56.240 align:middle line:90% And then this-- 00:22:56.240 --> 00:22:59.010 align:middle line:84% AUDIENCE: I took the idea from, like this here, we 00:22:59.010 --> 00:23:00.533 align:middle line:90% had death and recovery. 00:23:00.533 --> 00:23:01.450 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:23:01.450 --> 00:23:04.970 align:middle line:84% So in a way, you're saying at the end 00:23:04.970 --> 00:23:10.010 align:middle line:84% of their life of the buildings, you 00:23:10.010 --> 00:23:12.450 align:middle line:84% may be doing one of the two things. 00:23:12.450 --> 00:23:15.540 align:middle line:84% Either you demolish it or you retrofit it. 00:23:15.540 --> 00:23:17.790 align:middle line:84% That's what you are modeling, the way you're modeling. 00:23:17.790 --> 00:23:19.290 align:middle line:90% Is that what you wanted to do? 00:23:19.290 --> 00:23:20.790 align:middle line:90% OK. 00:23:20.790 --> 00:23:22.450 align:middle line:90% So again, that's an assumption. 00:23:22.450 --> 00:23:25.250 align:middle line:84% If you make that assumption, that's how the world works, 00:23:25.250 --> 00:23:26.590 align:middle line:90% that's OK. 00:23:26.590 --> 00:23:28.770 align:middle line:84% We need to be clear about that assumption. 00:23:28.770 --> 00:23:32.350 align:middle line:84% So here you're calculating total removal rate. 00:23:32.350 --> 00:23:34.310 align:middle line:84% A fraction of it gets demolished. 00:23:34.310 --> 00:23:37.990 align:middle line:84% 1 minus that fraction goes retrofitted or vice versa. 00:23:37.990 --> 00:23:43.510 align:middle line:84% And that retrofit rate, then these buildings 00:23:43.510 --> 00:23:48.470 align:middle line:84% have a new life, which is how long they 00:23:48.470 --> 00:23:54.650 align:middle line:84% will stay in this third stage or in fourth stage. 00:23:54.650 --> 00:23:57.310 align:middle line:84% Now, it is really a fourth stage, not a third stage. 00:23:57.310 --> 00:23:59.950 align:middle line:84% And you're assuming that residence time 00:23:59.950 --> 00:24:03.770 align:middle line:84% is the same as the last stage demolition rate. 00:24:03.770 --> 00:24:07.630 align:middle line:84% So these are the assumptions that go into Ali's model. 00:24:07.630 --> 00:24:12.390 align:middle line:84% That is, the retrofit is kind of giving it a new life or 1/3 00:24:12.390 --> 00:24:18.470 align:middle line:84% of a new life with a new level of consumption of energy that 00:24:18.470 --> 00:24:25.370 align:middle line:84% comes from whatever that initial retrofit technology is. 00:24:25.370 --> 00:24:27.730 align:middle line:84% So with those assumptions, this model 00:24:27.730 --> 00:24:30.830 align:middle line:84% is doing it correctly, at least for this third stage. 00:24:30.830 --> 00:24:33.750 align:middle line:84% Now, for the previous stages, you haven't added it. 00:24:33.750 --> 00:24:37.770 align:middle line:84% And that adds a few complexities because then you 00:24:37.770 --> 00:24:41.650 align:middle line:84% are creating different lives for retrofitted versus not 00:24:41.650 --> 00:24:43.090 align:middle line:90% retrofitted buildings. 00:24:43.090 --> 00:24:45.990 align:middle line:84% And those different lives, you have to track them separately, 00:24:45.990 --> 00:24:47.610 align:middle line:84% so it creates kind of a stock and flow 00:24:47.610 --> 00:24:50.690 align:middle line:84% change for those other stages that may 00:24:50.690 --> 00:24:53.610 align:middle line:90% feel a little bit intimidating. 00:24:53.610 --> 00:24:58.510 align:middle line:84% Now there is the New Building Energy Consumption. 00:24:58.510 --> 00:25:02.810 align:middle line:90% 00:25:02.810 --> 00:25:09.250 align:middle line:84% AUDIENCE: So the idea was, whatever the new technology is, 00:25:09.250 --> 00:25:15.050 align:middle line:84% we're going to take an average with the potential maximum we 00:25:15.050 --> 00:25:15.550 align:middle line:90% can get. 00:25:15.550 --> 00:25:19.140 align:middle line:84% It's like a weighted average so that we can account 00:25:19.140 --> 00:25:26.320 align:middle line:84% for the maximum efficiency that these buildings can get, 00:25:26.320 --> 00:25:29.340 align:middle line:84% because these are old buildings, so they cannot achieve 00:25:29.340 --> 00:25:33.540 align:middle line:84% the efficiency of the new buildings. 00:25:33.540 --> 00:25:36.460 align:middle line:84% HAZHIR RAHMANDAD: So what you need to do here 00:25:36.460 --> 00:25:42.180 align:middle line:84% is to be tracking how much improvement you 00:25:42.180 --> 00:25:45.220 align:middle line:90% can do for each vintage. 00:25:45.220 --> 00:25:47.900 align:middle line:84% And that improvement that you can do for each vintage 00:25:47.900 --> 00:25:52.820 align:middle line:84% is a characteristic of that vintage itself. 00:25:52.820 --> 00:25:56.500 align:middle line:84% So it requires a coflow that tracks 00:25:56.500 --> 00:26:00.900 align:middle line:90% that characteristic over time. 00:26:00.900 --> 00:26:05.420 align:middle line:84% So this one doesn't seem to be doing that. 00:26:05.420 --> 00:26:06.310 align:middle line:90% Is that correct? 00:26:06.310 --> 00:26:07.060 align:middle line:90% AUDIENCE: Exactly. 00:26:07.060 --> 00:26:11.040 align:middle line:84% It just assumes whatever the best technologies out there, 00:26:11.040 --> 00:26:12.440 align:middle line:90% just a fraction of those. 00:26:12.440 --> 00:26:13.357 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:26:13.357 --> 00:26:17.655 align:middle line:84% So it makes some fractional assumption. 00:26:17.655 --> 00:26:19.280 align:middle line:84% AUDIENCE: And that fraction is actually 00:26:19.280 --> 00:26:21.000 align:middle line:84% coming from the average consumption, 00:26:21.000 --> 00:26:24.040 align:middle line:90% like before being retrofitted. 00:26:24.040 --> 00:26:27.080 align:middle line:84% So because the average consumption of the old building 00:26:27.080 --> 00:26:30.200 align:middle line:84% is already low, it kind of adjusts for that. 00:26:30.200 --> 00:26:31.120 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:26:31.120 --> 00:26:35.280 align:middle line:84% So you are getting the average consumption 00:26:35.280 --> 00:26:41.572 align:middle line:84% from the old building energy efficiency. 00:26:41.572 --> 00:26:44.280 align:middle line:84% AUDIENCE: That sort of was the characteristics 00:26:44.280 --> 00:26:46.258 align:middle line:90% of that group of buildings. 00:26:46.258 --> 00:26:47.800 align:middle line:84% HAZHIR RAHMANDAD: Yeah, that's how it 00:26:47.800 --> 00:26:49.300 align:middle line:90% is working as a characteristic. 00:26:49.300 --> 00:26:54.040 align:middle line:84% And because you are separating retrofitted versus old buildings 00:26:54.040 --> 00:26:57.620 align:middle line:84% that have not been retrofitted here, it kind of works. 00:26:57.620 --> 00:27:00.920 align:middle line:84% That is, that characteristic is telling where it currently 00:27:00.920 --> 00:27:01.760 align:middle line:90% stands. 00:27:01.760 --> 00:27:07.980 align:middle line:84% You are putting, now, the bottom in a time-moving parameter. 00:27:07.980 --> 00:27:13.160 align:middle line:84% And then just say a fraction of that is what you can achieve. 00:27:13.160 --> 00:27:16.680 align:middle line:90% So I think it can work. 00:27:16.680 --> 00:27:19.940 align:middle line:84% I haven't looked through this specific formulation closely 00:27:19.940 --> 00:27:21.640 align:middle line:90% enough to see what is happening. 00:27:21.640 --> 00:27:24.740 align:middle line:90% OK, good. 00:27:24.740 --> 00:27:29.620 align:middle line:84% This is doing something that is reasonable. 00:27:29.620 --> 00:27:31.960 align:middle line:90% Nothing is obviously wrong. 00:27:31.960 --> 00:27:36.100 align:middle line:84% Now, this part I haven't thought through the extreme conditions 00:27:36.100 --> 00:27:37.360 align:middle line:90% for the formulation you have. 00:27:37.360 --> 00:27:41.097 align:middle line:84% This is a little bit complex, but it's probably a good time 00:27:41.097 --> 00:27:42.680 align:middle line:84% to switch to some of the other models, 00:27:42.680 --> 00:27:45.700 align:middle line:90% see how they are laid out. 00:27:45.700 --> 00:27:48.240 align:middle line:84% But here, let me just understand what is this. 00:27:48.240 --> 00:27:51.780 align:middle line:84% This is the New Building Energy Consumption. 00:27:51.780 --> 00:27:55.420 align:middle line:84% So this is capturing the change in technology. 00:27:55.420 --> 00:28:00.012 align:middle line:84% And this is exogenous, basically. 00:28:00.012 --> 00:28:02.220 align:middle line:84% AUDIENCE: We're assuming that the baseline technology 00:28:02.220 --> 00:28:04.540 align:middle line:84% consumption is 1 and whatever innovation 00:28:04.540 --> 00:28:08.960 align:middle line:84% that we have is trying to reduce that maximum 1, 00:28:08.960 --> 00:28:10.100 align:middle line:90% that maximum value. 00:28:10.100 --> 00:28:13.405 align:middle line:90% 00:28:13.405 --> 00:28:14.280 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:28:14.280 --> 00:28:17.700 align:middle line:84% So the technology can be exogenous here. 00:28:17.700 --> 00:28:21.740 align:middle line:84% By and large, that's not a problematic assumption. 00:28:21.740 --> 00:28:24.600 align:middle line:90% 00:28:24.600 --> 00:28:26.220 align:middle line:90% So I'm OK with that. 00:28:26.220 --> 00:28:30.080 align:middle line:84% Although, a better formulation would 00:28:30.080 --> 00:28:35.440 align:middle line:84% allow the limits of technology to depend on the vintage 00:28:35.440 --> 00:28:37.080 align:middle line:90% as well. 00:28:37.080 --> 00:28:40.140 align:middle line:84% But this formulation wouldn't capture that. 00:28:40.140 --> 00:28:45.800 align:middle line:90% 00:28:45.800 --> 00:28:47.760 align:middle line:84% Yeah, so for me, the better formulation 00:28:47.760 --> 00:28:53.280 align:middle line:84% would be a coflow that captures the potential for improvements 00:28:53.280 --> 00:28:54.680 align:middle line:90% for each vintage. 00:28:54.680 --> 00:29:00.160 align:middle line:84% And then you can change that potential endogenously. 00:29:00.160 --> 00:29:03.060 align:middle line:84% OK, let's look at some other models. 00:29:03.060 --> 00:29:07.560 align:middle line:90% 00:29:07.560 --> 00:29:11.630 align:middle line:90% Next one is Jake's. 00:29:11.630 --> 00:29:14.377 align:middle line:90% 00:29:14.377 --> 00:29:16.710 align:middle line:84% AUDIENCE: First time working with coflows or subscripts, 00:29:16.710 --> 00:29:17.750 align:middle line:90% so I learned a lot. 00:29:17.750 --> 00:29:20.250 align:middle line:90% HAZHIR RAHMANDAD: OK, good. 00:29:20.250 --> 00:29:23.450 align:middle line:90% That was a challenge. 00:29:23.450 --> 00:29:28.410 align:middle line:84% So you have your three vintages-- 00:29:28.410 --> 00:29:31.930 align:middle line:84% new buildings, mature buildings, old buildings. 00:29:31.930 --> 00:29:33.450 align:middle line:84% You have the three time constants 00:29:33.450 --> 00:29:37.330 align:middle line:84% for them, some construction rate, which is exogenous. 00:29:37.330 --> 00:29:38.530 align:middle line:90% That's good. 00:29:38.530 --> 00:29:42.550 align:middle line:84% Then, we have the energy usage of new buildings, 00:29:42.550 --> 00:29:44.190 align:middle line:84% energy usage of mature buildings, 00:29:44.190 --> 00:29:45.870 align:middle line:90% energy usage of old buildings. 00:29:45.870 --> 00:29:50.330 align:middle line:84% So these are the coflows similar to Ali's formulation. 00:29:50.330 --> 00:29:53.050 align:middle line:84% You're calculating the averages, pushing things forward 00:29:53.050 --> 00:29:54.890 align:middle line:90% based on the averages. 00:29:54.890 --> 00:29:56.450 align:middle line:90% That's also fine. 00:29:56.450 --> 00:30:00.815 align:middle line:90% 00:30:00.815 --> 00:30:02.190 align:middle line:84% AUDIENCE: So for those two flows, 00:30:02.190 --> 00:30:04.670 align:middle line:84% I had an assumption that for energy usage, 00:30:04.670 --> 00:30:07.410 align:middle line:84% there would be some, as you age, that there 00:30:07.410 --> 00:30:09.670 align:middle line:84% would be some inefficiency that's 00:30:09.670 --> 00:30:11.910 align:middle line:84% added in to energy consumption kind of is 00:30:11.910 --> 00:30:12.990 align:middle line:90% how I thought about it. 00:30:12.990 --> 00:30:14.150 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:30:14.150 --> 00:30:17.630 align:middle line:84% So that's basically kind of wear and tear reduces 00:30:17.630 --> 00:30:20.190 align:middle line:90% energy efficiency idea. 00:30:20.190 --> 00:30:22.750 align:middle line:84% So that's an interesting mechanism. 00:30:22.750 --> 00:30:24.370 align:middle line:84% Even though we didn't ask for it, 00:30:24.370 --> 00:30:25.690 align:middle line:90% it's nice that you captured it. 00:30:25.690 --> 00:30:30.070 align:middle line:90% I think it's a meaningful idea. 00:30:30.070 --> 00:30:32.750 align:middle line:84% Perhaps you could include it for the new buildings 00:30:32.750 --> 00:30:34.510 align:middle line:84% as well, because new buildings are 00:30:34.510 --> 00:30:38.490 align:middle line:84% subject to the same type of dynamics. 00:30:38.490 --> 00:30:40.810 align:middle line:84% Let's look at the equation for that. 00:30:40.810 --> 00:30:46.830 align:middle line:84% So you're saying the mature buildings are increasing 00:30:46.830 --> 00:30:53.230 align:middle line:84% their energy consumption with a rate that 00:30:53.230 --> 00:31:00.110 align:middle line:84% is coming from new buildings aging and mature building energy 00:31:00.110 --> 00:31:01.370 align:middle line:90% flows per unit. 00:31:01.370 --> 00:31:04.070 align:middle line:84% So in a way, if I'm understanding you, 00:31:04.070 --> 00:31:07.950 align:middle line:84% and tell me if that's an incorrect assessment, 00:31:07.950 --> 00:31:10.930 align:middle line:84% you are saying as soon as you enter this stage, 00:31:10.930 --> 00:31:16.490 align:middle line:84% some additional flaws come with you, which increases your energy 00:31:16.490 --> 00:31:18.090 align:middle line:90% consumption per unit. 00:31:18.090 --> 00:31:23.930 align:middle line:84% So that's why you're using the inflow into this stock 00:31:23.930 --> 00:31:26.770 align:middle line:90% for adding these flaws. 00:31:26.770 --> 00:31:29.690 align:middle line:90% And that's fine. 00:31:29.690 --> 00:31:33.890 align:middle line:84% Conceptually, that's one way to capture it. 00:31:33.890 --> 00:31:39.450 align:middle line:84% Now, it has a little bit of a challenge in terms of robustness 00:31:39.450 --> 00:31:44.850 align:middle line:84% when I change the time constant, for example, for becoming old. 00:31:44.850 --> 00:31:46.210 align:middle line:90% So why is that? 00:31:46.210 --> 00:31:49.350 align:middle line:84% So this is an interesting kind of wrinkle here. 00:31:49.350 --> 00:31:53.170 align:middle line:84% So we have these mature buildings 00:31:53.170 --> 00:31:56.210 align:middle line:84% staying in this stock for time to become old. 00:31:56.210 --> 00:32:00.130 align:middle line:84% And during that time, they are accumulating these flaws. 00:32:00.130 --> 00:32:01.450 align:middle line:90% That's the idea. 00:32:01.450 --> 00:32:05.170 align:middle line:84% But to keep things simple, Jake said, OK, well, 00:32:05.170 --> 00:32:08.250 align:middle line:84% as soon as these guys go into the next stage, 00:32:08.250 --> 00:32:11.710 align:middle line:84% I'm going to give them all of the flaws they will acquire 00:32:11.710 --> 00:32:16.990 align:middle line:84% or half of the flaws they will acquire, some measure of that, 00:32:16.990 --> 00:32:18.590 align:middle line:84% and be done with it and not worry 00:32:18.590 --> 00:32:22.150 align:middle line:84% about this introduction of flaws during the time you 00:32:22.150 --> 00:32:24.030 align:middle line:90% are in this stock. 00:32:24.030 --> 00:32:26.490 align:middle line:84% So that means if I change this time constant 00:32:26.490 --> 00:32:30.750 align:middle line:84% because I want to have more stocks, 00:32:30.750 --> 00:32:34.310 align:middle line:84% so I break it down into smaller steps, 00:32:34.310 --> 00:32:38.350 align:middle line:84% the mature building energy flaws per unit 00:32:38.350 --> 00:32:41.750 align:middle line:90% will not change automatically. 00:32:41.750 --> 00:32:43.410 align:middle line:90% Whereas, it actually has to. 00:32:43.410 --> 00:32:48.790 align:middle line:84% In fact, it is something about per unit of time, 00:32:48.790 --> 00:32:54.670 align:middle line:84% how much kilowatt hour per square foot you are adding, 00:32:54.670 --> 00:32:59.190 align:middle line:84% you multiply that by time to becoming old to get 00:32:59.190 --> 00:33:01.070 align:middle line:90% this parameter you have. 00:33:01.070 --> 00:33:04.810 align:middle line:84% So doing that makes it robust to this extreme condition 00:33:04.810 --> 00:33:06.130 align:middle line:90% I'm talking about. 00:33:06.130 --> 00:33:09.770 align:middle line:84% Now, this is one way to do it, which puts everything 00:33:09.770 --> 00:33:11.170 align:middle line:90% at the beginning. 00:33:11.170 --> 00:33:14.410 align:middle line:84% What's an alternative way to do this? 00:33:14.410 --> 00:33:18.890 align:middle line:84% AUDIENCE: You can separate the time constant to accumulate. 00:33:18.890 --> 00:33:21.290 align:middle line:84% HAZHIR RAHMANDAD: So can you speak up, Aldan, and explain 00:33:21.290 --> 00:33:23.050 align:middle line:90% what you're trying to? 00:33:23.050 --> 00:33:25.850 align:middle line:84% AUDIENCE: So I think you can separate the time to become old 00:33:25.850 --> 00:33:29.470 align:middle line:84% and the time to accumulate those flaws. 00:33:29.470 --> 00:33:37.650 align:middle line:84% So you can have the rate, so you can 00:33:37.650 --> 00:33:40.850 align:middle line:84% have another auxiliary variable coming 00:33:40.850 --> 00:33:45.050 align:middle line:84% from the start, the maturing building, for example, 00:33:45.050 --> 00:33:50.170 align:middle line:84% and divide it by time to the flaw. 00:33:50.170 --> 00:33:53.970 align:middle line:84% HAZHIR RAHMANDAD: So you could take that new parameter 00:33:53.970 --> 00:33:56.090 align:middle line:84% that I mentioned, which is how many flaws 00:33:56.090 --> 00:34:00.090 align:middle line:84% per unit of time per mature building will be added, 00:34:00.090 --> 00:34:04.420 align:middle line:84% and use that parameter, multiply that 00:34:04.420 --> 00:34:07.340 align:middle line:84% by the number of mature buildings 00:34:07.340 --> 00:34:11.060 align:middle line:84% to create a new flow into the energy 00:34:11.060 --> 00:34:13.100 align:middle line:90% usage of mature buildings. 00:34:13.100 --> 00:34:16.500 align:middle line:84% That works just as fine and gives very similar results 00:34:16.500 --> 00:34:17.400 align:middle line:90% to what Jake has. 00:34:17.400 --> 00:34:21.139 align:middle line:84% So I slightly prefer that alternative 00:34:21.139 --> 00:34:23.620 align:middle line:84% because it is a little bit closer to how 00:34:23.620 --> 00:34:25.880 align:middle line:90% things happen in reality. 00:34:25.880 --> 00:34:27.340 align:middle line:84% That is, continuously, these things 00:34:27.340 --> 00:34:30.037 align:middle line:84% are being added based on how many buildings you have, 00:34:30.037 --> 00:34:31.620 align:middle line:84% rather than at the very beginning when 00:34:31.620 --> 00:34:34.980 align:middle line:84% these buildings come in, you're dumping them 00:34:34.980 --> 00:34:42.260 align:middle line:84% with this kind of step function reduction in energy efficiency. 00:34:42.260 --> 00:34:47.260 align:middle line:84% But that's a nice addition that Jake had conceptualized. 00:34:47.260 --> 00:34:50.880 align:middle line:84% Now let's look at the thing we were focusing on, 00:34:50.880 --> 00:34:55.060 align:middle line:84% which is the energy efficiency gains for mature buildings 00:34:55.060 --> 00:34:57.340 align:middle line:90% coming from retrofits. 00:34:57.340 --> 00:35:04.280 align:middle line:84% So that flow variable is, if average efficiency 00:35:04.280 --> 00:35:07.720 align:middle line:84% of mature buildings is higher than the lowest 00:35:07.720 --> 00:35:19.360 align:middle line:84% feasible efficiency, then retrofit benefit, otherwise 0. 00:35:19.360 --> 00:35:21.120 align:middle line:90% Yeah, tell us. 00:35:21.120 --> 00:35:24.160 align:middle line:84% AUDIENCE: I don't know that this is necessarily the best way. 00:35:24.160 --> 00:35:28.800 align:middle line:84% I unfortunately did two ways of getting the retrofit benefit 00:35:28.800 --> 00:35:29.620 align:middle line:90% from technology. 00:35:29.620 --> 00:35:31.320 align:middle line:84% One is on these two flows, and then one 00:35:31.320 --> 00:35:35.880 align:middle line:84% is going to be on the new building, like new stock. 00:35:35.880 --> 00:35:38.080 align:middle line:84% So the idea was, I just didn't want 00:35:38.080 --> 00:35:44.240 align:middle line:84% the benefit you would gain from efficiency to bring you 00:35:44.240 --> 00:35:48.800 align:middle line:84% below a minimum average efficiency for the buildings 00:35:48.800 --> 00:35:54.320 align:middle line:84% there because they can't go below a theoretical minimum. 00:35:54.320 --> 00:35:57.120 align:middle line:84% And I was running into issues specifically 00:35:57.120 --> 00:35:59.980 align:middle line:84% with these flows where it was, even though I 00:35:59.980 --> 00:36:01.720 align:middle line:90% have limits involved elsewhere. 00:36:01.720 --> 00:36:03.540 align:middle line:90% So I add it here. 00:36:03.540 --> 00:36:04.820 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:36:04.820 --> 00:36:07.700 align:middle line:84% So whenever you see if-then-else, 00:36:07.700 --> 00:36:09.680 align:middle line:84% you need to be a little bit kind of thinking, 00:36:09.680 --> 00:36:11.380 align:middle line:90% is there a better way to do it? 00:36:11.380 --> 00:36:16.140 align:middle line:84% Not always, but sometimes, most often actually you can find one. 00:36:16.140 --> 00:36:19.020 align:middle line:84% Here, you have also mature and the cohort 00:36:19.020 --> 00:36:21.440 align:middle line:84% subscripts, which kind of confuses me. 00:36:21.440 --> 00:36:24.120 align:middle line:84% So can you tell what the subscripts are doing here? 00:36:24.120 --> 00:36:27.980 align:middle line:84% Because I didn't realize this is also subscripted here. 00:36:27.980 --> 00:36:32.440 align:middle line:84% AUDIENCE: So that's a bit of me learning how to use subscripts. 00:36:32.440 --> 00:36:36.200 align:middle line:84% Everything in this whole model has cohort basically on it. 00:36:36.200 --> 00:36:39.180 align:middle line:84% But the lowest feasible efficiencies, 00:36:39.180 --> 00:36:42.540 align:middle line:84% there is a different lowest feasible efficiency 00:36:42.540 --> 00:36:46.940 align:middle line:84% of kilowatt hours per square foot for old, new, and mature. 00:36:46.940 --> 00:36:49.580 align:middle line:84% And so I basically wanted it to be, 00:36:49.580 --> 00:36:54.300 align:middle line:84% as soon as new buildings enter into these mature or old stocks, 00:36:54.300 --> 00:36:57.180 align:middle line:90% you get some inefficiencies. 00:36:57.180 --> 00:37:00.460 align:middle line:84% That whole average is going to go up above that. 00:37:00.460 --> 00:37:02.778 align:middle line:84% So you're going to get retrofit benefit bringing back. 00:37:02.778 --> 00:37:03.820 align:middle line:90% HAZHIR RAHMANDAD: Got it. 00:37:03.820 --> 00:37:04.640 align:middle line:90% Got it. 00:37:04.640 --> 00:37:09.760 align:middle line:84% So first of all, I think let's recognize 00:37:09.760 --> 00:37:13.440 align:middle line:84% what Jake is doing here with the cohort subscript. 00:37:13.440 --> 00:37:18.080 align:middle line:84% So he's creating a copy of the model, the model that we 00:37:18.080 --> 00:37:21.280 align:middle line:84% are seeing on the screen, for different cohorts 00:37:21.280 --> 00:37:26.120 align:middle line:84% and running that through the simulation 00:37:26.120 --> 00:37:28.260 align:middle line:84% for different cohorts, which is good. 00:37:28.260 --> 00:37:32.800 align:middle line:84% It's actually a better way to capture the cohorts than just 00:37:32.800 --> 00:37:35.400 align:middle line:90% age-tracking the cohorts. 00:37:35.400 --> 00:37:38.820 align:middle line:84% I didn't tell you to do it this way just to keep things simple, 00:37:38.820 --> 00:37:42.640 align:middle line:84% but if you have done it, that's great. 00:37:42.640 --> 00:37:44.720 align:middle line:84% The formulation here is then saying 00:37:44.720 --> 00:37:50.200 align:middle line:84% there is a lowest feasible efficiency for the mature stage 00:37:50.200 --> 00:37:57.470 align:middle line:84% for any of the cohorts, that if you're above that, 00:37:57.470 --> 00:37:59.150 align:middle line:84% you can get benefits of retrofits, 00:37:59.150 --> 00:38:01.550 align:middle line:84% otherwise not with this if-then-else. 00:38:01.550 --> 00:38:02.610 align:middle line:90% That's the idea. 00:38:02.610 --> 00:38:06.990 align:middle line:84% Now let's see where this lowest efficiency comes from. 00:38:06.990 --> 00:38:07.910 align:middle line:90% It's just a number. 00:38:07.910 --> 00:38:16.190 align:middle line:84% So this one, for new versus mature versus old, 00:38:16.190 --> 00:38:21.410 align:middle line:90% it is using different numbers. 00:38:21.410 --> 00:38:23.210 align:middle line:90% So that's just the parameter. 00:38:23.210 --> 00:38:27.850 align:middle line:84% So this parameter is the thing that we thought 00:38:27.850 --> 00:38:33.670 align:middle line:90% could depend on the technology. 00:38:33.670 --> 00:38:37.610 align:middle line:84% That is, basically the technology for retrofits 00:38:37.610 --> 00:38:40.350 align:middle line:84% could shift up or down this parameter. 00:38:40.350 --> 00:38:50.090 align:middle line:84% So the idea was to capture the technology through this lowest 00:38:50.090 --> 00:38:53.690 align:middle line:90% feasible efficiency. 00:38:53.690 --> 00:38:56.390 align:middle line:84% Or at least that was the idea that I had in mind 00:38:56.390 --> 00:38:57.782 align:middle line:90% for the technology effect. 00:38:57.782 --> 00:38:59.490 align:middle line:84% Now, that is not what you are doing here. 00:38:59.490 --> 00:39:04.270 align:middle line:84% So what you are doing is changing the technology 00:39:04.270 --> 00:39:09.270 align:middle line:84% for the new buildings, if I'm getting it correctly. 00:39:09.270 --> 00:39:13.150 align:middle line:84% AUDIENCE: So realistically, at the top of this model, 00:39:13.150 --> 00:39:15.310 align:middle line:90% there's technological limits. 00:39:15.310 --> 00:39:19.390 align:middle line:90% 00:39:19.390 --> 00:39:22.590 align:middle line:84% And that's coming to a value, technological effectiveness 00:39:22.590 --> 00:39:23.270 align:middle line:90% of retrofits. 00:39:23.270 --> 00:39:26.270 align:middle line:84% I have that as like, it becomes an S-curve 00:39:26.270 --> 00:39:29.070 align:middle line:90% as there's more investment. 00:39:29.070 --> 00:39:35.070 align:middle line:84% And then when I was trying to think about how to really get 00:39:35.070 --> 00:39:38.750 align:middle line:84% the benefit from that, incorporating it below, 00:39:38.750 --> 00:39:43.030 align:middle line:84% I introduced what I think is probably wrong of another. 00:39:43.030 --> 00:39:45.110 align:middle line:84% There's technological limits overall 00:39:45.110 --> 00:39:50.830 align:middle line:84% that come from what the overall benefit would be 00:39:50.830 --> 00:39:52.630 align:middle line:90% and then for each cohort. 00:39:52.630 --> 00:39:55.570 align:middle line:84% Or for each stage of building, I wanted 00:39:55.570 --> 00:39:59.010 align:middle line:84% there to be its own minimum efficiency 00:39:59.010 --> 00:40:00.350 align:middle line:90% that you're working toward. 00:40:00.350 --> 00:40:01.350 align:middle line:90% HAZHIR RAHMANDAD: I see. 00:40:01.350 --> 00:40:04.930 align:middle line:84% So this technological effectiveness of retrofits 00:40:04.930 --> 00:40:07.150 align:middle line:90% is subscripted based on cohort. 00:40:07.150 --> 00:40:12.730 align:middle line:84% So you are getting a change in the technological effectiveness 00:40:12.730 --> 00:40:14.570 align:middle line:90% per cohort. 00:40:14.570 --> 00:40:18.110 align:middle line:90% And then where does it go? 00:40:18.110 --> 00:40:19.850 align:middle line:84% And, Anne, you asked a question, we 00:40:19.850 --> 00:40:24.370 align:middle line:84% should get to that, if I didn't, please bring it up again. 00:40:24.370 --> 00:40:29.170 align:middle line:84% So it's going into New Building Tech-Enabled. 00:40:29.170 --> 00:40:30.770 align:middle line:84% AUDIENCE: Yes, it goes both into, 00:40:30.770 --> 00:40:36.490 align:middle line:84% there's a retrofit benefit for new buildings and one 00:40:36.490 --> 00:40:37.570 align:middle line:90% to retrofit. 00:40:37.570 --> 00:40:38.570 align:middle line:90% HAZHIR RAHMANDAD: I see. 00:40:38.570 --> 00:40:43.930 align:middle line:84% So this is a little bit doing two different things 00:40:43.930 --> 00:40:45.350 align:middle line:90% with this concept. 00:40:45.350 --> 00:40:48.330 align:middle line:84% One is that for new buildings, you 00:40:48.330 --> 00:40:53.910 align:middle line:84% are able to have lower energy efficiency to start with. 00:40:53.910 --> 00:40:55.990 align:middle line:84% Is that how it operates down here? 00:40:55.990 --> 00:40:57.170 align:middle line:90% New building efficiency? 00:40:57.170 --> 00:40:57.425 align:middle line:90% AUDIENCE: Yeah. 00:40:57.425 --> 00:40:58.342 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:40:58.342 --> 00:41:01.090 align:middle line:90% So that would be one path. 00:41:01.090 --> 00:41:05.950 align:middle line:84% And then it is also helping with retrofit benefits, 00:41:05.950 --> 00:41:10.070 align:middle line:84% which comes from the effectiveness of retrofits. 00:41:10.070 --> 00:41:18.310 align:middle line:84% So per unit of investment or per unit of retrofitting, 00:41:18.310 --> 00:41:22.730 align:middle line:84% how much benefit you will get, how much reduction you will get. 00:41:22.730 --> 00:41:26.250 align:middle line:84% So that's, I think, what Jake is trying to capture here. 00:41:26.250 --> 00:41:29.110 align:middle line:90% 00:41:29.110 --> 00:41:29.835 align:middle line:90% AUDIENCE: Yeah. 00:41:29.835 --> 00:41:30.710 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:41:30.710 --> 00:41:35.470 align:middle line:90% So it may work. 00:41:35.470 --> 00:41:41.070 align:middle line:84% It is also complex because this concept here, 00:41:41.070 --> 00:41:46.470 align:middle line:84% really, one thing is how much retrofits can bring down 00:41:46.470 --> 00:41:51.890 align:middle line:84% your energy efficiency, another is, per unit of investment. 00:41:51.890 --> 00:41:54.010 align:middle line:84% And you don't have investment explicitly, 00:41:54.010 --> 00:41:58.210 align:middle line:84% you're just doing a fractional thing, but per unit of activity, 00:41:58.210 --> 00:42:02.110 align:middle line:84% how much consumption do you bring down? 00:42:02.110 --> 00:42:04.370 align:middle line:84% How much do you bring down the energy consumption? 00:42:04.370 --> 00:42:08.490 align:middle line:84% These two are kind of convoluted here a little bit. 00:42:08.490 --> 00:42:13.570 align:middle line:84% The affect through the retrofit benefit captures the second one. 00:42:13.570 --> 00:42:18.130 align:middle line:84% The effect on the original level of energy efficiency 00:42:18.130 --> 00:42:21.850 align:middle line:84% that goes through the new building minimum efficiency 00:42:21.850 --> 00:42:26.690 align:middle line:90% is setting the baseline level. 00:42:26.690 --> 00:42:30.530 align:middle line:84% But neither of those actually captures the effect 00:42:30.530 --> 00:42:33.230 align:middle line:84% on how far down you can bring it, 00:42:33.230 --> 00:42:37.770 align:middle line:84% which is the lowest feasible efficiency. 00:42:37.770 --> 00:42:40.510 align:middle line:84% So this is all about assumptions. 00:42:40.510 --> 00:42:43.650 align:middle line:84% If you assume the mechanisms that are important 00:42:43.650 --> 00:42:47.330 align:middle line:90% are these ones, that's OK. 00:42:47.330 --> 00:42:51.440 align:middle line:84% But what I think I had, at least in mind in defining the problem, 00:42:51.440 --> 00:42:54.100 align:middle line:84% was more focused on changing this lower 00:42:54.100 --> 00:43:02.260 align:middle line:84% limit and how much you can bring it down with retrofits. 00:43:02.260 --> 00:43:04.740 align:middle line:84% And then the efficiency of retrofits 00:43:04.740 --> 00:43:07.900 align:middle line:84% per unit of investment, we could still 00:43:07.900 --> 00:43:12.320 align:middle line:84% make that dynamic based on how close you are to that limit. 00:43:12.320 --> 00:43:15.220 align:middle line:84% That is typically the efficiency of investment 00:43:15.220 --> 00:43:18.580 align:middle line:84% goes down as you get closer to the limit. 00:43:18.580 --> 00:43:23.080 align:middle line:84% So the first units of retrofits are very cheap, very effective. 00:43:23.080 --> 00:43:25.220 align:middle line:84% They bring down things very quickly. 00:43:25.220 --> 00:43:28.300 align:middle line:84% The later units are less effective and so on. 00:43:28.300 --> 00:43:32.560 align:middle line:84% But we could have that conversation separately. 00:43:32.560 --> 00:43:38.700 align:middle line:84% Anne, bring up your question, I didn't get it. 00:43:38.700 --> 00:43:42.180 align:middle line:84% AUDIENCE: Yeah, I thought that for one of the parameters, 00:43:42.180 --> 00:43:44.263 align:middle line:90% he had like an if-then-else. 00:43:44.263 --> 00:43:45.180 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:43:45.180 --> 00:43:48.200 align:middle line:90% 00:43:48.200 --> 00:43:50.700 align:middle line:84% AUDIENCE: It's just more of like a methodological question. 00:43:50.700 --> 00:43:54.080 align:middle line:84% I was wondering if that was necessary? 00:43:54.080 --> 00:43:56.760 align:middle line:90% HAZHIR RAHMANDAD: So, no. 00:43:56.760 --> 00:43:58.060 align:middle line:90% Yeah, it is not necessary. 00:43:58.060 --> 00:44:06.440 align:middle line:84% So basically this equation, and this is just kind of simple, 00:44:06.440 --> 00:44:11.720 align:middle line:84% you can just write it as 5, 6, 7, and that's it. 00:44:11.720 --> 00:44:15.120 align:middle line:84% And it should never be 0 because the cohort will always 00:44:15.120 --> 00:44:16.560 align:middle line:90% be one of those three. 00:44:16.560 --> 00:44:19.160 align:middle line:84% So this is how you define parameters that 00:44:19.160 --> 00:44:23.300 align:middle line:90% depend on the subscript levels. 00:44:23.300 --> 00:44:26.120 align:middle line:84% You just put the three numbers separated or N numbers 00:44:26.120 --> 00:44:28.307 align:middle line:90% for the N different elements. 00:44:28.307 --> 00:44:29.640 align:middle line:90% AUDIENCE: Now I've learned more. 00:44:29.640 --> 00:44:31.680 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:44:31.680 --> 00:44:33.000 align:middle line:90% Great. 00:44:33.000 --> 00:44:36.640 align:middle line:84% OK, let's switch to another model. 00:44:36.640 --> 00:44:39.360 align:middle line:84% For each of these models, we could go one level deeper 00:44:39.360 --> 00:44:44.180 align:middle line:84% and do some more real analysis of seeing how well they behave. 00:44:44.180 --> 00:44:48.620 align:middle line:84% But I want to get more of the different conceptualizations 00:44:48.620 --> 00:44:51.480 align:middle line:84% in place before we do any deep dive. 00:44:51.480 --> 00:44:53.980 align:middle line:84% If we get a chance, we will do some deep dives. 00:44:53.980 --> 00:44:56.520 align:middle line:84% OK, next one is coming from Jason. 00:44:56.520 --> 00:45:05.220 align:middle line:90% 00:45:05.220 --> 00:45:11.900 align:middle line:84% OK, so we have the buildings, similar story-- 00:45:11.900 --> 00:45:15.780 align:middle line:84% average building life divided into three. 00:45:15.780 --> 00:45:19.540 align:middle line:84% That's all standard, straightforward. 00:45:19.540 --> 00:45:24.440 align:middle line:84% Then, energy for new buildings, energy for mature buildings, 00:45:24.440 --> 00:45:26.380 align:middle line:90% energy for old buildings-- 00:45:26.380 --> 00:45:28.940 align:middle line:90% pretty similar. 00:45:28.940 --> 00:45:31.960 align:middle line:90% Those are all in place. 00:45:31.960 --> 00:45:34.420 align:middle line:84% Then there is the energy reduction. 00:45:34.420 --> 00:45:37.420 align:middle line:84% And this one, again, you could have it for new buildings 00:45:37.420 --> 00:45:38.080 align:middle line:90% as well. 00:45:38.080 --> 00:45:42.300 align:middle line:90% 00:45:42.300 --> 00:45:49.480 align:middle line:84% And the amount of energy that you can bring down, here, let's 00:45:49.480 --> 00:45:52.280 align:middle line:84% look at the equations you're using here, Jason. 00:45:52.280 --> 00:45:55.020 align:middle line:90% 00:45:55.020 --> 00:45:58.740 align:middle line:84% So you have a current energy efficiency factor, 00:45:58.740 --> 00:46:01.180 align:middle line:90% which I assume is time based. 00:46:01.180 --> 00:46:03.720 align:middle line:84% AUDIENCE: Yes, it's for new construction, 00:46:03.720 --> 00:46:05.400 align:middle line:90% they're being built with that. 00:46:05.400 --> 00:46:08.560 align:middle line:84% HAZHIR RAHMANDAD: Yes, so that's the current. 00:46:08.560 --> 00:46:12.200 align:middle line:84% And that sets the max achievable energy efficiency 00:46:12.200 --> 00:46:14.240 align:middle line:90% for mature buildings. 00:46:14.240 --> 00:46:15.840 align:middle line:90% AUDIENCE: With a delay. 00:46:15.840 --> 00:46:18.660 align:middle line:84% HAZHIR RAHMANDAD: So let's take a look at this formulation, 00:46:18.660 --> 00:46:20.800 align:middle line:90% see what is happening here. 00:46:20.800 --> 00:46:23.160 align:middle line:84% So you have a smooth function that says, 00:46:23.160 --> 00:46:26.520 align:middle line:84% take the current energy efficiency of buildings, 00:46:26.520 --> 00:46:35.280 align:middle line:84% delay it by some time, and that becomes the achievable energy 00:46:35.280 --> 00:46:39.360 align:middle line:90% efficiency for mature buildings. 00:46:39.360 --> 00:46:45.610 align:middle line:84% And what is this time to develop mature state of art? 00:46:45.610 --> 00:46:51.370 align:middle line:84% So you're saying, as we improve our energy efficiency technology 00:46:51.370 --> 00:46:55.490 align:middle line:84% for new buildings, that also determines 00:46:55.490 --> 00:46:59.770 align:middle line:84% our ability for retrofits, but with a delay 00:46:59.770 --> 00:47:02.890 align:middle line:84% for changing those technologies into technologies 00:47:02.890 --> 00:47:03.663 align:middle line:90% for retrofitting? 00:47:03.663 --> 00:47:04.330 align:middle line:90% AUDIENCE: Right. 00:47:04.330 --> 00:47:06.990 align:middle line:84% HAZHIR RAHMANDAD: Am I getting it correctly? 00:47:06.990 --> 00:47:09.530 align:middle line:84% AUDIENCE: That's the assumption I'm playing with. 00:47:09.530 --> 00:47:11.050 align:middle line:84% HAZHIR RAHMANDAD: Yeah, that's OK. 00:47:11.050 --> 00:47:13.750 align:middle line:84% We want to be clear about our assumptions first, 00:47:13.750 --> 00:47:15.890 align:middle line:84% and then we could discuss whether that 00:47:15.890 --> 00:47:17.770 align:middle line:90% is the best assumption or not. 00:47:17.770 --> 00:47:20.930 align:middle line:84% So the assumption here is that there 00:47:20.930 --> 00:47:25.510 align:middle line:84% is new building technology that improves energy efficiency. 00:47:25.510 --> 00:47:29.010 align:middle line:84% And then for retrofits, they basically 00:47:29.010 --> 00:47:30.790 align:middle line:90% follow the same technologies. 00:47:30.790 --> 00:47:37.370 align:middle line:84% That is the technology that sets the lower bound for energy 00:47:37.370 --> 00:47:38.910 align:middle line:90% consumption. 00:47:38.910 --> 00:47:43.390 align:middle line:84% So that only comes with a delay, and that 00:47:43.390 --> 00:47:48.710 align:middle line:84% sets the energy efficiency for the mature buildings 00:47:48.710 --> 00:47:50.330 align:middle line:90% at any point in time. 00:47:50.330 --> 00:47:52.770 align:middle line:84% And similarly, a very similar thing 00:47:52.770 --> 00:47:56.350 align:middle line:84% but with a different time delay impacts 00:47:56.350 --> 00:48:02.190 align:middle line:84% the old buildings maturity level or energy efficiency. 00:48:02.190 --> 00:48:03.470 align:middle line:90% AUDIENCE: Yeah. 00:48:03.470 --> 00:48:05.670 align:middle line:84% HAZHIR RAHMANDAD: OK, so that's the idea. 00:48:05.670 --> 00:48:10.630 align:middle line:84% Now let's do a few mental extreme conditions. 00:48:10.630 --> 00:48:15.710 align:middle line:84% So let's say buildings take a long time in this first state 00:48:15.710 --> 00:48:17.290 align:middle line:90% before they go to mature. 00:48:17.290 --> 00:48:20.270 align:middle line:84% So let's say this is 30 year before they 00:48:20.270 --> 00:48:23.830 align:middle line:90% go to the mature state. 00:48:23.830 --> 00:48:31.150 align:middle line:84% But the time to develop mature state of the art is very fast. 00:48:31.150 --> 00:48:32.730 align:middle line:90% Then, what will happen? 00:48:32.730 --> 00:48:40.330 align:middle line:84% We have buildings that are the old designs, 00:48:40.330 --> 00:48:50.890 align:middle line:84% but very soon they are able to absorb a lot better technology 00:48:50.890 --> 00:48:55.730 align:middle line:84% in terms of enhancing their energy efficiency. 00:48:55.730 --> 00:48:57.350 align:middle line:90% That's not fundamentally wrong. 00:48:57.350 --> 00:49:00.410 align:middle line:84% I don't think that's necessarily something that I can say 00:49:00.410 --> 00:49:04.330 align:middle line:90% is breaking some law. 00:49:04.330 --> 00:49:07.050 align:middle line:90% So it could happen. 00:49:07.050 --> 00:49:09.010 align:middle line:84% AUDIENCE: I considered anchoring that time 00:49:09.010 --> 00:49:15.410 align:middle line:84% to develop mature state of the art to that transition constant, 00:49:15.410 --> 00:49:18.290 align:middle line:84% but I couldn't come up with a good story to do it. 00:49:18.290 --> 00:49:21.170 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so it is really the question, 00:49:21.170 --> 00:49:24.170 align:middle line:84% the conceptual question is whether the technologies 00:49:24.170 --> 00:49:28.850 align:middle line:84% for improving energy efficiency are tied to the technology 00:49:28.850 --> 00:49:32.690 align:middle line:84% or to how the building is built or they 00:49:32.690 --> 00:49:35.570 align:middle line:84% are tied to some external technologies that 00:49:35.570 --> 00:49:39.590 align:middle line:84% are being renovated and improved regardless 00:49:39.590 --> 00:49:43.510 align:middle line:84% of how the building is built. And these two conceptualizations 00:49:43.510 --> 00:49:45.070 align:middle line:90% are not wrong. 00:49:45.070 --> 00:49:49.190 align:middle line:84% It really is a matter of expert opinion on how much 00:49:49.190 --> 00:49:52.590 align:middle line:84% you put a weight on one versus another. 00:49:52.590 --> 00:49:58.430 align:middle line:84% But what is, I think, helpful is to have something that really 00:49:58.430 --> 00:50:01.790 align:middle line:84% ties to the building, and then change that based 00:50:01.790 --> 00:50:03.910 align:middle line:90% on the technologies of the day. 00:50:03.910 --> 00:50:06.750 align:middle line:84% That gives you a lot more flexibility. 00:50:06.750 --> 00:50:13.510 align:middle line:84% So if you tie your ability to get mature buildings, 00:50:13.510 --> 00:50:16.370 align:middle line:84% bring down their energy efficiency to mature buildings, 00:50:16.370 --> 00:50:19.630 align:middle line:84% that is it is a feature of mature buildings, 00:50:19.630 --> 00:50:20.810 align:middle line:90% then you can play with that. 00:50:20.810 --> 00:50:23.910 align:middle line:84% You can bring it down faster or slower, 00:50:23.910 --> 00:50:26.630 align:middle line:84% and you can get that hint from the existing 00:50:26.630 --> 00:50:31.510 align:middle line:84% technologies in the marketplace and have any delay for that. 00:50:31.510 --> 00:50:32.730 align:middle line:90% That all works. 00:50:32.730 --> 00:50:36.290 align:middle line:84% And then you set that limit in a way that remains 00:50:36.290 --> 00:50:38.070 align:middle line:90% with that mature building. 00:50:38.070 --> 00:50:41.810 align:middle line:84% And when it goes to the old building stage, it goes with it. 00:50:41.810 --> 00:50:46.130 align:middle line:84% So it is a coflow that carries that underlying 00:50:46.130 --> 00:50:48.490 align:middle line:90% potential with it. 00:50:48.490 --> 00:50:51.130 align:middle line:84% So that would be a more robust, general way 00:50:51.130 --> 00:50:57.690 align:middle line:84% of doing it than what you have here, which kind of may work OK, 00:50:57.690 --> 00:51:03.910 align:middle line:84% but may also, in some settings, miss this correspondence. 00:51:03.910 --> 00:51:05.730 align:middle line:90% And that creates a problem. 00:51:05.730 --> 00:51:09.990 align:middle line:84% So I think the rest of this model is fairly straightforward. 00:51:09.990 --> 00:51:13.550 align:middle line:84% It's doing the same thing for the energy of old buildings. 00:51:13.550 --> 00:51:17.285 align:middle line:84% And then there is some kind of aggregation, correct? 00:51:17.285 --> 00:51:18.410 align:middle line:90% Or is there something else? 00:51:18.410 --> 00:51:21.107 align:middle line:90% 00:51:21.107 --> 00:51:22.690 align:middle line:84% AUDIENCE: That's all that's happening. 00:51:22.690 --> 00:51:25.850 align:middle line:90% 00:51:25.850 --> 00:51:30.050 align:middle line:84% I just averaged over all of them to get the full, 00:51:30.050 --> 00:51:33.252 align:middle line:84% so I could compare system level and cohort effects. 00:51:33.252 --> 00:51:34.460 align:middle line:90% HAZHIR RAHMANDAD: Yeah, yeah. 00:51:34.460 --> 00:51:39.875 align:middle line:84% And you do want to have an improvement here as well. 00:51:39.875 --> 00:51:40.500 align:middle line:90% AUDIENCE: Yeah. 00:51:40.500 --> 00:51:42.940 align:middle line:84% HAZHIR RAHMANDAD: So conceptually, there 00:51:42.940 --> 00:51:45.780 align:middle line:84% is nothing different from old building versus new buildings 00:51:45.780 --> 00:51:50.780 align:middle line:84% versus mature buildings for being candidate for energy 00:51:50.780 --> 00:51:52.740 align:middle line:90% efficiency retrofits and so on. 00:51:52.740 --> 00:51:56.020 align:middle line:84% But because they have better energy efficiency 00:51:56.020 --> 00:51:59.780 align:middle line:84% at the beginning, they are closer to that potential. 00:51:59.780 --> 00:52:02.640 align:middle line:84% It's not very cost effective, so people may not do it. 00:52:02.640 --> 00:52:08.380 align:middle line:84% So that decision to how much you invest in energy efficiency 00:52:08.380 --> 00:52:09.500 align:middle line:90% is important. 00:52:09.500 --> 00:52:12.100 align:middle line:84% Right now, you're taking that decision just 00:52:12.100 --> 00:52:13.280 align:middle line:90% buy some time constant. 00:52:13.280 --> 00:52:18.100 align:middle line:90% 00:52:18.100 --> 00:52:19.880 align:middle line:84% Actually, let's look at that equation. 00:52:19.880 --> 00:52:24.000 align:middle line:84% So right now, you're saying we take the energy efficiency, 00:52:24.000 --> 00:52:27.280 align:middle line:84% we compare it with the minimum, and you just close that gap. 00:52:27.280 --> 00:52:38.640 align:middle line:90% 00:52:38.640 --> 00:52:39.440 align:middle line:90% Yes. 00:52:39.440 --> 00:52:42.480 align:middle line:84% So this minimum energy required for mature buildings 00:52:42.480 --> 00:52:46.520 align:middle line:84% is coming from the technology and how many buildings you have. 00:52:46.520 --> 00:52:51.120 align:middle line:84% And you try to close that gap over a time constant. 00:52:51.120 --> 00:52:54.160 align:middle line:84% That's an OK first-order approximation but really kind 00:52:54.160 --> 00:52:57.240 align:middle line:84% of skips all of the decisions on how 00:52:57.240 --> 00:52:59.600 align:middle line:84% do you allocate limited resources, how 00:52:59.600 --> 00:53:01.980 align:middle line:84% do you decide whether it is cost effective, and so on. 00:53:01.980 --> 00:53:04.380 align:middle line:84% You can't do that with this formulation. 00:53:04.380 --> 00:53:08.680 align:middle line:84% But as a first cut, it is a decent starting point. 00:53:08.680 --> 00:53:10.320 align:middle line:90% AUDIENCE: Can I ask a question? 00:53:10.320 --> 00:53:13.000 align:middle line:84% We're just talking about potential retrofitting 00:53:13.000 --> 00:53:14.960 align:middle line:90% for new buildings. 00:53:14.960 --> 00:53:18.533 align:middle line:84% I think it actually may be very cost 00:53:18.533 --> 00:53:20.700 align:middle line:84% effective to do this when you're building a building 00:53:20.700 --> 00:53:22.327 align:middle line:90% if there is a recent jump. 00:53:22.327 --> 00:53:23.660 align:middle line:90% HAZHIR RAHMANDAD: Yeah, exactly. 00:53:23.660 --> 00:53:25.440 align:middle line:84% AUDIENCE: Because they last a lot longer. 00:53:25.440 --> 00:53:26.040 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 00:53:26.040 --> 00:53:27.360 align:middle line:90% AUDIENCE: They're not as close. 00:53:27.360 --> 00:53:30.340 align:middle line:84% HAZHIR RAHMANDAD: Exactly, exactly. 00:53:30.340 --> 00:53:30.940 align:middle line:90% Yeah. 00:53:30.940 --> 00:53:35.580 align:middle line:84% And that's actually a good reason also to include them, 00:53:35.580 --> 00:53:41.220 align:middle line:84% but also to make the decisions on retrofit investment subject 00:53:41.220 --> 00:53:45.560 align:middle line:84% to some measurement of lifecycle cost 00:53:45.560 --> 00:53:50.900 align:middle line:84% benefits of doing the retrofits at that stage for that building. 00:53:50.900 --> 00:53:55.460 align:middle line:84% So you would basically have the life expectancy of building 00:53:55.460 --> 00:53:57.780 align:middle line:84% and the delta in energy consumption 00:53:57.780 --> 00:54:00.580 align:middle line:90% that you will get from that. 00:54:00.580 --> 00:54:05.140 align:middle line:84% And then that marginal benefit multiplied by the time horizon 00:54:05.140 --> 00:54:07.000 align:middle line:90% gives you the total benefit. 00:54:07.000 --> 00:54:11.320 align:middle line:84% And then you can compare that with the total cost of retrofit. 00:54:11.320 --> 00:54:17.320 align:middle line:84% And that becomes a more solid decision heuristic. 00:54:17.320 --> 00:54:18.780 align:middle line:84% AUDIENCE: Just one last question. 00:54:18.780 --> 00:54:20.860 align:middle line:84% Regarding that second coflow part, 00:54:20.860 --> 00:54:24.980 align:middle line:84% I didn't have that much information. 00:54:24.980 --> 00:54:27.760 align:middle line:84% Is the reason that we need that coflow, is it 00:54:27.760 --> 00:54:32.237 align:middle line:84% because that this first coflow gets contaminated by the cost? 00:54:32.237 --> 00:54:33.320 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 00:54:33.320 --> 00:54:35.960 align:middle line:84% AUDIENCE: It's not in the original. 00:54:35.960 --> 00:54:37.920 align:middle line:84% HAZHIR RAHMANDAD: So it is really 00:54:37.920 --> 00:54:39.840 align:middle line:84% that they have different purposes. 00:54:39.840 --> 00:54:43.960 align:middle line:84% So one of them is tracking what is happening now 00:54:43.960 --> 00:54:47.440 align:middle line:84% inside the energy consumption story. 00:54:47.440 --> 00:54:51.100 align:middle line:84% The other is tracking some underlying feature, 00:54:51.100 --> 00:54:54.520 align:middle line:84% some underlying feature about how much you can actually 00:54:54.520 --> 00:54:57.780 align:middle line:84% go towards building more efficient. 00:54:57.780 --> 00:55:00.420 align:middle line:84% So these are two different features of buildings. 00:55:00.420 --> 00:55:02.580 align:middle line:84% So you need two different coflows for them. 00:55:02.580 --> 00:55:06.000 align:middle line:84% That's basically the core insight from this. 00:55:06.000 --> 00:55:08.500 align:middle line:90% So let's look at another model. 00:55:08.500 --> 00:55:20.600 align:middle line:90% 00:55:20.600 --> 00:55:22.540 align:middle line:90% So Gerardo has a simpler model. 00:55:22.540 --> 00:55:26.262 align:middle line:90% I suspect it is not. 00:55:26.262 --> 00:55:27.970 align:middle line:84% AUDIENCE: Yeah, I didn't want to remove-- 00:55:27.970 --> 00:55:30.050 align:middle line:84% HAZHIR RAHMANDAD: OK, you have subscripts here 00:55:30.050 --> 00:55:32.570 align:middle line:90% for building type. 00:55:32.570 --> 00:55:38.370 align:middle line:84% And what you're doing is that technology advancement brings 00:55:38.370 --> 00:55:45.370 align:middle line:90% down the cost of energies. 00:55:45.370 --> 00:55:46.930 align:middle line:84% AUDIENCE: I have different groups. 00:55:46.930 --> 00:55:49.130 align:middle line:84% HAZHIR RAHMANDAD: Oh, you have different, 00:55:49.130 --> 00:55:50.630 align:middle line:84% also, you have building groups here. 00:55:50.630 --> 00:55:51.490 align:middle line:90% Got it. 00:55:51.490 --> 00:55:53.130 align:middle line:90% Yes. 00:55:53.130 --> 00:55:54.490 align:middle line:90% Yes. 00:55:54.490 --> 00:55:56.650 align:middle line:84% I see, I see, I see, OK, thank you. 00:55:56.650 --> 00:56:03.290 align:middle line:84% So you have the buildings that are constructed. 00:56:03.290 --> 00:56:04.210 align:middle line:90% Interesting. 00:56:04.210 --> 00:56:11.130 align:middle line:84% And so basically you have built-- 00:56:11.130 --> 00:56:13.170 align:middle line:90% yeah, tell us. 00:56:13.170 --> 00:56:21.910 align:middle line:84% AUDIENCE: I use subscript for how buildings are built. 00:56:21.910 --> 00:56:36.990 align:middle line:84% Like, for example, for the three types of buildings in subscript. 00:56:36.990 --> 00:56:43.910 align:middle line:84% And that, in my opinion, my assumption 00:56:43.910 --> 00:56:47.950 align:middle line:84% would be the winter effect in the subscript. 00:56:47.950 --> 00:56:56.950 align:middle line:84% And I would put improvement with the retrofit in the float. 00:56:56.950 --> 00:56:59.553 align:middle line:90% And so this is our-- 00:56:59.553 --> 00:57:00.470 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:57:00.470 --> 00:57:05.070 align:middle line:84% So actually, one thing, so this is a general comment 00:57:05.070 --> 00:57:08.430 align:middle line:84% beyond this specific case, is that if you 00:57:08.430 --> 00:57:14.270 align:middle line:84% have a subscript like here, TypeA, TypeB, TypeC-- 00:57:14.270 --> 00:57:17.370 align:middle line:84% you also have Class A, Class B, Class C buildings. 00:57:17.370 --> 00:57:20.750 align:middle line:84% It just makes it hard for us to follow. 00:57:20.750 --> 00:57:22.770 align:middle line:84% I don't know whether, for example, these 00:57:22.770 --> 00:57:25.130 align:middle line:84% are the same thing you're trying to model 00:57:25.130 --> 00:57:27.090 align:middle line:90% or very different concepts. 00:57:27.090 --> 00:57:29.550 align:middle line:84% Class and type are the same or are they different? 00:57:29.550 --> 00:57:32.530 align:middle line:84% Can you tell what is TypeA, TypeB, TypeC versus Class 00:57:32.530 --> 00:57:34.610 align:middle line:90% A, Class B, Class C? 00:57:34.610 --> 00:57:35.550 align:middle line:90% AUDIENCE: Yes, OK. 00:57:35.550 --> 00:57:36.970 align:middle line:90% I'll explain it to you. 00:57:36.970 --> 00:57:42.870 align:middle line:84% So in my assumption, the subscript, 00:57:42.870 --> 00:57:49.990 align:middle line:84% I did subscripts for modeling the technological, for example, 00:57:49.990 --> 00:57:58.650 align:middle line:84% I was thinking about a good house more or a house building 00:57:58.650 --> 00:58:03.470 align:middle line:84% segment or technological type of building. 00:58:03.470 --> 00:58:05.970 align:middle line:84% HAZHIR RAHMANDAD: OK, so that's the type? 00:58:05.970 --> 00:58:07.190 align:middle line:90% AUDIENCE: The type, exactly. 00:58:07.190 --> 00:58:10.870 align:middle line:84% And the class is the energy class. 00:58:10.870 --> 00:58:12.570 align:middle line:90% HAZHIR RAHMANDAD: Yes, got it. 00:58:12.570 --> 00:58:15.650 align:middle line:84% So basically, you are capturing retrofits 00:58:15.650 --> 00:58:20.490 align:middle line:84% through moving buildings in different categories. 00:58:20.490 --> 00:58:24.730 align:middle line:84% So it kind of gets close to Ali's formulation. 00:58:24.730 --> 00:58:28.230 align:middle line:84% That is, you're moving buildings from those 00:58:28.230 --> 00:58:29.650 align:middle line:90% that don't have retrofits. 00:58:29.650 --> 00:58:34.590 align:middle line:84% So call it building Class C, to Class B to Class A. 00:58:34.590 --> 00:58:36.990 align:middle line:84% So rather than a continuous conception 00:58:36.990 --> 00:58:42.030 align:middle line:84% of, OK, we invest and we bring retrofits continuously, 00:58:42.030 --> 00:58:45.910 align:middle line:84% this is kind of two steps for bringing things down. 00:58:45.910 --> 00:58:51.430 align:middle line:90% 00:58:51.430 --> 00:58:53.990 align:middle line:84% And then there is a cost for each 00:58:53.990 --> 00:58:56.710 align:middle line:90% of these steps of improvement. 00:58:56.710 --> 00:59:00.830 align:middle line:84% And you may have a budget, so that tells you 00:59:00.830 --> 00:59:03.730 align:middle line:90% how much the building goes down. 00:59:03.730 --> 00:59:09.510 align:middle line:90% And this is a messy formulation. 00:59:09.510 --> 00:59:13.070 align:middle line:84% So let's actually look at this formulation that 00:59:13.070 --> 00:59:16.370 align:middle line:84% has a few things that should be done in a different way. 00:59:16.370 --> 00:59:19.850 align:middle line:84% So first of all, you have this if-then-else Buildings Class 00:59:19.850 --> 00:59:20.890 align:middle line:90% Type. 00:59:20.890 --> 00:59:23.270 align:middle line:84% Don't worry about the subscripts BuildingType. 00:59:23.270 --> 00:59:25.090 align:middle line:90% It's the same. 00:59:25.090 --> 00:59:27.070 align:middle line:84% The formulation is the same for all of them, 00:59:27.070 --> 00:59:28.850 align:middle line:90% so it doesn't matter here. 00:59:28.850 --> 00:59:33.610 align:middle line:84% If this thing is above 0, do drain it. 00:59:33.610 --> 00:59:37.250 align:middle line:90% Otherwise, go to 0. 00:59:37.250 --> 00:59:44.770 align:middle line:84% So this is basically what Gerardo 00:59:44.770 --> 00:59:52.050 align:middle line:84% has done to avoid draining the stock Class C below 0. 00:59:52.050 --> 00:59:56.210 align:middle line:84% And this is not a good way of doing that. 00:59:56.210 --> 00:59:59.250 align:middle line:84% It's basically a very hard constraint 00:59:59.250 --> 01:00:01.930 align:middle line:84% that says, do whatever rate you want 01:00:01.930 --> 01:00:07.090 align:middle line:84% to do, and then kill the outflow as soon as you get to 0. 01:00:07.090 --> 01:00:12.930 align:middle line:84% And this is a recipe for going under 0, small amounts under 0, 01:00:12.930 --> 01:00:18.620 align:middle line:84% because it has to go under 0 for this solution to kick in. 01:00:18.620 --> 01:00:23.020 align:middle line:84% It also kind assumes that every last building 01:00:23.020 --> 01:00:28.240 align:middle line:84% is available for retrofits, for improvements, it's visible, 01:00:28.240 --> 01:00:30.620 align:middle line:84% it's easy to find it, it's easy to convince 01:00:30.620 --> 01:00:34.300 align:middle line:90% the owners to do the retrofits. 01:00:34.300 --> 01:00:38.340 align:middle line:84% So that's also another problem with this formulation. 01:00:38.340 --> 01:00:40.360 align:middle line:84% So what's the standard formulation here? 01:00:40.360 --> 01:00:45.220 align:middle line:84% We have seen versions of this in the basic course. 01:00:45.220 --> 01:00:49.140 align:middle line:84% Anybody wants to share what the standard solution to this 01:00:49.140 --> 01:00:51.980 align:middle line:90% might be? 01:00:51.980 --> 01:00:53.640 align:middle line:84% Kathy, do you want to take a stab? 01:00:53.640 --> 01:01:06.240 align:middle line:90% 01:01:06.240 --> 01:01:08.680 align:middle line:84% So don't worry about the rest of the formulation. 01:01:08.680 --> 01:01:10.900 align:middle line:84% Just how to get rid of the if-then-else 01:01:10.900 --> 01:01:14.180 align:middle line:84% and replace it with something that is 01:01:14.180 --> 01:01:16.360 align:middle line:90% a bit more robust and cleaner? 01:01:16.360 --> 01:01:25.000 align:middle line:90% 01:01:25.000 --> 01:01:28.958 align:middle line:84% AUDIENCE: Would you just want a first-order draining? 01:01:28.958 --> 01:01:30.500 align:middle line:84% HAZHIR RAHMANDAD: Would you speak up? 01:01:30.500 --> 01:01:34.760 align:middle line:84% AUDIENCE: Would you just want a first-order draining? 01:01:34.760 --> 01:01:36.120 align:middle line:90% HAZHIR RAHMANDAD: I can't hear. 01:01:36.120 --> 01:01:36.787 align:middle line:90% AUDIENCE: Sorry. 01:01:36.787 --> 01:01:41.480 align:middle line:84% Would you just want to do a first-order draining? 01:01:41.480 --> 01:01:45.160 align:middle line:84% HAZHIR RAHMANDAD: So you could do a first-order limit 01:01:45.160 --> 01:01:46.100 align:middle line:90% on draining. 01:01:46.100 --> 01:01:49.280 align:middle line:84% That is, you say maximum drain rate, 01:01:49.280 --> 01:01:52.120 align:middle line:84% and that maximum drain rate is the stock divided 01:01:52.120 --> 01:01:55.960 align:middle line:90% by a minimum time to retrofit. 01:01:55.960 --> 01:02:00.740 align:middle line:84% And then that becomes the constraint as a maximum level. 01:02:00.740 --> 01:02:03.680 align:middle line:84% Then you take the minimum of that maximum drain rate 01:02:03.680 --> 01:02:06.120 align:middle line:84% and whatever is your formulation. 01:02:06.120 --> 01:02:06.980 align:middle line:90% So is that clear? 01:02:06.980 --> 01:02:09.600 align:middle line:84% That's a very simple, standard solution 01:02:09.600 --> 01:02:14.740 align:middle line:84% that we use whenever we want to put a first-order constraint 01:02:14.740 --> 01:02:16.260 align:middle line:90% on how fast we are draining. 01:02:16.260 --> 01:02:19.100 align:middle line:84% So stock of tasks in a project model, 01:02:19.100 --> 01:02:22.800 align:middle line:84% you don't put a if-then-else tasks are above 0, 01:02:22.800 --> 01:02:24.160 align:middle line:90% do it, otherwise don't do it. 01:02:24.160 --> 01:02:29.580 align:middle line:84% You put, it's the minimum of max task completion and task 01:02:29.580 --> 01:02:32.980 align:middle line:90% completion from resources. 01:02:32.980 --> 01:02:36.900 align:middle line:84% For shipments, it's a minimum of maximum shipment rate 01:02:36.900 --> 01:02:41.320 align:middle line:84% and shipment from demand or whatever you want it to be. 01:02:41.320 --> 01:02:47.400 align:middle line:84% OK, so that's kind of basic stuff on that front. 01:02:47.400 --> 01:02:51.620 align:middle line:84% Then, you have other things coming into this efficiency 01:02:51.620 --> 01:02:56.860 align:middle line:84% improvement for classes, which is the budget divided by cost 01:02:56.860 --> 01:02:59.680 align:middle line:84% multiplied by building type, cost sensitivity, 01:02:59.680 --> 01:03:02.280 align:middle line:90% some sensitivity fraction. 01:03:02.280 --> 01:03:07.780 align:middle line:90% 01:03:07.780 --> 01:03:09.840 align:middle line:84% So why do you need two parameters? 01:03:09.840 --> 01:03:12.100 align:middle line:84% Why do you have cost for improved building 01:03:12.100 --> 01:03:15.540 align:middle line:84% from C to B and building type cost sensitivity? 01:03:15.540 --> 01:03:18.600 align:middle line:84% Can you tell what was the idea, Gerardo? 01:03:18.600 --> 01:03:22.800 align:middle line:84% AUDIENCE: The idea was that for the type of buildings 01:03:22.800 --> 01:03:25.960 align:middle line:84% that we add into the subset, it will 01:03:25.960 --> 01:03:30.220 align:middle line:84% be different for how much you need to deliver. 01:03:30.220 --> 01:03:31.720 align:middle line:84% HAZHIR RAHMANDAD: Yes, so that would 01:03:31.720 --> 01:03:36.720 align:middle line:84% be the cost for improving building from C to B. 01:03:36.720 --> 01:03:39.340 align:middle line:84% Why do you need a separate sensitivity parameter? 01:03:39.340 --> 01:03:43.100 align:middle line:84% I'm just not following the need for two different. 01:03:43.100 --> 01:03:52.360 align:middle line:90% 01:03:52.360 --> 01:03:53.600 align:middle line:90% AUDIENCE: One's enough? 01:03:53.600 --> 01:03:54.558 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:03:54.558 --> 01:03:57.600 align:middle line:90% 01:03:57.600 --> 01:04:01.980 align:middle line:84% Yeah, because this also has three different drivers. 01:04:01.980 --> 01:04:04.520 align:middle line:84% So there is a little bit of a proliferation of parameters 01:04:04.520 --> 01:04:06.220 align:middle line:90% that don't do anything here. 01:04:06.220 --> 01:04:07.900 align:middle line:90% So you don't want to have that. 01:04:07.900 --> 01:04:10.940 align:middle line:90% That's generally the idea. 01:04:10.940 --> 01:04:14.140 align:middle line:84% So this is taking buildings one level down 01:04:14.140 --> 01:04:17.740 align:middle line:90% and allows that to happen. 01:04:17.740 --> 01:04:22.860 align:middle line:84% Right now, your demolition is 0 for all of these things, which 01:04:22.860 --> 01:04:25.280 align:middle line:90% is not going to work well. 01:04:25.280 --> 01:04:27.140 align:middle line:84% You would just accumulate buildings 01:04:27.140 --> 01:04:28.820 align:middle line:84% and they will never be demolished. 01:04:28.820 --> 01:04:31.780 align:middle line:90% 01:04:31.780 --> 01:04:32.300 align:middle line:90% Yes. 01:04:32.300 --> 01:04:36.140 align:middle line:84% So the demolition rates, right now 01:04:36.140 --> 01:04:37.760 align:middle line:84% you don't have aging of buildings, 01:04:37.760 --> 01:04:38.880 align:middle line:90% which is another problem. 01:04:38.880 --> 01:04:41.740 align:middle line:84% But putting that aside, you definitely 01:04:41.740 --> 01:04:44.520 align:middle line:84% need to have outflows from these stocks of buildings. 01:04:44.520 --> 01:04:47.240 align:middle line:84% Otherwise, buildings will stay around forever. 01:04:47.240 --> 01:04:51.860 align:middle line:84% So a set first-order delay, a first-order draining 01:04:51.860 --> 01:04:53.660 align:middle line:84% would be the simplest formulation 01:04:53.660 --> 01:04:55.900 align:middle line:84% that would be Building Class C divided 01:04:55.900 --> 01:05:02.660 align:middle line:84% by life of Building Class C or lifetime of building in general. 01:05:02.660 --> 01:05:07.800 align:middle line:84% So those are some of the key feedback here. 01:05:07.800 --> 01:05:10.070 align:middle line:84% Then you have all of these buildings 01:05:10.070 --> 01:05:14.750 align:middle line:84% at different classes being accumulated into Cumulative 01:05:14.750 --> 01:05:16.730 align:middle line:90% Building Type Consumption. 01:05:16.730 --> 01:05:21.850 align:middle line:84% So tell me what this thing is doing. 01:05:21.850 --> 01:05:25.650 align:middle line:84% So I think I know what it is doing. 01:05:25.650 --> 01:05:28.090 align:middle line:84% And it is not the exact right way to do it. 01:05:28.090 --> 01:05:31.790 align:middle line:84% So basically, what you need here, 01:05:31.790 --> 01:05:35.110 align:middle line:84% you are trying to add up what is the total building's 01:05:35.110 --> 01:05:41.990 align:middle line:84% consumption of energy or consumption rate for energy. 01:05:41.990 --> 01:05:42.990 align:middle line:90% AUDIENCE: Yeah. 01:05:42.990 --> 01:05:49.270 align:middle line:84% HAZHIR RAHMANDAD: And that is the sum 01:05:49.270 --> 01:05:55.930 align:middle line:84% of the buildings multiplied by energy use per building, 01:05:55.930 --> 01:05:58.870 align:middle line:90% in this case. 01:05:58.870 --> 01:06:03.070 align:middle line:90% And this is in kBTU per month. 01:06:03.070 --> 01:06:06.730 align:middle line:84% Yes, so this is your total energy consumption, I see. 01:06:06.730 --> 01:06:09.090 align:middle line:84% And then you have the cumulative energy consumption 01:06:09.090 --> 01:06:10.750 align:middle line:84% from beginning of the time up to now. 01:06:10.750 --> 01:06:11.670 align:middle line:90% So this is not wrong. 01:06:11.670 --> 01:06:13.330 align:middle line:90% This is also fine. 01:06:13.330 --> 01:06:20.930 align:middle line:84% So the core idea is now you have this other technology 01:06:20.930 --> 01:06:28.210 align:middle line:84% side that is changing the cost of efficiency improvements, 01:06:28.210 --> 01:06:29.110 align:middle line:90% I think. 01:06:29.110 --> 01:06:32.130 align:middle line:90% 01:06:32.130 --> 01:06:32.970 align:middle line:90% Yes. 01:06:32.970 --> 01:06:36.650 align:middle line:84% So the cost of energy efficiency improvements in this model 01:06:36.650 --> 01:06:39.850 align:middle line:84% is being improved exogenously through 01:06:39.850 --> 01:06:43.130 align:middle line:90% some technological advancement. 01:06:43.130 --> 01:06:49.770 align:middle line:84% And then that makes it cheaper to shift buildings 01:06:49.770 --> 01:06:53.210 align:middle line:90% from one stage to the other one. 01:06:53.210 --> 01:06:56.090 align:middle line:84% Now this one is not capturing the effect 01:06:56.090 --> 01:06:57.562 align:middle line:90% we were talking about. 01:06:57.562 --> 01:06:59.270 align:middle line:84% So there are two different possibilities. 01:06:59.270 --> 01:07:03.970 align:middle line:84% One is that I'm making it cheaper to bring down the cost 01:07:03.970 --> 01:07:06.930 align:middle line:90% to retrofit. 01:07:06.930 --> 01:07:11.330 align:middle line:84% The other is, I'm making it possible to do more retrofits, 01:07:11.330 --> 01:07:14.070 align:middle line:84% that is, get to lower levels of energy 01:07:14.070 --> 01:07:17.470 align:middle line:90% consumption per square foot. 01:07:17.470 --> 01:07:19.750 align:middle line:84% I was more focused on the latter. 01:07:19.750 --> 01:07:22.130 align:middle line:84% This formulation tackles the former. 01:07:22.130 --> 01:07:26.310 align:middle line:84% This captures reductions in the cost of energy efficiency, 01:07:26.310 --> 01:07:32.310 align:middle line:84% but doesn't capture the fact that your Building Class 01:07:32.310 --> 01:07:38.030 align:middle line:84% A may now have even a lower energy efficiency because now we 01:07:38.030 --> 01:07:39.930 align:middle line:84% have developed better technologies. 01:07:39.930 --> 01:07:44.790 align:middle line:84% Or you could, in fact, think of other classes that are not 01:07:44.790 --> 01:07:48.070 align:middle line:84% typically available to be visited at the beginning 01:07:48.070 --> 01:07:53.230 align:middle line:84% of time, but then by 2000s, you have new classes of buildings 01:07:53.230 --> 01:07:58.870 align:middle line:84% in terms of energy efficiency that become available to others. 01:07:58.870 --> 01:08:02.690 align:middle line:84% So that's kind of the effect we are talking about. 01:08:02.690 --> 01:08:06.370 align:middle line:84% And then the other problem is that every building, 01:08:06.370 --> 01:08:08.990 align:middle line:84% with enough investment, can go all the way to Class A, 01:08:08.990 --> 01:08:11.690 align:middle line:84% so this is missing on the part about, 01:08:11.690 --> 01:08:15.290 align:middle line:84% OK, some things are just not realistic or feasible. 01:08:15.290 --> 01:08:20.950 align:middle line:84% For that vintage of buildings that was built in 1950s, 01:08:20.950 --> 01:08:26.850 align:middle line:84% you can't make them zero homes unless you completely got them 01:08:26.850 --> 01:08:31.370 align:middle line:84% and rebuild them, which is a different story than retrofits. 01:08:31.370 --> 01:08:36.510 align:middle line:84% OK, so that's a good conversation on this model. 01:08:36.510 --> 01:08:38.109 align:middle line:90% Let's go to the next one. 01:08:38.109 --> 01:08:41.130 align:middle line:90% 01:08:41.130 --> 01:08:42.890 align:middle line:90% This is Hassam's. 01:08:42.890 --> 01:08:48.032 align:middle line:90% 01:08:48.032 --> 01:08:50.490 align:middle line:84% AUDIENCE: Presentation on this maybe a little bit different 01:08:50.490 --> 01:08:53.290 align:middle line:84% from how we worked on the conceptualization together. 01:08:53.290 --> 01:08:54.848 align:middle line:90% It has a subscript. 01:08:54.848 --> 01:08:56.390 align:middle line:84% HAZHIR RAHMANDAD: This is subscripted 01:08:56.390 --> 01:09:03.220 align:middle line:84% so that you can basically add the number of vintages 01:09:03.220 --> 01:09:04.460 align:middle line:90% as you want. 01:09:04.460 --> 01:09:05.040 align:middle line:90% Great. 01:09:05.040 --> 01:09:07.779 align:middle line:84% So you have the built area, which is buildings, 01:09:07.779 --> 01:09:13.979 align:middle line:90% and you have retrofitted areas. 01:09:13.979 --> 01:09:15.819 align:middle line:84% So let's look at the subscripting part 01:09:15.819 --> 01:09:19.819 align:middle line:84% because that's something that is new for some of the folks here. 01:09:19.819 --> 01:09:29.479 align:middle line:84% So here, Hassam is subscripting items on vintage ranges. 01:09:29.479 --> 01:09:31.862 align:middle line:84% AUDIENCE: These are subranges I ended up using. 01:09:31.862 --> 01:09:32.779 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:09:32.779 --> 01:09:38.740 align:middle line:84% So you have the subscript range vintage. 01:09:38.740 --> 01:09:42.380 align:middle line:84% And this vintage accounts for, so you 01:09:42.380 --> 01:09:47.080 align:middle line:90% can have V1, V2, V3, et cetera. 01:09:47.080 --> 01:09:50.220 align:middle line:90% 01:09:50.220 --> 01:09:54.940 align:middle line:84% And if I look at the vintage members, elements, 01:09:54.940 --> 01:09:57.580 align:middle line:90% right now it is only 3. 01:09:57.580 --> 01:10:04.820 align:middle line:84% So the way this formulation is formulated, it is not incorrect. 01:10:04.820 --> 01:10:07.640 align:middle line:84% This is fine, but it is not the most efficient way 01:10:07.640 --> 01:10:09.440 align:middle line:90% to formulating these. 01:10:09.440 --> 01:10:13.980 align:middle line:84% And the reason is that now if I want to add a force element, 01:10:13.980 --> 01:10:17.620 align:middle line:84% I have to define a force formulation. 01:10:17.620 --> 01:10:20.080 align:middle line:84% But that force formulation would basically 01:10:20.080 --> 01:10:23.100 align:middle line:90% be the same as V3 formulation. 01:10:23.100 --> 01:10:27.360 align:middle line:90% 01:10:27.360 --> 01:10:29.902 align:middle line:84% AUDIENCE: The goal was to have a first, a middle, and an end. 01:10:29.902 --> 01:10:30.985 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 01:10:30.985 --> 01:10:32.180 align:middle line:90% So that's how you would do. 01:10:32.180 --> 01:10:34.980 align:middle line:84% AUDIENCE: But it didn't work well, so I ended up using this. 01:10:34.980 --> 01:10:36.813 align:middle line:84% HAZHIR RAHMANDAD: So you couldn't figure out 01:10:36.813 --> 01:10:41.360 align:middle line:84% how to do the subranges so that you can get the first, last, 01:10:41.360 --> 01:10:43.780 align:middle line:90% and middle formulation to work. 01:10:43.780 --> 01:10:44.340 align:middle line:90% That's fair. 01:10:44.340 --> 01:10:46.380 align:middle line:90% It's not a trivial thing. 01:10:46.380 --> 01:10:48.200 align:middle line:90% It needs playing around. 01:10:48.200 --> 01:10:52.220 align:middle line:84% I gave an example age model inside Vensim that does it, 01:10:52.220 --> 01:10:53.560 align:middle line:90% I think. 01:10:53.560 --> 01:10:55.000 align:middle line:90% So check that out. 01:10:55.000 --> 01:10:56.440 align:middle line:90% That's a good way. 01:10:56.440 --> 01:10:59.900 align:middle line:84% But for those who are not yet following what this is doing 01:10:59.900 --> 01:11:05.380 align:middle line:84% or what this one can do, right now we have three vintages. 01:11:05.380 --> 01:11:06.320 align:middle line:90% That's easy. 01:11:06.320 --> 01:11:07.360 align:middle line:90% You just build them. 01:11:07.360 --> 01:11:10.140 align:middle line:84% But if you wanted to have 100, then 01:11:10.140 --> 01:11:13.680 align:middle line:84% doing it manually just becomes so messy, 01:11:13.680 --> 01:11:16.180 align:middle line:90% you're not going to even try it. 01:11:16.180 --> 01:11:20.180 align:middle line:84% The structure that Hassam has here 01:11:20.180 --> 01:11:25.860 align:middle line:84% allows him to basically do that without creating 01:11:25.860 --> 01:11:29.420 align:middle line:90% copies of the model 100 times. 01:11:29.420 --> 01:11:32.060 align:middle line:84% You can just do it with the same formulation 01:11:32.060 --> 01:11:33.780 align:middle line:90% that you have done for three. 01:11:33.780 --> 01:11:36.540 align:middle line:84% So that's the thing that is nice about it. 01:11:36.540 --> 01:11:40.100 align:middle line:84% Now, for that to work, you need to do 01:11:40.100 --> 01:11:43.080 align:middle line:84% a little bit of subscript manipulation in Vensim. 01:11:43.080 --> 01:11:47.820 align:middle line:84% That is, you would say, OK, new buildings only 01:11:47.820 --> 01:11:52.340 align:middle line:84% enter into the first element of the subscript, 01:11:52.340 --> 01:11:57.760 align:middle line:84% and demolition only happens to the last element of subscript. 01:11:57.760 --> 01:12:00.920 align:middle line:84% For everything in between, what is happening 01:12:00.920 --> 01:12:05.600 align:middle line:84% is that they are getting aging buildings 01:12:05.600 --> 01:12:10.080 align:middle line:84% from the previous cohort and they are sending elements 01:12:10.080 --> 01:12:12.440 align:middle line:90% to the next cohort. 01:12:12.440 --> 01:12:19.720 align:middle line:84% So you need to do that using subranges, in Vensim lingo, 01:12:19.720 --> 01:12:22.760 align:middle line:90% to do it effectively. 01:12:22.760 --> 01:12:25.240 align:middle line:84% It takes a little bit more time than I want 01:12:25.240 --> 01:12:27.260 align:middle line:90% to allocate to do that here. 01:12:27.260 --> 01:12:29.740 align:middle line:90% So let's not do it together. 01:12:29.740 --> 01:12:32.740 align:middle line:84% If I get the chance, I may put together a model that has that, 01:12:32.740 --> 01:12:34.580 align:middle line:90% but that's the idea. 01:12:34.580 --> 01:12:37.360 align:middle line:84% And then conceptually, essentially, you 01:12:37.360 --> 01:12:40.680 align:middle line:84% are doing a similar thing as Ali, 01:12:40.680 --> 01:12:45.680 align:middle line:84% in terms of moving buildings into a retrofitted stage 01:12:45.680 --> 01:12:51.400 align:middle line:84% and with that, moving their energy consumption 01:12:51.400 --> 01:12:53.680 align:middle line:84% to the level that is corresponding 01:12:53.680 --> 01:12:55.340 align:middle line:90% to the retrofitted ones. 01:12:55.340 --> 01:12:57.340 align:middle line:84% AUDIENCE: This allows for retrofitting 01:12:57.340 --> 01:12:58.423 align:middle line:90% on all three vintages. 01:12:58.423 --> 01:12:59.340 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:12:59.340 --> 01:13:03.900 align:middle line:84% And this allows for retrofitting on everything. 01:13:03.900 --> 01:13:07.638 align:middle line:90% The technology for retrofits-- 01:13:07.638 --> 01:13:09.180 align:middle line:84% AUDIENCE: So I'm doing the same thing 01:13:09.180 --> 01:13:12.000 align:middle line:84% that Ali did, which I have a new technology 01:13:12.000 --> 01:13:15.740 align:middle line:84% and I'm assuming that the new technology for new buildings 01:13:15.740 --> 01:13:20.480 align:middle line:84% is the same as the gold standard for retrofitting. 01:13:20.480 --> 01:13:22.340 align:middle line:84% So the new technology for retrofitting 01:13:22.340 --> 01:13:25.500 align:middle line:84% will be a weighted average between the current energy 01:13:25.500 --> 01:13:29.103 align:middle line:84% efficiency and the best that they can get right now. 01:13:29.103 --> 01:13:30.020 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:13:30.020 --> 01:13:34.820 align:middle line:90% 01:13:34.820 --> 01:13:38.340 align:middle line:84% OK, weighted average between the current energy efficiency 01:13:38.340 --> 01:13:39.048 align:middle line:90% of that cohort. 01:13:39.048 --> 01:13:40.840 align:middle line:84% AUDIENCE: And it's going in to retrofitted. 01:13:40.840 --> 01:13:43.180 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:13:43.180 --> 01:13:46.780 align:middle line:90% OK, OK, good. 01:13:46.780 --> 01:13:51.980 align:middle line:84% Yeah, that basically hard codes the limit 01:13:51.980 --> 01:13:55.630 align:middle line:84% that you can achieve as this weighted average. 01:13:55.630 --> 01:13:58.270 align:middle line:84% It doesn't allow you to dynamically change 01:13:58.270 --> 01:14:00.650 align:middle line:84% that based on new technologies and so on. 01:14:00.650 --> 01:14:04.910 align:middle line:84% So that's kind of the downside of not having a third coflow. 01:14:04.910 --> 01:14:06.470 align:middle line:84% AUDIENCE: The impact of retrofitting, 01:14:06.470 --> 01:14:08.890 align:middle line:84% for example, which can make it endogenous, 01:14:08.890 --> 01:14:11.030 align:middle line:90% but that is not trivial. 01:14:11.030 --> 01:14:12.790 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:14:12.790 --> 01:14:17.330 align:middle line:90% Well, but that limit is the key. 01:14:17.330 --> 01:14:20.470 align:middle line:84% That is, right now you are basically getting everybody 01:14:20.470 --> 01:14:22.890 align:middle line:90% to this new retrofit level. 01:14:22.890 --> 01:14:26.950 align:middle line:90% 01:14:26.950 --> 01:14:28.990 align:middle line:84% AUDIENCE: Yeah, the new retrofit level, but it 01:14:28.990 --> 01:14:30.712 align:middle line:90% is a weighted average between-- 01:14:30.712 --> 01:14:31.670 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:14:31.670 --> 01:14:36.950 align:middle line:90% 01:14:36.950 --> 01:14:39.710 align:middle line:84% AUDIENCE: Actually, we were thinking that the new efficiency 01:14:39.710 --> 01:14:41.430 align:middle line:84% or energy consumption is somewhere 01:14:41.430 --> 01:14:48.750 align:middle line:84% between the maximum and the original of that cohort. 01:14:48.750 --> 01:14:50.850 align:middle line:84% The simplest way is taking the average. 01:14:50.850 --> 01:14:52.730 align:middle line:84% It will be exactly the middle point. 01:14:52.730 --> 01:14:55.490 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:14:55.490 --> 01:14:57.610 align:middle line:84% And that parameter impact of retrofitting 01:14:57.610 --> 01:15:00.930 align:middle line:84% is shifting whether it is in the middle or not. 01:15:00.930 --> 01:15:03.570 align:middle line:90% Yeah. 01:15:03.570 --> 01:15:12.330 align:middle line:84% So you could make that parameter a function 01:15:12.330 --> 01:15:16.070 align:middle line:84% of basically the cohort you are looking at, 01:15:16.070 --> 01:15:17.390 align:middle line:90% the vintage you are looking at. 01:15:17.390 --> 01:15:22.430 align:middle line:84% And then that could change dynamically in some way. 01:15:22.430 --> 01:15:26.970 align:middle line:84% That would be how you would do the history 01:15:26.970 --> 01:15:29.370 align:middle line:90% or kind of capture the history. 01:15:29.370 --> 01:15:31.650 align:middle line:90% Good. 01:15:31.650 --> 01:15:34.070 align:middle line:84% I'm not going through the details here. 01:15:34.070 --> 01:15:37.610 align:middle line:84% I think the rest is probably sound. 01:15:37.610 --> 01:15:46.210 align:middle line:84% So let's look at maybe one more model before we take a break. 01:15:46.210 --> 01:15:49.470 align:middle line:90% So let me do this. 01:15:49.470 --> 01:15:51.150 align:middle line:90% Yes. 01:15:51.150 --> 01:15:52.730 align:middle line:90% So this is Anne's. 01:15:52.730 --> 01:16:08.150 align:middle line:90% 01:16:08.150 --> 01:16:10.070 align:middle line:90% Go ahead, Anne. 01:16:10.070 --> 01:16:14.030 align:middle line:84% AUDIENCE: I tried to do like the subscripts thing. 01:16:14.030 --> 01:16:16.750 align:middle line:84% But there's also a very big wrong, 01:16:16.750 --> 01:16:18.550 align:middle line:84% as I'm showing here, where I don't 01:16:18.550 --> 01:16:22.110 align:middle line:84% know why I thought that an efficient building consumes 01:16:22.110 --> 01:16:22.970 align:middle line:90% more energy. 01:16:22.970 --> 01:16:24.830 align:middle line:90% I think I did it late at night. 01:16:24.830 --> 01:16:25.747 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:16:25.747 --> 01:16:26.910 align:middle line:90% AUDIENCE: Yeah. 01:16:26.910 --> 01:16:28.590 align:middle line:90% HAZHIR RAHMANDAD: It's OK. 01:16:28.590 --> 01:16:31.510 align:middle line:84% We can define efficient as inefficient. 01:16:31.510 --> 01:16:33.470 align:middle line:84% So energy inefficiency of building vintage. 01:16:33.470 --> 01:16:34.870 align:middle line:90% AUDIENCE: Yes, that's the word. 01:16:34.870 --> 01:16:36.190 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:16:36.190 --> 01:16:38.710 align:middle line:90% Yeah. 01:16:38.710 --> 01:16:43.150 align:middle line:84% So basically, this is energy consumption type of a thing, so 01:16:43.150 --> 01:16:45.390 align:middle line:90% variable namings. 01:16:45.390 --> 01:16:47.402 align:middle line:84% AUDIENCE: Yes, the variable name is off as well. 01:16:47.402 --> 01:16:50.772 align:middle line:90% It should be energy consumption. 01:16:50.772 --> 01:16:51.730 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:16:51.730 --> 01:16:54.670 align:middle line:90% So the units are OK but not OK. 01:16:54.670 --> 01:16:59.290 align:middle line:84% So you have kilowatt hour per square meter, which 01:16:59.290 --> 01:17:02.330 align:middle line:84% is the right unit, but it should be kilowatt hour divided 01:17:02.330 --> 01:17:05.450 align:middle line:84% by square meter so that your buildings would 01:17:05.450 --> 01:17:10.010 align:middle line:84% be in a square meter and then the average energy efficiency-- 01:17:10.010 --> 01:17:11.510 align:middle line:90% OK, you have the units building. 01:17:11.510 --> 01:17:19.010 align:middle line:84% So this is actually important for unit consistency. 01:17:19.010 --> 01:17:21.530 align:middle line:84% Yeah, this is hard to make unit consistent 01:17:21.530 --> 01:17:23.870 align:middle line:90% if you don't do it right. 01:17:23.870 --> 01:17:27.790 align:middle line:84% So the buildings, they are in square meters. 01:17:27.790 --> 01:17:28.450 align:middle line:90% That's easy. 01:17:28.450 --> 01:17:31.550 align:middle line:84% You could also go with just number of buildings, 01:17:31.550 --> 01:17:34.290 align:middle line:84% but then you're missing the square meter, which is probably 01:17:34.290 --> 01:17:36.250 align:middle line:84% better, or square feet, which is a better. 01:17:36.250 --> 01:17:39.493 align:middle line:84% AUDIENCE: Yeah, I think went with number of buildings. 01:17:39.493 --> 01:17:40.410 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:17:40.410 --> 01:17:44.690 align:middle line:84% So if you do that, then the unit for energy consumption 01:17:44.690 --> 01:17:48.380 align:middle line:90% per building would be kilowatt-- 01:17:48.380 --> 01:17:50.860 align:middle line:84% it's actually not kilowatt hour, it's 01:17:50.860 --> 01:17:56.460 align:middle line:84% kilowatt per building rather than per square meter. 01:17:56.460 --> 01:18:00.780 align:middle line:84% Or you could make it kilowatt hour per year per building 01:18:00.780 --> 01:18:02.500 align:middle line:90% or per square meter. 01:18:02.500 --> 01:18:05.100 align:middle line:90% So those are the options. 01:18:05.100 --> 01:18:08.983 align:middle line:84% AUDIENCE: The averages, it was then per building. 01:18:08.983 --> 01:18:09.900 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:18:09.900 --> 01:18:15.180 align:middle line:84% But I'm just saying the units that you are putting here 01:18:15.180 --> 01:18:29.860 align:middle line:84% should be kilowatt hour per building per year or something 01:18:29.860 --> 01:18:34.620 align:middle line:84% like that so that when you multiply that 01:18:34.620 --> 01:18:41.180 align:middle line:84% by the number of buildings, the total energy consumption-- 01:18:41.180 --> 01:18:45.480 align:middle line:84% or actually, no, this is not per building. 01:18:45.480 --> 01:18:47.260 align:middle line:90% This is for all buildings. 01:18:47.260 --> 01:18:49.060 align:middle line:90% This is kilowatt hour per year. 01:18:49.060 --> 01:18:52.560 align:middle line:90% This is for the stock. 01:18:52.560 --> 01:18:58.320 align:middle line:84% And then for per building value, it 01:18:58.320 --> 01:19:04.920 align:middle line:84% becomes kilowatt hour per building per year. 01:19:04.920 --> 01:19:09.760 align:middle line:84% So the time units are kind of missing from this formulation. 01:19:09.760 --> 01:19:13.160 align:middle line:84% And the unit consistency is not enforced 01:19:13.160 --> 01:19:16.220 align:middle line:84% when you don't have the right units here. 01:19:16.220 --> 01:19:18.820 align:middle line:90% So that's the unit part. 01:19:18.820 --> 01:19:21.760 align:middle line:84% Now let's look at the constructs. 01:19:21.760 --> 01:19:30.220 align:middle line:84% So you have one stock for buildings, 01:19:30.220 --> 01:19:34.600 align:middle line:84% so you don't have multiple life stages. 01:19:34.600 --> 01:19:37.680 align:middle line:84% You have the vintages captured using subscripts, 01:19:37.680 --> 01:19:39.740 align:middle line:84% if I'm understanding you correctly. 01:19:39.740 --> 01:19:42.080 align:middle line:90% So you're using subscript year. 01:19:42.080 --> 01:19:44.200 align:middle line:84% And by the way, using the subscript year 01:19:44.200 --> 01:19:46.300 align:middle line:84% is going to be very confusing because you 01:19:46.300 --> 01:19:51.060 align:middle line:84% can have built-in units of year, so things will become messier 01:19:51.060 --> 01:19:55.340 align:middle line:84% when you use year as your subscript name. 01:19:55.340 --> 01:19:59.740 align:middle line:84% It may even result in some errors in Vensim. 01:19:59.740 --> 01:20:06.380 align:middle line:84% But let's not waste time on that. 01:20:06.380 --> 01:20:09.100 align:middle line:84% So the way you are capturing it is 01:20:09.100 --> 01:20:13.060 align:middle line:84% that you are looking at the retrofit potential, which 01:20:13.060 --> 01:20:19.940 align:middle line:84% is coming from maximum possible efficiency of building vintages, 01:20:19.940 --> 01:20:27.300 align:middle line:84% and that is determined by the technology that is affecting 01:20:27.300 --> 01:20:31.300 align:middle line:90% that max possibility. 01:20:31.300 --> 01:20:36.780 align:middle line:84% So the way you are capturing that is for each unit, 01:20:36.780 --> 01:20:41.780 align:middle line:84% there is an initial vintage, then 01:20:41.780 --> 01:20:47.120 align:middle line:84% there is a gain from technology for each type of a unit. 01:20:47.120 --> 01:20:52.280 align:middle line:84% And then the technology goes up that shifts the marginal unit 01:20:52.280 --> 01:20:56.680 align:middle line:90% of benefit from retrofits. 01:20:56.680 --> 01:21:00.680 align:middle line:84% And this creates the maximum possible efficiency. 01:21:00.680 --> 01:21:06.000 align:middle line:84% And then you look at the gap between the current energy 01:21:06.000 --> 01:21:14.220 align:middle line:84% efficiency, minus current energy efficiency. 01:21:14.220 --> 01:21:18.060 align:middle line:90% 01:21:18.060 --> 01:21:22.560 align:middle line:84% So this is kind of where, again, lack of units become a problem. 01:21:22.560 --> 01:21:28.020 align:middle line:84% Because right now, retrofit potential is going to impact. 01:21:28.020 --> 01:21:33.000 align:middle line:90% 01:21:33.000 --> 01:21:35.240 align:middle line:84% OK, you're looking at the gap and then closing 01:21:35.240 --> 01:21:36.740 align:middle line:90% the gap with the time constant. 01:21:36.740 --> 01:21:41.500 align:middle line:84% So that's kind of similar to Jason's formulation. 01:21:41.500 --> 01:21:45.740 align:middle line:84% But here, for different, what you call vintages, 01:21:45.740 --> 01:21:48.100 align:middle line:84% which are not aging, but that's OK, 01:21:48.100 --> 01:21:54.560 align:middle line:84% you have for different vintages, different potentials. 01:21:54.560 --> 01:22:00.620 align:middle line:84% So that's nice because now you do have that underlying 01:22:00.620 --> 01:22:06.480 align:middle line:84% feature of vintage captured kind of inside these two parameters. 01:22:06.480 --> 01:22:10.020 align:middle line:84% So in the marginal gain and initial possible efficiency 01:22:10.020 --> 01:22:13.980 align:middle line:84% parameters, you have captured how much 01:22:13.980 --> 01:22:19.960 align:middle line:84% energy efficiency is feasible to get for different buildings. 01:22:19.960 --> 01:22:23.220 align:middle line:84% Now we have this confusion about energy efficiency versus energy 01:22:23.220 --> 01:22:26.080 align:middle line:84% consumption that may actually create weird behaviors here. 01:22:26.080 --> 01:22:30.340 align:middle line:90% I haven't thought that through. 01:22:30.340 --> 01:22:31.280 align:middle line:90% OK, good. 01:22:31.280 --> 01:22:32.700 align:middle line:90% Thank you, Anne. 01:22:32.700 --> 01:22:37.780 align:middle line:84% Any questions, comments on this one? 01:22:37.780 --> 01:22:40.390 align:middle line:90% Why don't we now take a break? 01:22:40.390 --> 01:22:43.550 align:middle line:84% I think it's a good time to spend a few minutes 01:22:43.550 --> 01:22:46.110 align:middle line:90% resting and refreshing. 01:22:46.110 --> 01:22:51.525 align:middle line:90% It's dense, looking at models. 01:22:51.525 --> 01:22:58.710 align:middle line:84% So perfect mixing assumption comes basically with everything. 01:22:58.710 --> 01:23:01.150 align:middle line:90% You can't get rid of it. 01:23:01.150 --> 01:23:03.230 align:middle line:90% So it will always be there. 01:23:03.230 --> 01:23:06.750 align:middle line:84% If you need more resolution, that is, 01:23:06.750 --> 01:23:10.910 align:middle line:84% separating whatever you have into categories based 01:23:10.910 --> 01:23:13.490 align:middle line:84% on some feature, you need more stocks. 01:23:13.490 --> 01:23:17.350 align:middle line:84% That is, you need to explicitly separate them. 01:23:17.350 --> 01:23:19.770 align:middle line:90% So there is no avoidance. 01:23:19.770 --> 01:23:21.950 align:middle line:84% Once you have a single stock, you 01:23:21.950 --> 01:23:24.250 align:middle line:84% have the perfect mixing assumption. 01:23:24.250 --> 01:23:27.750 align:middle line:84% Now, in these cases, you may think 01:23:27.750 --> 01:23:30.710 align:middle line:84% that I'm doing something that removes perfect 01:23:30.710 --> 01:23:32.250 align:middle line:90% mixing by doing a fixed delay. 01:23:32.250 --> 01:23:35.210 align:middle line:84% So I have entry and the removal with a fixed delay, 01:23:35.210 --> 01:23:39.450 align:middle line:84% or with the first sixth-order delay or whatever. 01:23:39.450 --> 01:23:42.850 align:middle line:84% That is actually not doing the job 01:23:42.850 --> 01:23:47.290 align:middle line:84% in the way your mind kind of sees, because it creates 01:23:47.290 --> 01:23:50.450 align:middle line:84% six different stocks for a sixth-order delay that 01:23:50.450 --> 01:23:52.150 align:middle line:90% is in the background happening. 01:23:52.150 --> 01:23:55.750 align:middle line:84% So it is doing the disaggregation. 01:23:55.750 --> 01:23:58.530 align:middle line:84% It is just not showing it to you. 01:23:58.530 --> 01:24:02.810 align:middle line:84% But you don't have access to those intermediate stocks 01:24:02.810 --> 01:24:07.130 align:middle line:84% and therefore you can't manipulate them directly. 01:24:07.130 --> 01:24:13.810 align:middle line:84% So that means you cannot fully use the additional complexity 01:24:13.810 --> 01:24:15.530 align:middle line:90% you have introduced. 01:24:15.530 --> 01:24:19.290 align:middle line:84% You cannot really get information from those 01:24:19.290 --> 01:24:24.570 align:middle line:84% intermediate stocks, and that makes it harder to actually do 01:24:24.570 --> 01:24:25.710 align:middle line:90% things consistently. 01:24:25.710 --> 01:24:26.950 align:middle line:90% Now sometimes that is OK. 01:24:26.950 --> 01:24:30.310 align:middle line:84% That's why we do use higher-order delays. 01:24:30.310 --> 01:24:33.090 align:middle line:84% But as soon as you use higher-order delays, usually 01:24:33.090 --> 01:24:37.110 align:middle line:84% the stock that is capturing the sum in the middle, 01:24:37.110 --> 01:24:39.490 align:middle line:84% you can't do other things with it. 01:24:39.490 --> 01:24:45.212 align:middle line:84% You can't add a flow variable to it because you lose control. 01:24:45.212 --> 01:24:46.670 align:middle line:84% You don't have control over what is 01:24:46.670 --> 01:24:50.550 align:middle line:84% happening in the 6 stocks that need to, in parallel, happen 01:24:50.550 --> 01:24:51.370 align:middle line:90% to this. 01:24:51.370 --> 01:24:55.790 align:middle line:84% So that's why it's better to just not do it in most cases. 01:24:55.790 --> 01:25:00.233 align:middle line:84% AUDIENCE: So just be comfortable with that. 01:25:00.233 --> 01:25:01.150 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:25:01.150 --> 01:25:02.370 align:middle line:84% AUDIENCE: Know that it's happening. 01:25:02.370 --> 01:25:03.287 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:25:03.287 --> 01:25:06.910 align:middle line:84% But the bigger kind of the process lesson 01:25:06.910 --> 01:25:12.470 align:middle line:84% is, if you need heterogeneity, you need to disaggregate. 01:25:12.470 --> 01:25:18.510 align:middle line:84% And if you are using higher-order delays going around 01:25:18.510 --> 01:25:22.870 align:middle line:84% the stocks-- that is, you also have the stock that is impacted 01:25:22.870 --> 01:25:27.230 align:middle line:84% by inflow and outflow of that higher-order delay-- 01:25:27.230 --> 01:25:29.930 align:middle line:84% don't manipulate anything else inside that stock. 01:25:29.930 --> 01:25:32.630 align:middle line:84% That is, don't use other flows coming in or out of it, 01:25:32.630 --> 01:25:36.530 align:middle line:84% or otherwise you lose control because now you 01:25:36.530 --> 01:25:41.210 align:middle line:84% have lost your parallelism with the hidden stocks in your delay 01:25:41.210 --> 01:25:42.130 align:middle line:90% function. 01:25:42.130 --> 01:25:44.410 align:middle line:90% Those are the key ideas. 01:25:44.410 --> 01:25:49.910 align:middle line:84% OK, I think we have one more model left and that is Alban's. 01:25:49.910 --> 01:25:51.310 align:middle line:90% So let's bring that up. 01:25:51.310 --> 01:25:54.210 align:middle line:90% 01:25:54.210 --> 01:26:03.050 align:middle line:84% So this one is also doing the subscript-based formulation 01:26:03.050 --> 01:26:08.850 align:middle line:84% for the cohorts or for the vintages. 01:26:08.850 --> 01:26:15.350 align:middle line:84% So this is similar to Hassam's model. 01:26:15.350 --> 01:26:22.250 align:middle line:90% 01:26:22.250 --> 01:26:28.490 align:middle line:84% If you look at the formulation here, for C1, the cohort 1, 01:26:28.490 --> 01:26:31.270 align:middle line:84% the inflow is New Building Construction. 01:26:31.270 --> 01:26:34.620 align:middle line:84% The outflow is Building Aging for C1. 01:26:34.620 --> 01:26:38.840 align:middle line:84% For C2, it is Building Aging for C1 that is increasing it, 01:26:38.840 --> 01:26:42.260 align:middle line:84% Building Aging for C2 that decreases it. 01:26:42.260 --> 01:26:46.880 align:middle line:84% For C3, it is Building Aging C2 minus Building Demolition. 01:26:46.880 --> 01:26:52.540 align:middle line:84% So very similar, and also Alban hasn't done the more general 01:26:52.540 --> 01:26:59.500 align:middle line:84% formulation that would allow him to basically solve 01:26:59.500 --> 01:27:02.680 align:middle line:84% this problem at a scale without adding new equations, 01:27:02.680 --> 01:27:04.920 align:middle line:90% but that's a separate thing. 01:27:04.920 --> 01:27:08.780 align:middle line:84% We can actually probably do that, take a quick look at that 01:27:08.780 --> 01:27:10.700 align:middle line:90% together. 01:27:10.700 --> 01:27:15.480 align:middle line:84% OK, so Building Demolition and Time for Demolition, 01:27:15.480 --> 01:27:19.040 align:middle line:84% et cetera, those are straightforward, I think. 01:27:19.040 --> 01:27:23.780 align:middle line:90% 01:27:23.780 --> 01:27:25.320 align:middle line:84% So that's for just the demolition. 01:27:25.320 --> 01:27:25.820 align:middle line:90% Sorry. 01:27:25.820 --> 01:27:28.080 align:middle line:84% And the Building Aging is aging cohort. 01:27:28.080 --> 01:27:30.980 align:middle line:90% 01:27:30.980 --> 01:27:35.340 align:middle line:84% So this Average Time for Demolition should be 30 years. 01:27:35.340 --> 01:27:38.220 align:middle line:84% So after you got 40, then you have another 30 years to go. 01:27:38.220 --> 01:27:39.540 align:middle line:90% Is that how things are working? 01:27:39.540 --> 01:27:40.120 align:middle line:90% OK. 01:27:40.120 --> 01:27:43.400 align:middle line:84% So this is not the uniform distribution that others had 01:27:43.400 --> 01:27:48.120 align:middle line:84% used, 20-20-20 or something, this is 20-20-30. 01:27:48.120 --> 01:27:49.060 align:middle line:90% And that's OK. 01:27:49.060 --> 01:27:52.400 align:middle line:84% There is nothing wrong with that. 01:27:52.400 --> 01:27:54.380 align:middle line:84% So building aging is straightforward. 01:27:54.380 --> 01:27:57.280 align:middle line:84% Then you have the total energy consumption 01:27:57.280 --> 01:28:00.160 align:middle line:90% for buildings of each age. 01:28:00.160 --> 01:28:04.080 align:middle line:84% You have the average energy intensity of buildings. 01:28:04.080 --> 01:28:10.400 align:middle line:84% So that average energy intensity controls the movement of item. 01:28:10.400 --> 01:28:14.400 align:middle line:84% And then you have the increasing energy consumption that 01:28:14.400 --> 01:28:16.140 align:middle line:90% is coming from new buildings. 01:28:16.140 --> 01:28:19.300 align:middle line:90% This is fine. 01:28:19.300 --> 01:28:20.900 align:middle line:90% And then you have the retrofit. 01:28:20.900 --> 01:28:25.840 align:middle line:84% So this is really the interesting space that we have. 01:28:25.840 --> 01:28:31.820 align:middle line:84% And this is done through comparing indicated total energy 01:28:31.820 --> 01:28:34.860 align:middle line:84% consumption after retrofit versus the current total energy 01:28:34.860 --> 01:28:37.240 align:middle line:84% consumption divided by time constant. 01:28:37.240 --> 01:28:38.980 align:middle line:84% So this is a very similar formulation 01:28:38.980 --> 01:28:43.420 align:middle line:84% to a couple other formulations we saw. 01:28:43.420 --> 01:28:48.100 align:middle line:84% You just look at the total minus indicated divided 01:28:48.100 --> 01:28:54.280 align:middle line:90% by time to finish retrofit. 01:28:54.280 --> 01:28:58.820 align:middle line:84% And this is because it is decreasing, so it is an outflow. 01:28:58.820 --> 01:29:02.440 align:middle line:90% It is the total minus indicated. 01:29:02.440 --> 01:29:07.260 align:middle line:84% If it was an inflow, it would be indicated minus total. 01:29:07.260 --> 01:29:10.500 align:middle line:90% So this is working fine. 01:29:10.500 --> 01:29:12.900 align:middle line:84% Again, with the caveats that we mentioned, 01:29:12.900 --> 01:29:15.180 align:middle line:84% that this kind of time-constant-based 01:29:15.180 --> 01:29:17.460 align:middle line:84% doesn't allow you to think about investment 01:29:17.460 --> 01:29:21.820 align:middle line:84% and allocation and all those things that you may care about. 01:29:21.820 --> 01:29:24.220 align:middle line:84% And then where does the indicated come from? 01:29:24.220 --> 01:29:27.920 align:middle line:84% It is total buildings multiplied by average energy 01:29:27.920 --> 01:29:32.320 align:middle line:84% intensity of buildings that are retrofitted. 01:29:32.320 --> 01:29:34.880 align:middle line:84% And we have this thing that is fraction 01:29:34.880 --> 01:29:36.543 align:middle line:90% of buildings under retrofit. 01:29:36.543 --> 01:29:37.460 align:middle line:90% So let's look at this. 01:29:37.460 --> 01:29:41.360 align:middle line:84% I don't know what's happening inside this. 01:29:41.360 --> 01:29:44.320 align:middle line:90% So you have buildings. 01:29:44.320 --> 01:29:48.560 align:middle line:84% This is just for units, for scaling of the per building 01:29:48.560 --> 01:29:50.560 align:middle line:90% item to everything. 01:29:50.560 --> 01:29:53.280 align:middle line:84% So this part you don't need to worry about. 01:29:53.280 --> 01:29:57.700 align:middle line:84% The next part is what the meat of the equation is. 01:29:57.700 --> 01:30:01.000 align:middle line:84% So fraction of buildings under retrofit multiplied 01:30:01.000 --> 01:30:04.440 align:middle line:84% by average energy intensity of building 01:30:04.440 --> 01:30:11.760 align:middle line:84% retrofitted plus 1 minus fraction 01:30:11.760 --> 01:30:14.080 align:middle line:84% of buildings under retrofit multiplied 01:30:14.080 --> 01:30:19.680 align:middle line:84% by average energy intensity of buildings for this cohort. 01:30:19.680 --> 01:30:22.220 align:middle line:84% So tell us what you are trying to do, Alban, here. 01:30:22.220 --> 01:30:24.060 align:middle line:90% I'm not completely sure. 01:30:24.060 --> 01:30:26.700 align:middle line:84% AUDIENCE: So the fraction of building under the retrofit 01:30:26.700 --> 01:30:29.100 align:middle line:90% is controlled by investment. 01:30:29.100 --> 01:30:31.700 align:middle line:84% So the investment increased the fraction 01:30:31.700 --> 01:30:35.340 align:middle line:90% of building under retrofit. 01:30:35.340 --> 01:30:38.980 align:middle line:84% And then the indicator total energy consumption 01:30:38.980 --> 01:30:44.100 align:middle line:84% is lowest retrofitted multiplied by the energy intensity of those 01:30:44.100 --> 01:30:49.940 align:middle line:84% retrofitted plus those not retrofitted multiplied 01:30:49.940 --> 01:30:53.220 align:middle line:84% by the energy intensity of those not retrofitted. 01:30:53.220 --> 01:30:56.220 align:middle line:84% HAZHIR RAHMANDAD: So at any point in time, 01:30:56.220 --> 01:30:58.540 align:middle line:84% you're saying there is a fraction of buildings 01:30:58.540 --> 01:31:00.700 align:middle line:90% that are being retrofitted. 01:31:00.700 --> 01:31:03.080 align:middle line:90% Is that the idea? 01:31:03.080 --> 01:31:10.580 align:middle line:90% 01:31:10.580 --> 01:31:19.720 align:middle line:84% So if that fraction is small, then everything will be smaller. 01:31:19.720 --> 01:31:25.110 align:middle line:90% 01:31:25.110 --> 01:31:29.030 align:middle line:90% AUDIENCE: If it's zero, then-- 01:31:29.030 --> 01:31:31.590 align:middle line:84% HAZHIR RAHMANDAD: Nothing happening, yes. 01:31:31.590 --> 01:31:36.150 align:middle line:84% And if that fraction is 1, then everybody is moving towards-- 01:31:36.150 --> 01:31:37.670 align:middle line:90% AUDIENCE: The retrofitted. 01:31:37.670 --> 01:31:39.170 align:middle line:84% HAZHIR RAHMANDAD: --the retrofitted. 01:31:39.170 --> 01:31:41.190 align:middle line:84% So this is kind of thinking of retrofitting 01:31:41.190 --> 01:31:43.430 align:middle line:90% as a continuous process. 01:31:43.430 --> 01:31:51.010 align:middle line:84% And at any point in time, you could be retrofitting, 01:31:51.010 --> 01:31:55.590 align:middle line:84% or some subset of buildings could be retrofitting. 01:31:55.590 --> 01:31:57.410 align:middle line:90% And it is a random subset. 01:31:57.410 --> 01:31:58.150 align:middle line:90% AUDIENCE: Right. 01:31:58.150 --> 01:32:01.990 align:middle line:84% HAZHIR RAHMANDAD: So that allows for assuming 01:32:01.990 --> 01:32:03.550 align:middle line:90% that they are the average. 01:32:03.550 --> 01:32:06.190 align:middle line:84% They have the average and they can go down 01:32:06.190 --> 01:32:09.890 align:middle line:90% to the required level. 01:32:09.890 --> 01:32:14.310 align:middle line:90% 01:32:14.310 --> 01:32:20.110 align:middle line:84% Yeah, I think this should work because as you turn it on, 01:32:20.110 --> 01:32:21.970 align:middle line:90% it will drain things. 01:32:21.970 --> 01:32:26.090 align:middle line:84% You turn it off, the average has come down 01:32:26.090 --> 01:32:30.910 align:middle line:84% and there is less room to do, but there is still room to do. 01:32:30.910 --> 01:32:34.450 align:middle line:90% OK, yeah, this looks fine. 01:32:34.450 --> 01:32:37.810 align:middle line:84% And then that gives you flexibility 01:32:37.810 --> 01:32:45.250 align:middle line:84% for investment formulation that determines fraction of buildings 01:32:45.250 --> 01:32:47.650 align:middle line:90% that are under retrofit. 01:32:47.650 --> 01:32:52.290 align:middle line:84% Now, this is a little bit more tricky. 01:32:52.290 --> 01:32:53.670 align:middle line:90% So you have the fraction. 01:32:53.670 --> 01:32:55.550 align:middle line:84% You get a number between 0 and 1. 01:32:55.550 --> 01:32:58.830 align:middle line:84% And you can do a step function or whatever you do. 01:32:58.830 --> 01:33:04.850 align:middle line:90% 01:33:04.850 --> 01:33:08.830 align:middle line:84% And you are saying retrofit cost per square foot. 01:33:08.830 --> 01:33:12.610 align:middle line:90% 01:33:12.610 --> 01:33:14.850 align:middle line:84% How do you make sure this fraction remains 01:33:14.850 --> 01:33:16.510 align:middle line:90% between 0 and 1? 01:33:16.510 --> 01:33:25.310 align:middle line:90% 01:33:25.310 --> 01:33:26.690 align:middle line:90% AUDIENCE: Yeah, I missed it. 01:33:26.690 --> 01:33:29.443 align:middle line:90% Yeah, this is not accurate. 01:33:29.443 --> 01:33:31.110 align:middle line:84% HAZHIR RAHMANDAD: Yeah, it's not obvious 01:33:31.110 --> 01:33:33.050 align:middle line:84% that it would remain between 0 and 1. 01:33:33.050 --> 01:33:38.350 align:middle line:90% 01:33:38.350 --> 01:33:40.970 align:middle line:84% Because that fraction needs to be between 0 and 1. 01:33:40.970 --> 01:33:44.510 align:middle line:84% Now, what is conceptually also tricky 01:33:44.510 --> 01:33:49.830 align:middle line:84% here is that you have a cost for retrofitting 01:33:49.830 --> 01:33:52.950 align:middle line:84% that you're trying to reflect in this parameter, 01:33:52.950 --> 01:33:58.110 align:middle line:84% retrofit per square foot, but you also 01:33:58.110 --> 01:34:07.670 align:middle line:84% have the time to finish retrofit, 01:34:07.670 --> 01:34:11.090 align:middle line:84% which controls how much retrofitting actually happens. 01:34:11.090 --> 01:34:17.150 align:middle line:90% 01:34:17.150 --> 01:34:21.190 align:middle line:84% So if I allocate some amount of investment, 01:34:21.190 --> 01:34:29.250 align:middle line:84% so this is investment in retrofit that I allocate, 01:34:29.250 --> 01:34:35.090 align:middle line:90% how do I know? 01:34:35.090 --> 01:34:42.130 align:middle line:90% 01:34:42.130 --> 01:34:45.050 align:middle line:84% OK, so let's actually run this model because you have a step 01:34:45.050 --> 01:34:45.550 align:middle line:90% function. 01:34:45.550 --> 01:34:52.350 align:middle line:84% So it's possible to see what's happening. 01:34:52.350 --> 01:34:57.590 align:middle line:84% So we can have an investment that goes up. 01:34:57.590 --> 01:35:03.410 align:middle line:90% 01:35:03.410 --> 01:35:07.290 align:middle line:84% So the fraction of buildings goes to 0.2 or something, 01:35:07.290 --> 01:35:09.250 align:middle line:90% I think. 01:35:09.250 --> 01:35:10.170 align:middle line:90% Yeah. 01:35:10.170 --> 01:35:12.650 align:middle line:90% OK, so that's good. 01:35:12.650 --> 01:35:25.190 align:middle line:84% Then, average energy consumption is going down beforehand 01:35:25.190 --> 01:35:29.230 align:middle line:84% because newer buildings are coming in 01:35:29.230 --> 01:35:32.230 align:middle line:90% with lower energy efficiency. 01:35:32.230 --> 01:35:35.710 align:middle line:90% And then retrofits turn on. 01:35:35.710 --> 01:35:45.150 align:middle line:84% And average energy intensity can go down even further. 01:35:45.150 --> 01:36:08.310 align:middle line:84% Max energy efficiency here is, for C1 is 0.2, for C2 it is-- 01:36:08.310 --> 01:36:14.670 align:middle line:84% so we have that same issue that these maxes are now fixed. 01:36:14.670 --> 01:36:17.880 align:middle line:84% Of course, you could, I guess, change them 01:36:17.880 --> 01:36:19.540 align:middle line:90% with the step functions here. 01:36:19.540 --> 01:36:25.040 align:middle line:84% So that is where you would be changing those. 01:36:25.040 --> 01:36:31.800 align:middle line:84% But they are applying to the C1, C2, C3 rather than 01:36:31.800 --> 01:36:33.280 align:middle line:90% the buildings. 01:36:33.280 --> 01:36:37.920 align:middle line:84% So this is kind of where a coflow would 01:36:37.920 --> 01:36:42.320 align:middle line:84% associate these maximums to the underlying buildings 01:36:42.320 --> 01:36:44.920 align:middle line:84% and track them moving with the buildings 01:36:44.920 --> 01:36:47.640 align:middle line:84% as new buildings are added and so on. 01:36:47.640 --> 01:36:50.100 align:middle line:84% Whereas the current formulation fixes them. 01:36:50.100 --> 01:36:56.600 align:middle line:84% So this, you start in year 1900, you 01:36:56.600 --> 01:37:01.320 align:middle line:84% have the same underlying values as you 01:37:01.320 --> 01:37:04.840 align:middle line:84% would have for buildings that are introduced in 2000 01:37:04.840 --> 01:37:05.500 align:middle line:90% and so on. 01:37:05.500 --> 01:37:08.185 align:middle line:84% So that's why this is not the best way to do it, 01:37:08.185 --> 01:37:10.560 align:middle line:84% even though it is good that it is separated for the three 01:37:10.560 --> 01:37:17.580 align:middle line:84% different cohorts and allows you to set them separately, 01:37:17.580 --> 01:37:18.760 align:middle line:90% how far they can go down. 01:37:18.760 --> 01:37:22.300 align:middle line:84% And you have formulations here with investment that similarly 01:37:22.300 --> 01:37:25.100 align:middle line:90% would bring down this. 01:37:25.100 --> 01:37:29.580 align:middle line:84% Now, OK, let's look what is happening here 01:37:29.580 --> 01:37:35.060 align:middle line:84% in energy intensity of buildings. 01:37:35.060 --> 01:37:55.620 align:middle line:84% And so for C1, we had higher or we had lower. 01:37:55.620 --> 01:38:01.340 align:middle line:84% We could get a lot of efficiencies that what C1 has. 01:38:01.340 --> 01:38:04.760 align:middle line:90% C1 has a gain of 2. 01:38:04.760 --> 01:38:07.520 align:middle line:84% So what is this gain doing exactly? 01:38:07.520 --> 01:38:10.420 align:middle line:84% So that's the formulation for average energy intensity 01:38:10.420 --> 01:38:13.680 align:middle line:90% of retrofitted building. 01:38:13.680 --> 01:38:26.960 align:middle line:84% So that formulation is 1 minus this max. 01:38:26.960 --> 01:38:32.946 align:middle line:90% 01:38:32.946 --> 01:38:38.380 align:middle line:84% Ah, so this is actually an interesting formulation. 01:38:38.380 --> 01:38:44.220 align:middle line:84% So who wants to take a stab at critiquing this formulation? 01:38:44.220 --> 01:38:46.640 align:middle line:84% So we have the max energy gain from retrofit. 01:38:46.640 --> 01:38:48.340 align:middle line:84% For now, assume it is a constant. 01:38:48.340 --> 01:38:54.460 align:middle line:84% Right now, it was 0.2 for C1 and 0 for C3, I think. 01:38:54.460 --> 01:38:59.672 align:middle line:90% 01:38:59.672 --> 01:39:02.520 align:middle line:84% And then average energy intensity of buildings 01:39:02.520 --> 01:39:05.840 align:middle line:90% is the average for that cohort. 01:39:05.840 --> 01:39:08.900 align:middle line:84% So what could go wrong with this formulation? 01:39:08.900 --> 01:39:18.420 align:middle line:90% 01:39:18.420 --> 01:39:20.020 align:middle line:90% AUDIENCE: Where is average? 01:39:20.020 --> 01:39:22.328 align:middle line:90% Where is the output variable? 01:39:22.328 --> 01:39:24.120 align:middle line:84% HAZHIR RAHMANDAD: Yeah, let's look at that. 01:39:24.120 --> 01:39:30.060 align:middle line:84% So the average energy intensity of buildings is distinct here. 01:39:30.060 --> 01:39:34.020 align:middle line:84% And then the output of this average energy intensity 01:39:34.020 --> 01:39:35.900 align:middle line:84% of buildings retrofitted is going 01:39:35.900 --> 01:39:38.620 align:middle line:84% to the indicated total energy consumption, 01:39:38.620 --> 01:39:43.500 align:middle line:84% which later brings down the total energy consumption. 01:39:43.500 --> 01:39:46.160 align:middle line:90% So what can go wrong here? 01:39:46.160 --> 01:39:53.660 align:middle line:90% 01:39:53.660 --> 01:39:58.380 align:middle line:84% To see what can go wrong, let's run this simulation a little bit 01:39:58.380 --> 01:39:59.820 align:middle line:90% longer. 01:39:59.820 --> 01:40:02.480 align:middle line:90% So do we have final time here? 01:40:02.480 --> 01:40:06.540 align:middle line:90% 01:40:06.540 --> 01:40:07.160 align:middle line:90% Oh, no. 01:40:07.160 --> 01:40:11.950 align:middle line:90% 01:40:11.950 --> 01:40:13.370 align:middle line:90% OK, let hit stop. 01:40:13.370 --> 01:40:27.990 align:middle line:90% 01:40:27.990 --> 01:40:30.730 align:middle line:84% OK, so we added a little bit of investment. 01:40:30.730 --> 01:40:33.870 align:middle line:84% Actually, quite a bit of investment. 01:40:33.870 --> 01:40:38.910 align:middle line:84% And now rather than going to whatever year we are going, 01:40:38.910 --> 01:40:40.730 align:middle line:90% let's go a little bit longer. 01:40:40.730 --> 01:40:50.510 align:middle line:90% 01:40:50.510 --> 01:40:55.670 align:middle line:84% OK, let's see what is happening here. 01:40:55.670 --> 01:40:58.890 align:middle line:90% Average energy efficiency. 01:40:58.890 --> 01:41:02.710 align:middle line:90% 01:41:02.710 --> 01:41:04.210 align:middle line:90% Oh, sorry. 01:41:04.210 --> 01:41:07.150 align:middle line:90% 01:41:07.150 --> 01:41:09.370 align:middle line:90% So this is 2060. 01:41:09.370 --> 01:41:20.210 align:middle line:84% So let's make this between 2050 and 2100 01:41:20.210 --> 01:41:25.130 align:middle line:84% so that we don't get weird behaviors here. 01:41:25.130 --> 01:41:29.830 align:middle line:84% And now if I increase it to a little bit longer, 01:41:29.830 --> 01:41:31.510 align:middle line:90% let's see what happens. 01:41:31.510 --> 01:41:36.290 align:middle line:90% 01:41:36.290 --> 01:41:46.090 align:middle line:84% Let's actually go further than 2100. 01:41:46.090 --> 01:41:58.250 align:middle line:90% 2200, OK. 01:41:58.250 --> 01:41:59.250 align:middle line:90% AUDIENCE: Negative. 01:41:59.250 --> 01:42:00.770 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:42:00.770 --> 01:42:09.510 align:middle line:84% So total energy consumption is going negative actually 01:42:09.510 --> 01:42:11.345 align:middle line:90% for one of the groups. 01:42:11.345 --> 01:42:12.470 align:middle line:90% AUDIENCE: The first cohort. 01:42:12.470 --> 01:42:14.110 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:42:14.110 --> 01:42:18.010 align:middle line:84% And average energy consumption also going 0 and negative. 01:42:18.010 --> 01:42:20.190 align:middle line:90% So why is this happening? 01:42:20.190 --> 01:42:25.230 align:middle line:84% Well, first of all, why is it going to 0? 01:42:25.230 --> 01:42:31.410 align:middle line:84% Because Alban put a constraint, 10% or 20% improvement. 01:42:31.410 --> 01:42:33.750 align:middle line:84% How is it going 90% improvement and it's still 01:42:33.750 --> 01:42:37.090 align:middle line:90% continuing improving? 01:42:37.090 --> 01:42:38.990 align:middle line:90% AUDIENCE: It's a different time. 01:42:38.990 --> 01:42:41.610 align:middle line:84% 90% of that fraction is being improved. 01:42:41.610 --> 01:42:43.310 align:middle line:90% HAZHIR RAHMANDAD: Yeah, exactly. 01:42:43.310 --> 01:42:49.590 align:middle line:84% So this is the problematic assumption in the formulation 01:42:49.590 --> 01:42:54.310 align:middle line:84% here, is that the average energy intensity of buildings that 01:42:54.310 --> 01:43:00.190 align:middle line:84% are retrofitted is whatever is this max efficiency gain, or 1 01:43:00.190 --> 01:43:03.150 align:middle line:84% minus that max efficiency gain, multiplied 01:43:03.150 --> 01:43:06.250 align:middle line:84% by current average energy efficiency. 01:43:06.250 --> 01:43:09.510 align:middle line:84% So if I brought down average energy efficiency, 01:43:09.510 --> 01:43:11.750 align:middle line:84% let's say, from energy consumption, 01:43:11.750 --> 01:43:16.730 align:middle line:84% let's call it, intensity, from 1, I brought it down to 0.8. 01:43:16.730 --> 01:43:19.690 align:middle line:84% It should stop there, but it doesn't because now 01:43:19.690 --> 01:43:22.470 align:middle line:90% it is 0.8 multiplied by 0.8. 01:43:22.470 --> 01:43:24.370 align:middle line:90% Now it can go 0.64. 01:43:24.370 --> 01:43:27.190 align:middle line:84% And then it is 0.64 multiplied by 0.8. 01:43:27.190 --> 01:43:29.250 align:middle line:90% And it continues to go down. 01:43:29.250 --> 01:43:38.610 align:middle line:84% So that's why this can go down to any number. 01:43:38.610 --> 01:43:41.010 align:middle line:90% Now, that's number one. 01:43:41.010 --> 01:43:45.330 align:middle line:84% The second thing is, why does it go negative? 01:43:45.330 --> 01:43:48.650 align:middle line:84% AUDIENCE: Because of the time step maybe. 01:43:48.650 --> 01:43:50.590 align:middle line:90% It should have been stopped. 01:43:50.590 --> 01:43:53.570 align:middle line:84% HAZHIR RAHMANDAD: Yes, so this process 01:43:53.570 --> 01:43:57.090 align:middle line:90% should have stopped it at 0. 01:43:57.090 --> 01:43:59.530 align:middle line:84% And therefore a little bit surprised why this 01:43:59.530 --> 01:44:04.230 align:middle line:90% is going to negative values. 01:44:04.230 --> 01:44:08.750 align:middle line:84% So for that, I like Ali's suggestion 01:44:08.750 --> 01:44:18.630 align:middle line:84% of looking at the simulation time step. 01:44:18.630 --> 01:44:21.870 align:middle line:90% That could be a culprit. 01:44:21.870 --> 01:44:23.050 align:middle line:90% Looks small enough. 01:44:23.050 --> 01:44:27.830 align:middle line:84% I'm not sure if that would explain it. 01:44:27.830 --> 01:44:30.550 align:middle line:84% AUDIENCE: Isn't the average going below 0? 01:44:30.550 --> 01:44:33.650 align:middle line:84% HAZHIR RAHMANDAD: So the average is going below 0 as well. 01:44:33.650 --> 01:44:35.250 align:middle line:90% So let's look at this. 01:44:35.250 --> 01:44:38.310 align:middle line:90% 01:44:38.310 --> 01:44:42.710 align:middle line:84% You see at the very end, you get negative numbers here. 01:44:42.710 --> 01:44:43.670 align:middle line:90% AUDIENCE: For the blue. 01:44:43.670 --> 01:44:44.730 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:44:44.730 --> 01:44:45.480 align:middle line:90% It doesn't matter. 01:44:45.480 --> 01:44:48.510 align:middle line:84% If you get it for one, there is a problem. 01:44:48.510 --> 01:44:53.550 align:middle line:84% So this should not go negative at any point in time. 01:44:53.550 --> 01:44:54.640 align:middle line:90% The buildings are there. 01:44:54.640 --> 01:44:56.390 align:middle line:84% Let's just make sure the buildings are not 01:44:56.390 --> 01:44:58.030 align:middle line:90% doing something weird. 01:44:58.030 --> 01:45:00.330 align:middle line:84% No, the buildings are in equilibrium, so that's good. 01:45:00.330 --> 01:45:19.760 align:middle line:90% 01:45:19.760 --> 01:45:29.120 align:middle line:84% And then energy consumption is just going out from the stock. 01:45:29.120 --> 01:45:36.440 align:middle line:84% AUDIENCE: It's probably the intensity for the new building. 01:45:36.440 --> 01:45:37.863 align:middle line:90% The red string going down. 01:45:37.863 --> 01:45:39.280 align:middle line:84% HAZHIR RAHMANDAD: Ah, it might be. 01:45:39.280 --> 01:45:40.760 align:middle line:90% It might be. 01:45:40.760 --> 01:45:43.680 align:middle line:84% Yeah, so if the intensity for new buildings 01:45:43.680 --> 01:45:49.800 align:middle line:84% is going to negative values, then we would have that problem. 01:45:49.800 --> 01:45:51.380 align:middle line:90% Yes, so that's the reason. 01:45:51.380 --> 01:45:55.180 align:middle line:84% So that's just the ramp function. 01:45:55.180 --> 01:45:57.640 align:middle line:84% So this is not a formulation issue. 01:45:57.640 --> 01:46:06.700 align:middle line:84% So this is a good summary on this one. 01:46:06.700 --> 01:46:14.140 align:middle line:84% OK, I think, kind of big picture, the formulations 01:46:14.140 --> 01:46:17.260 align:middle line:84% that several of you have for multiple vintages 01:46:17.260 --> 01:46:20.480 align:middle line:84% and capturing the energy consumption, those are good. 01:46:20.480 --> 01:46:24.020 align:middle line:84% That's the basics you want to have. 01:46:24.020 --> 01:46:26.260 align:middle line:84% Everybody is missing kind of the best 01:46:26.260 --> 01:46:30.780 align:middle line:84% way of formulating the underlying potential 01:46:30.780 --> 01:46:36.700 align:middle line:84% for enhancing energy efficiency, which you should 01:46:36.700 --> 01:46:44.180 align:middle line:84% do as a separate coflow, as a separate coflow that tracks what 01:46:44.180 --> 01:46:46.540 align:middle line:90% is the underlying potential. 01:46:46.540 --> 01:46:52.060 align:middle line:84% And that can go up and down with investments in its own sake. 01:46:52.060 --> 01:46:55.180 align:middle line:84% So that would be the cleanest way 01:46:55.180 --> 01:46:59.400 align:middle line:84% to capture all the things that we want to capture. 01:46:59.400 --> 01:47:01.720 align:middle line:84% Then, there are two additional things 01:47:01.720 --> 01:47:04.120 align:middle line:84% that you can do to enhance the model. 01:47:04.120 --> 01:47:08.760 align:middle line:84% One is this way of building the model with subscripts 01:47:08.760 --> 01:47:12.600 align:middle line:84% so that you can add more cohorts or less cohorts, or more or less 01:47:12.600 --> 01:47:14.940 align:middle line:90% vintages without any problem. 01:47:14.940 --> 01:47:19.280 align:middle line:84% I'll show you how to do that in a simple example. 01:47:19.280 --> 01:47:22.760 align:middle line:84% Second is thinking through the allocation 01:47:22.760 --> 01:47:25.840 align:middle line:84% of resources, or whether it is cost effective 01:47:25.840 --> 01:47:30.440 align:middle line:84% to invest in energy efficiency based 01:47:30.440 --> 01:47:36.200 align:middle line:84% on the parameters of the model in a more rational formulation. 01:47:36.200 --> 01:47:38.820 align:middle line:84% That starts to become more challenging. 01:47:38.820 --> 01:47:42.120 align:middle line:84% And that wasn't really part of the problem definition the way 01:47:42.120 --> 01:47:45.180 align:middle line:84% I set it up, but it's a nice challenge. 01:47:45.180 --> 01:47:47.940 align:middle line:90% So those are the two things. 01:47:47.940 --> 01:47:51.140 align:middle line:84% If I get the chance, I may try to do something around those, 01:47:51.140 --> 01:47:55.400 align:middle line:84% but I don't know how much time I will have for that. 01:47:55.400 --> 01:47:57.700 align:middle line:84% Let's do, then, one other thing, and that 01:47:57.700 --> 01:48:08.340 align:middle line:84% is looking at this subscript-based way of doing 01:48:08.340 --> 01:48:10.600 align:middle line:90% cohorts or doing vintages. 01:48:10.600 --> 01:48:11.903 align:middle line:90% AUDIENCE: I have a question. 01:48:11.903 --> 01:48:12.820 align:middle line:90% HAZHIR RAHMANDAD: Yes? 01:48:12.820 --> 01:48:16.920 align:middle line:84% AUDIENCE: Is there a way to rescue Alvin's formulation 01:48:16.920 --> 01:48:17.670 align:middle line:90% with the averages? 01:48:17.670 --> 01:48:19.587 align:middle line:84% HAZHIR RAHMANDAD: Yes, so that's a good point. 01:48:19.587 --> 01:48:20.180 align:middle line:90% Sorry. 01:48:20.180 --> 01:48:21.440 align:middle line:90% Thanks for bringing that up. 01:48:21.440 --> 01:48:23.820 align:middle line:84% So basically, this formulation doesn't 01:48:23.820 --> 01:48:27.620 align:middle line:84% need the effect of this average intensity of buildings. 01:48:27.620 --> 01:48:31.060 align:middle line:84% So to rescue the formulation, the simplest 01:48:31.060 --> 01:48:35.060 align:middle line:84% is to make the average intensity of building 01:48:35.060 --> 01:48:39.580 align:middle line:84% after retrofit a number that is coming from the underlying 01:48:39.580 --> 01:48:40.822 align:middle line:90% technology. 01:48:40.822 --> 01:48:42.280 align:middle line:84% AUDIENCE: And not anchored to that. 01:48:42.280 --> 01:48:46.780 align:middle line:84% HAZHIR RAHMANDAD: Not anchored to the current average energy 01:48:46.780 --> 01:48:47.480 align:middle line:90% intensity. 01:48:47.480 --> 01:48:50.580 align:middle line:84% So that would be a very easy solution. 01:48:50.580 --> 01:48:54.180 align:middle line:84% You just remove that multiplication, basically. 01:48:54.180 --> 01:48:56.530 align:middle line:84% Then, of course, you need to be unit consistent 01:48:56.530 --> 01:48:59.750 align:middle line:84% so the efficiency gain from retrofit cannot be 01:48:59.750 --> 01:49:00.530 align:middle line:90% dimensionless. 01:49:00.530 --> 01:49:04.150 align:middle line:84% It then needs to be the maximum energy efficiency 01:49:04.150 --> 01:49:06.110 align:middle line:84% or kind of minimum energy consumption 01:49:06.110 --> 01:49:09.650 align:middle line:84% feasible for that cohort or something like that, 01:49:09.650 --> 01:49:13.470 align:middle line:84% which is what we want to actually capture in a coflow 01:49:13.470 --> 01:49:14.190 align:middle line:90% explicitly. 01:49:14.190 --> 01:49:18.990 align:middle line:84% That's exactly what you would have in the coflow structure. 01:49:18.990 --> 01:49:22.710 align:middle line:84% Yeah, other questions on this one? 01:49:22.710 --> 01:49:26.670 align:middle line:84% AUDIENCE: I just have a general question on multiple coflows. 01:49:26.670 --> 01:49:28.470 align:middle line:90% HAZHIR RAHMANDAD: Yes? 01:49:28.470 --> 01:49:31.118 align:middle line:84% AUDIENCE: When is a good place to start? 01:49:31.118 --> 01:49:32.410 align:middle line:90% Where is a good place to start? 01:49:32.410 --> 01:49:35.120 align:middle line:84% Because I was working on a model, 01:49:35.120 --> 01:49:38.990 align:middle line:84% which I can't remember how many complex chain, 01:49:38.990 --> 01:49:41.190 align:middle line:90% maybe like 20 or so. 01:49:41.190 --> 01:49:43.630 align:middle line:90% And it was just very bizarre. 01:49:43.630 --> 01:49:46.090 align:middle line:84% HAZHIR RAHMANDAD: So why did you need 20 different? 01:49:46.090 --> 01:49:50.030 align:middle line:84% AUDIENCE: I was working on developing it. 01:49:50.030 --> 01:49:51.270 align:middle line:90% That was exactly my point. 01:49:51.270 --> 01:49:53.470 align:middle line:84% How do you reduce the number of coflows? 01:49:53.470 --> 01:49:55.850 align:middle line:84% Because it would have made the model very dense. 01:49:55.850 --> 01:49:59.933 align:middle line:84% That's grown an aversion to me in multiple coflows. 01:49:59.933 --> 01:50:00.850 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:50:00.850 --> 01:50:03.410 align:middle line:84% So I haven't actually seen anything 01:50:03.410 --> 01:50:05.550 align:middle line:90% with 20 different coflows. 01:50:05.550 --> 01:50:10.310 align:middle line:84% I have a hard time seeing the value of it, 01:50:10.310 --> 01:50:13.050 align:middle line:84% just because it is very hard to keep 01:50:13.050 --> 01:50:16.910 align:middle line:84% track of the interactions in a consistent way. 01:50:16.910 --> 01:50:17.910 align:middle line:90% That's the core issue. 01:50:17.910 --> 01:50:21.290 align:middle line:84% That is, you want to have these dynamic things 01:50:21.290 --> 01:50:24.590 align:middle line:84% if they're adding value for the dynamics of the model. 01:50:24.590 --> 01:50:27.850 align:middle line:84% But if you have 20 features, then the interaction 01:50:27.850 --> 01:50:30.870 align:middle line:84% between these features becomes a big mess. 01:50:30.870 --> 01:50:34.150 align:middle line:84% You can't really track in your mind how things are interacting. 01:50:34.150 --> 01:50:37.970 align:middle line:84% So I would be hesitant to have that many. 01:50:37.970 --> 01:50:41.010 align:middle line:84% AUDIENCE: My understanding from today's discussion 01:50:41.010 --> 01:50:44.050 align:middle line:84% was when you have two different characteristics 01:50:44.050 --> 01:50:47.210 align:middle line:84% of the main chain, which are inherently different, 01:50:47.210 --> 01:50:49.270 align:middle line:84% it makes sense to have multiple coflows. 01:50:49.270 --> 01:50:52.815 align:middle line:84% Then the question is, when is it way too many different tracks? 01:50:52.815 --> 01:50:54.190 align:middle line:84% HAZHIR RAHMANDAD: So it is really 01:50:54.190 --> 01:50:57.030 align:middle line:84% the question is, does it impact the dynamics you really 01:50:57.030 --> 01:50:58.250 align:middle line:90% want to capture? 01:50:58.250 --> 01:51:00.190 align:middle line:84% So in this case, the dynamics we really 01:51:00.190 --> 01:51:02.390 align:middle line:84% want to capture-- the first-order one 01:51:02.390 --> 01:51:04.650 align:middle line:84% is the energy efficiency that has to be there. 01:51:04.650 --> 01:51:06.610 align:middle line:84% It's kind of or energy consumption. 01:51:06.610 --> 01:51:12.590 align:middle line:84% And then the underlying limits or underlying opportunities 01:51:12.590 --> 01:51:13.730 align:middle line:90% is also important. 01:51:13.730 --> 01:51:15.590 align:middle line:84% That is the heart of retrofitting 01:51:15.590 --> 01:51:16.883 align:middle line:90% and how far you can retrofit. 01:51:16.883 --> 01:51:18.050 align:middle line:90% So that's why we include it. 01:51:18.050 --> 01:51:20.910 align:middle line:84% We are not including coflows for the color of buildings 01:51:20.910 --> 01:51:23.407 align:middle line:90% or whatever else. 01:51:23.407 --> 01:51:24.990 align:middle line:84% There are hundreds of other dimensions 01:51:24.990 --> 01:51:26.490 align:middle line:84% you can think about about buildings. 01:51:26.490 --> 01:51:29.870 align:middle line:90% What's the height of buildings? 01:51:29.870 --> 01:51:30.830 align:middle line:90% Yeah. 01:51:30.830 --> 01:51:33.350 align:middle line:84% AUDIENCE: I guess one signal that you would need one more 01:51:33.350 --> 01:51:37.150 align:middle line:84% is, as you're building this and this average thing 01:51:37.150 --> 01:51:40.790 align:middle line:84% that Alban has done, which is attempting to capture 01:51:40.790 --> 01:51:43.190 align:middle line:90% that effect doesn't work. 01:51:43.190 --> 01:51:46.230 align:middle line:84% You might be like, OK, there's some other dynamic attribute 01:51:46.230 --> 01:51:47.410 align:middle line:90% that needs to be tracked. 01:51:47.410 --> 01:51:50.570 align:middle line:90% 01:51:50.570 --> 01:51:52.570 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:51:52.570 --> 01:51:53.470 align:middle line:90% OK. 01:51:53.470 --> 01:51:56.250 align:middle line:90% Any other questions? 01:51:56.250 --> 01:51:58.910 align:middle line:90% Let's then take a look at this. 01:51:58.910 --> 01:52:01.210 align:middle line:84% This is a simple Vensim model that 01:52:01.210 --> 01:52:02.590 align:middle line:90% comes with Vensim installation. 01:52:02.590 --> 01:52:04.550 align:middle line:84% So you can inspect it yourself as well. 01:52:04.550 --> 01:52:09.730 align:middle line:84% But let me remove the subscripts for a second. 01:52:09.730 --> 01:52:16.890 align:middle line:84% So this is an aging chain model, age model, whatever you call it, 01:52:16.890 --> 01:52:22.310 align:middle line:84% that has births and aging, which aging includes death. 01:52:22.310 --> 01:52:25.270 align:middle line:84% That simplifies the formulation for reasons you will see. 01:52:25.270 --> 01:52:29.050 align:middle line:84% So rather than demolition in our previous example, 01:52:29.050 --> 01:52:33.090 align:middle line:84% you could just have aging to include demolition 01:52:33.090 --> 01:52:34.490 align:middle line:90% for the buildings. 01:52:34.490 --> 01:52:38.050 align:middle line:84% Now, let's look at the formulations here. 01:52:38.050 --> 01:52:45.490 align:middle line:84% So it is saying for population, it's 01:52:45.490 --> 01:52:49.830 align:middle line:90% coming on this other screen. 01:52:49.830 --> 01:52:52.430 align:middle line:90% So there are two equations. 01:52:52.430 --> 01:52:56.110 align:middle line:84% For infant group, their rate of change 01:52:56.110 --> 01:52:59.630 align:middle line:90% is birth minus aging of infants. 01:52:59.630 --> 01:53:02.110 align:middle line:90% Very straightforward. 01:53:02.110 --> 01:53:04.550 align:middle line:84% The trick is in the next equation. 01:53:04.550 --> 01:53:07.590 align:middle line:84% So for all but youngest group, which 01:53:07.590 --> 01:53:11.970 align:middle line:84% is a collection of all of the other groups-- 01:53:11.970 --> 01:53:17.550 align:middle line:84% so if you look at the age elements, 01:53:17.550 --> 01:53:21.670 align:middle line:84% it has child, teen, middle, and old as well as infant. 01:53:21.670 --> 01:53:27.710 align:middle line:84% So the model includes a subbranch 01:53:27.710 --> 01:53:33.270 align:middle line:84% which is a subset of the full range called All But Youngest, 01:53:33.270 --> 01:53:35.530 align:middle line:84% which includes child, teen, middle, and old. 01:53:35.530 --> 01:53:37.670 align:middle line:84% And I'll show you how to make that. 01:53:37.670 --> 01:53:40.070 align:middle line:84% It's saying for all of those guys, 01:53:40.070 --> 01:53:43.670 align:middle line:84% the formulation is aging of previous cohort 01:53:43.670 --> 01:53:46.720 align:middle line:90% minus aging of all but youngest. 01:53:46.720 --> 01:53:48.620 align:middle line:84% So now you have another complex thing. 01:53:48.620 --> 01:53:51.000 align:middle line:90% What is this previous cohort? 01:53:51.000 --> 01:53:56.640 align:middle line:84% So the previous cohort is another subrange 01:53:56.640 --> 01:54:01.760 align:middle line:84% consisting of infant, child, teen, and middle. 01:54:01.760 --> 01:54:05.200 align:middle line:84% This is the previous two All But Youngest. 01:54:05.200 --> 01:54:09.000 align:middle line:84% So it takes the previous element. 01:54:09.000 --> 01:54:11.880 align:middle line:84% So now think about what Vensim does. 01:54:11.880 --> 01:54:14.680 align:middle line:84% For every element of All But Youngest, 01:54:14.680 --> 01:54:18.600 align:middle line:84% so it starts with child, it says, OK, 01:54:18.600 --> 01:54:23.720 align:middle line:84% what is the aging of the previous cohort's first element. 01:54:23.720 --> 01:54:26.800 align:middle line:84% The previous cohort's first element is infant. 01:54:26.800 --> 01:54:29.520 align:middle line:84% So it looks at the aging of infant 01:54:29.520 --> 01:54:33.360 align:middle line:84% as the inflow and aging of that first element of All 01:54:33.360 --> 01:54:35.480 align:middle line:90% But Youngest as the outflow. 01:54:35.480 --> 01:54:37.600 align:middle line:84% Then it goes to the next element. 01:54:37.600 --> 01:54:42.800 align:middle line:84% For the teen, it says, what is the second element 01:54:42.800 --> 01:54:45.900 align:middle line:84% of previous cohort, which is child? 01:54:45.900 --> 01:54:49.000 align:middle line:84% And what is the second element of All But Youngest, 01:54:49.000 --> 01:54:50.180 align:middle line:90% which is teen? 01:54:50.180 --> 01:54:52.340 align:middle line:84% Calculates it and third and the fourth 01:54:52.340 --> 01:54:55.020 align:middle line:90% until it ends that subrange. 01:54:55.020 --> 01:54:57.900 align:middle line:84% That's how it calculates everything. 01:54:57.900 --> 01:54:59.520 align:middle line:90% So the logic is simple. 01:54:59.520 --> 01:55:00.900 align:middle line:90% That's all you need to do. 01:55:00.900 --> 01:55:03.900 align:middle line:84% But note that you need two new subranges 01:55:03.900 --> 01:55:09.060 align:middle line:84% to track what is happening and to make these movements. 01:55:09.060 --> 01:55:14.020 align:middle line:84% Now, all of this is fine, except that these subranges also need 01:55:14.020 --> 01:55:18.260 align:middle line:84% additional features for them to work, for Vensim to know 01:55:18.260 --> 01:55:22.460 align:middle line:84% that these two subranges are mapping to into each other, that 01:55:22.460 --> 01:55:24.720 align:middle line:84% is the first element of the first one, 01:55:24.720 --> 01:55:27.020 align:middle line:84% and the first element of the second one 01:55:27.020 --> 01:55:29.960 align:middle line:84% can work with each other in the same equation. 01:55:29.960 --> 01:55:32.860 align:middle line:84% Otherwise, Vensim will give you an error that you are 01:55:32.860 --> 01:55:35.760 align:middle line:90% comparing apples and oranges. 01:55:35.760 --> 01:55:40.400 align:middle line:84% You are trying to mix infants and children, I don't like that. 01:55:40.400 --> 01:55:42.820 align:middle line:84% So you have to instruct Vensim that it 01:55:42.820 --> 01:55:46.560 align:middle line:84% is legitimate to map the first element of this subrange 01:55:46.560 --> 01:55:49.000 align:middle line:84% to the first element of that subrange, and so on. 01:55:49.000 --> 01:55:54.800 align:middle line:84% So then you need to do that within the subscript definition 01:55:54.800 --> 01:55:58.460 align:middle line:84% thingy, which is usually somewhere around here. 01:55:58.460 --> 01:56:05.060 align:middle line:90% 01:56:05.060 --> 01:56:07.082 align:middle line:90% AUDIENCE: It's in the upper row. 01:56:07.082 --> 01:56:08.040 align:middle line:90% HAZHIR RAHMANDAD: Yeah? 01:56:08.040 --> 01:56:10.480 align:middle line:90% AUDIENCE: Yes. 01:56:10.480 --> 01:56:12.760 align:middle line:84% HAZHIR RAHMANDAD: Yes, here it is. 01:56:12.760 --> 01:56:16.700 align:middle line:90% So this is All But Youngest. 01:56:16.700 --> 01:56:19.800 align:middle line:84% You see when you go into this definition, 01:56:19.800 --> 01:56:22.480 align:middle line:84% it highlights these four elements. 01:56:22.480 --> 01:56:24.220 align:middle line:90% This is previous cohort. 01:56:24.220 --> 01:56:26.480 align:middle line:84% It shows the other four elements. 01:56:26.480 --> 01:56:29.880 align:middle line:84% The way you define these is you can 01:56:29.880 --> 01:56:35.800 align:middle line:84% New a subrange or you can Edit subranges. 01:56:35.800 --> 01:56:37.960 align:middle line:84% So I'm going to edit this subrange so that you 01:56:37.960 --> 01:56:40.560 align:middle line:90% can see how it is defined. 01:56:40.560 --> 01:56:45.260 align:middle line:84% So the previous cohort is defined as infant, child, teen, 01:56:45.260 --> 01:56:46.580 align:middle line:90% and middle. 01:56:46.580 --> 01:56:50.380 align:middle line:84% And then this is the critical piece that is not trivial. 01:56:50.380 --> 01:56:52.420 align:middle line:90% You need to do it. 01:56:52.420 --> 01:56:56.420 align:middle line:84% It takes it and says it maps into All But Youngest. 01:56:56.420 --> 01:57:00.300 align:middle line:84% That is, there is a one-to-one mapping from elements of this 01:57:00.300 --> 01:57:02.100 align:middle line:90% to All But Youngest. 01:57:02.100 --> 01:57:06.100 align:middle line:84% And you actually need to do it also for definition of All 01:57:06.100 --> 01:57:07.200 align:middle line:90% But Youngest. 01:57:07.200 --> 01:57:10.640 align:middle line:90% 01:57:10.640 --> 01:57:13.700 align:middle line:84% Oh, actually, it just needs one of them because in one equation 01:57:13.700 --> 01:57:16.440 align:middle line:84% it is using one mapping to the other, 01:57:16.440 --> 01:57:18.460 align:middle line:84% but not the other to the first one. 01:57:18.460 --> 01:57:19.100 align:middle line:90% Kathy? 01:57:19.100 --> 01:57:24.420 align:middle line:84% AUDIENCE: If you're using the previous cohort, 01:57:24.420 --> 01:57:26.220 align:middle line:84% if you're using a separate age that 01:57:26.220 --> 01:57:27.873 align:middle line:84% maps onto another for some reason, 01:57:27.873 --> 01:57:29.540 align:middle line:84% but you're not using it in a way that it 01:57:29.540 --> 01:57:34.595 align:middle line:84% has to map, does that mapping specification mess that up? 01:57:34.595 --> 01:57:36.220 align:middle line:84% HAZHIR RAHMANDAD: So the key to mapping 01:57:36.220 --> 01:57:38.940 align:middle line:84% is that they should have the same number. 01:57:38.940 --> 01:57:40.950 align:middle line:90% Otherwise, it wouldn't work. 01:57:40.950 --> 01:57:43.050 align:middle line:84% I don't know if it gives an error or not. 01:57:43.050 --> 01:57:45.070 align:middle line:90% It probably should. 01:57:45.070 --> 01:57:50.790 align:middle line:84% AUDIENCE: Yeah, I guess If you want to use the mapping 01:57:50.790 --> 01:57:54.750 align:middle line:84% we defined subrange for something 01:57:54.750 --> 01:57:57.790 align:middle line:84% separate for some reason with the fact 01:57:57.790 --> 01:58:00.950 align:middle line:84% that it maps onto something, like cause Vensim 01:58:00.950 --> 01:58:04.128 align:middle line:84% to say that you can't use it in isolation? 01:58:04.128 --> 01:58:05.170 align:middle line:90% HAZHIR RAHMANDAD: No, no. 01:58:05.170 --> 01:58:07.650 align:middle line:90% So mapping doesn't restrict you. 01:58:07.650 --> 01:58:10.010 align:middle line:84% It just gives you options that you can use. 01:58:10.010 --> 01:58:12.290 align:middle line:84% Mapping does not add any restriction. 01:58:12.290 --> 01:58:16.230 align:middle line:84% Now, let's see what this does for you that is valuable. 01:58:16.230 --> 01:58:20.550 align:middle line:84% So let's say rather than five groups of population, 01:58:20.550 --> 01:58:27.030 align:middle line:84% I wanted to have also another group, oldest. 01:58:27.030 --> 01:58:30.687 align:middle line:84% So I can just add in this subrange. 01:58:30.687 --> 01:58:32.770 align:middle line:84% Oh, actually, I shouldn't add it in this subrange. 01:58:32.770 --> 01:58:35.410 align:middle line:84% First, I should add it in the main range. 01:58:35.410 --> 01:58:39.810 align:middle line:84% Otherwise, this gets confused that this subrange includes 01:58:39.810 --> 01:58:41.350 align:middle line:84% elements that are not in the range. 01:58:41.350 --> 01:58:43.370 align:middle line:90% So let me close this. 01:58:43.370 --> 01:58:45.730 align:middle line:90% I would go into the age. 01:58:45.730 --> 01:58:48.310 align:middle line:90% I'll do Edit the range. 01:58:48.310 --> 01:58:50.850 align:middle line:90% 01:58:50.850 --> 01:58:56.050 align:middle line:84% And I'll add the oldest here, then close this. 01:58:56.050 --> 01:59:04.090 align:middle line:84% Then I can go into All But Youngest, edit subrange, 01:59:04.090 --> 01:59:08.210 align:middle line:90% add the oldest. 01:59:08.210 --> 01:59:15.310 align:middle line:84% And then I can go to previous cohort, edit subrange. 01:59:15.310 --> 01:59:18.130 align:middle line:90% 01:59:18.130 --> 01:59:21.650 align:middle line:90% And then what should I add here? 01:59:21.650 --> 01:59:22.618 align:middle line:90% AUDIENCE: Old. 01:59:22.618 --> 01:59:23.910 align:middle line:90% HAZHIR RAHMANDAD: Old, exactly. 01:59:23.910 --> 01:59:28.730 align:middle line:90% 01:59:28.730 --> 01:59:33.110 align:middle line:90% So now the model should be fine. 01:59:33.110 --> 01:59:36.190 align:middle line:84% That is, if we run this model, it just works OK. 01:59:36.190 --> 01:59:38.830 align:middle line:84% Now we have added another element to the cohort. 01:59:38.830 --> 01:59:42.150 align:middle line:90% So that's the basic idea. 01:59:42.150 --> 01:59:45.870 align:middle line:84% Now, you can do this in a much more flexible way 01:59:45.870 --> 01:59:49.390 align:middle line:84% even-- not much more, but more flexible than this even. 01:59:49.390 --> 01:59:51.590 align:middle line:84% And the way to do that would be, I'm 01:59:51.590 --> 01:59:57.110 align:middle line:84% going to create the subscripts here without applying it 01:59:57.110 --> 02:00:01.630 align:middle line:84% to the model so that you just see how to create subscripts 02:00:01.630 --> 02:00:03.790 align:middle line:90% that have this characteristic. 02:00:03.790 --> 02:00:09.990 align:middle line:84% So I'm going to say, I need a new subscript range. 02:00:09.990 --> 02:00:13.550 align:middle line:90% So let's call it test. 02:00:13.550 --> 02:00:23.870 align:middle line:84% And the way I define it is t1 and tlast. 02:00:23.870 --> 02:00:29.874 align:middle line:90% 02:00:29.874 --> 02:00:30.950 align:middle line:90% I'll call it tlastset. 02:00:30.950 --> 02:00:35.330 align:middle line:90% 02:00:35.330 --> 02:00:43.770 align:middle line:84% Or actually, let's do it this way, tmid, tlast. 02:00:43.770 --> 02:00:49.410 align:middle line:90% 02:00:49.410 --> 02:00:54.850 align:middle line:84% OK, so now it seems like it has three elements. 02:00:54.850 --> 02:00:59.210 align:middle line:84% But in reality, I'm going to add a lot more elements. 02:00:59.210 --> 02:01:04.810 align:middle line:84% So then, I'm going to create a new subrange. 02:01:04.810 --> 02:01:06.470 align:middle line:90% So let's look at test. 02:01:06.470 --> 02:01:10.010 align:middle line:84% Right now, test has only three elements. 02:01:10.010 --> 02:01:14.010 align:middle line:84% Now I can go and create a new subrange and call it tmid. 02:01:14.010 --> 02:01:16.970 align:middle line:90% 02:01:16.970 --> 02:01:18.590 align:middle line:90% Oh, it is already defined. 02:01:18.590 --> 02:01:20.230 align:middle line:84% So Vensim doesn't let me do that. 02:01:20.230 --> 02:01:25.750 align:middle line:84% So that means I have to first define tmid then do this. 02:01:25.750 --> 02:01:31.410 align:middle line:84% So that means I need to kill the equation for this range 02:01:31.410 --> 02:01:33.830 align:middle line:90% before I can do that. 02:01:33.830 --> 02:01:34.390 align:middle line:90% Sorry. 02:01:34.390 --> 02:01:50.430 align:middle line:90% 02:01:50.430 --> 02:01:50.930 align:middle line:90% OK. 02:01:50.930 --> 02:01:54.930 align:middle line:84% I can kill it on this screen, so I just delete that variable. 02:01:54.930 --> 02:01:58.430 align:middle line:90% 02:01:58.430 --> 02:02:00.330 align:middle line:90% And, yes. 02:02:00.330 --> 02:02:08.630 align:middle line:90% 02:02:08.630 --> 02:02:10.930 align:middle line:90% Yes, the best software ever. 02:02:10.930 --> 02:02:14.190 align:middle line:90% 02:02:14.190 --> 02:02:18.070 align:middle line:90% And somehow it didn't go away. 02:02:18.070 --> 02:02:20.710 align:middle line:84% I think Vensim is crashing on us. 02:02:20.710 --> 02:02:21.430 align:middle line:90% Oh, no. 02:02:21.430 --> 02:02:25.070 align:middle line:90% 02:02:25.070 --> 02:02:25.570 align:middle line:90% OK. 02:02:25.570 --> 02:02:26.630 align:middle line:90% Now it is removed. 02:02:26.630 --> 02:02:32.700 align:middle line:84% So first we create a new range, call it tmid. 02:02:32.700 --> 02:02:38.680 align:middle line:90% 02:02:38.680 --> 02:02:43.480 align:middle line:90% New Subscript Range, tmid. 02:02:43.480 --> 02:02:47.200 align:middle line:90% 02:02:47.200 --> 02:02:50.060 align:middle line:84% And the equation then comes here. 02:02:50.060 --> 02:02:52.320 align:middle line:84% Let me bring it to the other screen. 02:02:52.320 --> 02:03:00.160 align:middle line:84% So here, I'll just define it as t2 to t10 02:03:00.160 --> 02:03:03.600 align:middle line:84% or whatever you want the range to be. 02:03:03.600 --> 02:03:08.800 align:middle line:84% So now we have tmid that includes t2 to t10. 02:03:08.800 --> 02:03:16.040 align:middle line:84% Now, we define a new range, test. 02:03:16.040 --> 02:03:31.300 align:middle line:90% 02:03:31.300 --> 02:03:37.900 align:middle line:84% It consists of tfirst, tmid, tlast. 02:03:37.900 --> 02:03:41.020 align:middle line:90% 02:03:41.020 --> 02:03:45.860 align:middle line:84% Now you see that tmid thing went away. 02:03:45.860 --> 02:03:51.540 align:middle line:84% It's now incorporated into the test subscript range 02:03:51.540 --> 02:03:54.620 align:middle line:84% because it saw that, OK, it consists 02:03:54.620 --> 02:03:56.420 align:middle line:90% of tmid and other things. 02:03:56.420 --> 02:03:59.580 align:middle line:84% So now it has all of these elements built into it. 02:03:59.580 --> 02:04:02.700 align:middle line:90% Now we can create new subranges. 02:04:02.700 --> 02:04:07.380 align:middle line:84% So we can have a subrange for the first until number 10. 02:04:07.380 --> 02:04:11.180 align:middle line:84% And to do that, we would say tbefore. 02:04:11.180 --> 02:04:14.700 align:middle line:90% 02:04:14.700 --> 02:04:19.500 align:middle line:84% That consists of tfirst and tmid. 02:04:19.500 --> 02:04:23.060 align:middle line:90% 02:04:23.060 --> 02:04:28.200 align:middle line:84% So now tbefore is the first one until the 10th one. 02:04:28.200 --> 02:04:39.380 align:middle line:84% And then you do another one that says tafter, which is tmid, 02:04:39.380 --> 02:04:39.880 align:middle line:90% tlast. 02:04:39.880 --> 02:04:44.320 align:middle line:90% 02:04:44.320 --> 02:04:47.640 align:middle line:90% So tafter is now this subset. 02:04:47.640 --> 02:04:49.180 align:middle line:90% Now you do your mapping. 02:04:49.180 --> 02:04:53.660 align:middle line:84% So you can go into the equation here 02:04:53.660 --> 02:05:01.340 align:middle line:90% and say this maps into tbefore. 02:05:01.340 --> 02:05:01.940 align:middle line:90% Oops, sorry. 02:05:01.940 --> 02:05:05.240 align:middle line:90% 02:05:05.240 --> 02:05:08.680 align:middle line:84% And in fact, you can make the mapping two way 02:05:08.680 --> 02:05:15.560 align:middle line:84% by this sign, which will then take care of both way mappings. 02:05:15.560 --> 02:05:17.560 align:middle line:84% So this takes care of any equation 02:05:17.560 --> 02:05:22.100 align:middle line:84% that uses one for the other or the other for the one. 02:05:22.100 --> 02:05:26.700 align:middle line:84% Oops, maybe it doesn't like this. 02:05:26.700 --> 02:05:28.660 align:middle line:84% OK, so if it is not liking this, then you 02:05:28.660 --> 02:05:31.540 align:middle line:84% need to do the mapping separately. 02:05:31.540 --> 02:05:35.300 align:middle line:84% At some point, it used to be working that way, but that's OK. 02:05:35.300 --> 02:05:39.580 align:middle line:84% So now you can do also the same in the tbefore if you need to. 02:05:39.580 --> 02:05:43.180 align:middle line:84% So all of this mess that we did allows 02:05:43.180 --> 02:05:47.300 align:middle line:84% us to have very efficient editing 02:05:47.300 --> 02:05:51.120 align:middle line:84% of all of these subscripts in one step. 02:05:51.120 --> 02:05:56.060 align:middle line:84% So now I can go to subrange, editing tmid, 02:05:56.060 --> 02:05:58.540 align:middle line:84% and rather than t10, I will say no, I want 02:05:58.540 --> 02:06:01.300 align:middle line:90% to have 100 population groups. 02:06:01.300 --> 02:06:03.660 align:middle line:90% And voila, you have it all. 02:06:03.660 --> 02:06:06.080 align:middle line:84% And everything is internally consistent. 02:06:06.080 --> 02:06:08.540 align:middle line:84% And your model now goes from 10 subscripts 02:06:08.540 --> 02:06:12.780 align:middle line:84% to 100 subscripts with just one small edit. 02:06:12.780 --> 02:06:15.320 align:middle line:84% So this is a useful efficiency thing. 02:06:15.320 --> 02:06:18.420 align:middle line:84% Now, most of your normal models for this class 02:06:18.420 --> 02:06:20.020 align:middle line:90% doesn't need any of this. 02:06:20.020 --> 02:06:22.100 align:middle line:84% I just highlighted it as a capability 02:06:22.100 --> 02:06:27.590 align:middle line:84% you will benefit from for more operational models that 02:06:27.590 --> 02:06:30.270 align:middle line:90% do need detailed complexity. 02:06:30.270 --> 02:06:31.850 align:middle line:90% Any questions on this part? 02:06:31.850 --> 02:06:33.850 align:middle line:84% AUDIENCE: One detail I just want to deconstruct. 02:06:33.850 --> 02:06:40.770 align:middle line:84% When you did the mapping, why was it going into tbefore? 02:06:40.770 --> 02:06:42.430 align:middle line:90% I lost track of what you showed. 02:06:42.430 --> 02:06:43.350 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:06:43.350 --> 02:06:47.470 align:middle line:90% 02:06:47.470 --> 02:06:54.390 align:middle line:84% So for the other equations, in definition of tafter, 02:06:54.390 --> 02:06:56.390 align:middle line:90% I had it go into tbefore. 02:06:56.390 --> 02:06:57.770 align:middle line:90% So what does it mean? 02:06:57.770 --> 02:07:02.270 align:middle line:84% It means that when you are writing equations for tafter, 02:07:02.270 --> 02:07:05.910 align:middle line:84% elements of tafter, or equations that use tafter, 02:07:05.910 --> 02:07:09.190 align:middle line:84% you can use on the right-hand side of the equation, things 02:07:09.190 --> 02:07:12.030 align:middle line:84% that are subscripted with tbefore. 02:07:12.030 --> 02:07:19.350 align:middle line:84% So the bearers or the kind of aging of tbefore 02:07:19.350 --> 02:07:22.070 align:middle line:84% should come into the equation for tafter. 02:07:22.070 --> 02:07:25.010 align:middle line:90% That is why I need that mapping. 02:07:25.010 --> 02:07:27.350 align:middle line:90% So that's the idea. 02:07:27.350 --> 02:07:27.850 align:middle line:90% OK. 02:07:27.850 --> 02:07:30.890 align:middle line:90% 02:07:30.890 --> 02:07:33.890 align:middle line:84% This is really not in conceptual, just Vensim tips 02:07:33.890 --> 02:07:39.410 align:middle line:84% and tricks, but useful for building more complex models. 02:07:39.410 --> 02:07:41.250 align:middle line:90% Let's now switch. 02:07:41.250 --> 02:07:45.190 align:middle line:84% Any questions on the modeling task for this week? 02:07:45.190 --> 02:07:47.930 align:middle line:84% I think we actually haven't quite 02:07:47.930 --> 02:07:49.970 align:middle line:84% gone through showing one that has all 02:07:49.970 --> 02:07:53.170 align:middle line:90% of the characteristics we want. 02:07:53.170 --> 02:07:55.950 align:middle line:84% Again, if I get the chance, I'll try to build one. 02:07:55.950 --> 02:07:59.890 align:middle line:84% But I think we have discussed the core ideas. 02:07:59.890 --> 02:08:03.790 align:middle line:84% Let's then switch to our task for next week. 02:08:03.790 --> 02:08:15.690 align:middle line:90% 02:08:15.690 --> 02:08:22.270 align:middle line:84% OK, so next week in exercise 4, what you are going to build 02:08:22.270 --> 02:08:27.270 align:middle line:84% is a predator-prey model with carrying capacity for the prey. 02:08:27.270 --> 02:08:29.990 align:middle line:84% So think about it as kind of wolf and deer 02:08:29.990 --> 02:08:33.290 align:middle line:84% model or kind of different incarnations of this. 02:08:33.290 --> 02:08:36.950 align:middle line:84% There are different fishes that one is caught by the other one. 02:08:36.950 --> 02:08:39.070 align:middle line:90% There is rabbit and fox example. 02:08:39.070 --> 02:08:42.810 align:middle line:84% You can use your own favorite or unfavorite animal. 02:08:42.810 --> 02:08:47.270 align:middle line:84% But this version, what you want to build 02:08:47.270 --> 02:08:49.730 align:middle line:90% is also including vegetation. 02:08:49.730 --> 02:08:55.710 align:middle line:84% That is, the herbivore is going to need food 02:08:55.710 --> 02:08:58.330 align:middle line:84% for their own sustenance and survival. 02:08:58.330 --> 02:09:01.570 align:middle line:84% It's not that they'll grow infinitely no matter what. 02:09:01.570 --> 02:09:04.030 align:middle line:84% So this is a little bit more complex version 02:09:04.030 --> 02:09:09.390 align:middle line:84% of the traditional predator-prey model. 02:09:09.390 --> 02:09:12.950 align:middle line:84% So let's have a little bit of a conversation 02:09:12.950 --> 02:09:15.890 align:middle line:84% around the key architectural choices for this model 02:09:15.890 --> 02:09:19.350 align:middle line:84% so that we are aligned on that as you get started 02:09:19.350 --> 02:09:21.810 align:middle line:90% working on this for next week. 02:09:21.810 --> 02:09:27.530 align:middle line:84% This is perhaps less complex in terms of the detail complexity 02:09:27.530 --> 02:09:29.530 align:middle line:84% than what we worked on this week, 02:09:29.530 --> 02:09:34.090 align:middle line:84% but it is a dynamically more complex model. 02:09:34.090 --> 02:09:39.610 align:middle line:84% So going through the testing of the performance is really key. 02:09:39.610 --> 02:09:43.970 align:middle line:84% If you don't do the performance tests and understanding 02:09:43.970 --> 02:09:46.650 align:middle line:84% of the model, you are losing a lot of the value 02:09:46.650 --> 02:09:48.770 align:middle line:90% that this model may generate. 02:09:48.770 --> 02:09:51.990 align:middle line:84% Of course, you can go online and find predator-prey models. 02:09:51.990 --> 02:09:54.970 align:middle line:84% This is one of the oldest models in mathematical biology, 02:09:54.970 --> 02:10:00.130 align:middle line:84% going to 1920s, and Lotka and Volterra independently kind 02:10:00.130 --> 02:10:03.970 align:middle line:84% of formulated similar models in the 1920s. 02:10:03.970 --> 02:10:08.330 align:middle line:84% So it's now known as Lotka-Volterra model as well. 02:10:08.330 --> 02:10:10.830 align:middle line:84% Don't go and pick up other people's models. 02:10:10.830 --> 02:10:15.490 align:middle line:84% Just build it from scratch and wrestle with any challenges 02:10:15.490 --> 02:10:16.370 align:middle line:90% that you may see. 02:10:16.370 --> 02:10:22.510 align:middle line:84% With that in mind, let's define a good problem definition. 02:10:22.510 --> 02:10:29.470 align:middle line:84% So how would you see your model as a good model in this case? 02:10:29.470 --> 02:10:33.530 align:middle line:84% Or what's a good problem rather than the model? 02:10:33.530 --> 02:10:35.650 align:middle line:84% We'll talk about the model features later. 02:10:35.650 --> 02:10:48.942 align:middle line:90% 02:10:48.942 --> 02:10:52.710 align:middle line:84% AUDIENCE: We could talk about any challenges 02:10:52.710 --> 02:10:54.790 align:middle line:84% with the population of one type of animal 02:10:54.790 --> 02:10:57.630 align:middle line:84% can be addressed with this model. 02:10:57.630 --> 02:10:58.890 align:middle line:90% We have policymakers. 02:10:58.890 --> 02:11:03.370 align:middle line:84% We have, for example, too many animal crossings with deers. 02:11:03.370 --> 02:11:08.670 align:middle line:90% 02:11:08.670 --> 02:11:11.670 align:middle line:84% HAZHIR RAHMANDAD: Good, so kind of one policy-type 02:11:11.670 --> 02:11:15.650 align:middle line:84% of application is we care about an ecosystem 02:11:15.650 --> 02:11:21.040 align:middle line:84% and its sustainability, its effect on the surrounding 02:11:21.040 --> 02:11:23.280 align:middle line:90% environment. 02:11:23.280 --> 02:11:29.180 align:middle line:84% It might be side effects of animals who may act as pests. 02:11:29.180 --> 02:11:35.480 align:middle line:84% They may eat your crops, they may create accidents, 02:11:35.480 --> 02:11:38.120 align:middle line:84% or they may be threats for your wildlife. 02:11:38.120 --> 02:11:41.120 align:middle line:84% The question is, you need to understand 02:11:41.120 --> 02:11:44.960 align:middle line:84% what this ecosystem is doing before you can intervene 02:11:44.960 --> 02:11:48.580 align:middle line:84% in any meaningful way, because these things are very messy. 02:11:48.580 --> 02:11:53.760 align:middle line:84% You go and kill the predator, the whole ecosystem 02:11:53.760 --> 02:11:57.240 align:middle line:84% may collapse or get into weird dynamics that will create 02:11:57.240 --> 02:11:58.580 align:middle line:90% lots of side effects for you. 02:11:58.580 --> 02:12:01.580 align:middle line:84% So that's the policy space question. 02:12:01.580 --> 02:12:05.320 align:middle line:84% Now, for policy questions like that, 02:12:05.320 --> 02:12:10.080 align:middle line:84% this would probably be too simple a model because usually 02:12:10.080 --> 02:12:13.140 align:middle line:84% you just don't have just two species that are interacting. 02:12:13.140 --> 02:12:17.540 align:middle line:84% So then you need to actually capture the core species 02:12:17.540 --> 02:12:19.240 align:middle line:90% within the whole ecosystem. 02:12:19.240 --> 02:12:24.260 align:middle line:84% And that may end up to be a kind of a predator-prey model 02:12:24.260 --> 02:12:28.500 align:middle line:84% on a steroid, where you have multiple species that 02:12:28.500 --> 02:12:32.640 align:middle line:84% are eating each other or coexisting with each other, 02:12:32.640 --> 02:12:34.460 align:middle line:90% eating the same food. 02:12:34.460 --> 02:12:39.300 align:middle line:84% And so that becomes an extension of this model for the more 02:12:39.300 --> 02:12:41.120 align:middle line:90% serious policy applications. 02:12:41.120 --> 02:12:44.100 align:middle line:90% 02:12:44.100 --> 02:12:51.540 align:middle line:84% What else might be relevant as a problem definition for our case? 02:12:51.540 --> 02:12:53.080 align:middle line:90% The policy one is pretty good. 02:12:53.080 --> 02:12:55.180 align:middle line:84% It's a good guiding one, but also more 02:12:55.180 --> 02:12:59.140 align:middle line:84% complex than what you can handle in the one week time you have. 02:12:59.140 --> 02:13:06.260 align:middle line:90% 02:13:06.260 --> 02:13:09.020 align:middle line:84% AUDIENCE: Build a model for how can we 02:13:09.020 --> 02:13:16.120 align:middle line:84% explain oscillatory patterns of population sizes 02:13:16.120 --> 02:13:19.500 align:middle line:90% that have the same data. 02:13:19.500 --> 02:13:23.160 align:middle line:84% But what relationships give rise to this kind 02:13:23.160 --> 02:13:25.660 align:middle line:90% of repeated cycle of births? 02:13:25.660 --> 02:13:28.380 align:middle line:84% HAZHIR RAHMANDAD: Yeah, that's a good alternative formulation. 02:13:28.380 --> 02:13:32.080 align:middle line:84% So this is more reference-mode-based problem 02:13:32.080 --> 02:13:33.080 align:middle line:90% definition. 02:13:33.080 --> 02:13:35.380 align:middle line:84% There are good examples in the data. 02:13:35.380 --> 02:13:38.160 align:middle line:84% This is actually how, I don't remember whether it 02:13:38.160 --> 02:13:39.562 align:middle line:90% was Lotka or Volterra. 02:13:39.562 --> 02:13:40.520 align:middle line:90% One of them started it. 02:13:40.520 --> 02:13:43.240 align:middle line:84% It was basically the fish populations 02:13:43.240 --> 02:13:46.160 align:middle line:84% in the fisheries in Atlantic Ocean 02:13:46.160 --> 02:13:50.280 align:middle line:84% that they were measuring and seeing these oscillatory modes 02:13:50.280 --> 02:13:51.880 align:middle line:90% over multiple years. 02:13:51.880 --> 02:13:53.600 align:middle line:84% And it was very confusing what is 02:13:53.600 --> 02:13:56.160 align:middle line:84% happening that creates oscillations in the fish 02:13:56.160 --> 02:13:57.280 align:middle line:90% population. 02:13:57.280 --> 02:14:00.820 align:middle line:84% So that was kind of one of the major drivers. 02:14:00.820 --> 02:14:04.920 align:middle line:84% Now, if you focus only on the oscillatory mode of behavior, 02:14:04.920 --> 02:14:06.720 align:middle line:84% the way I'm defining the problem here 02:14:06.720 --> 02:14:09.800 align:middle line:84% to include the carrying capacity for the prey 02:14:09.800 --> 02:14:11.420 align:middle line:90% may not be that relevant. 02:14:11.420 --> 02:14:15.380 align:middle line:84% That is, down the line, you would say, why do I even include 02:14:15.380 --> 02:14:19.020 align:middle line:90% this carrying capacity thingy? 02:14:19.020 --> 02:14:25.580 align:middle line:84% So that, partly in this case, is a problem definition more driven 02:14:25.580 --> 02:14:28.940 align:middle line:84% by mechanisms that could then generate 02:14:28.940 --> 02:14:30.320 align:middle line:90% a few different reference modes. 02:14:30.320 --> 02:14:33.040 align:middle line:84% So oscillations would be one of those reference modes, 02:14:33.040 --> 02:14:35.780 align:middle line:84% but perhaps there would be overshoot and collapse 02:14:35.780 --> 02:14:37.420 align:middle line:90% possibility perhaps. 02:14:37.420 --> 02:14:43.860 align:middle line:84% So it is basically expanding the reference modes 02:14:43.860 --> 02:14:47.380 align:middle line:84% to include things that may come from these mechanisms, 02:14:47.380 --> 02:14:49.620 align:middle line:84% rather than just having a fixed reference mode 02:14:49.620 --> 02:14:52.500 align:middle line:90% that we are trying to replicate. 02:14:52.500 --> 02:14:57.060 align:middle line:84% And that means we are focusing on mechanisms 02:14:57.060 --> 02:15:02.140 align:middle line:84% and capturing them well without adding other mechanisms that 02:15:02.140 --> 02:15:08.860 align:middle line:84% don't directly help with this subset 02:15:08.860 --> 02:15:11.620 align:middle line:84% and seeing what kind of reference modes come out of it. 02:15:11.620 --> 02:15:15.160 align:middle line:84% That becomes a more interesting, relevant exercise 02:15:15.160 --> 02:15:18.680 align:middle line:84% for our purpose than just capturing a single reference 02:15:18.680 --> 02:15:19.600 align:middle line:90% mode. 02:15:19.600 --> 02:15:21.600 align:middle line:84% AUDIENCE: That makes sense to me. 02:15:21.600 --> 02:15:24.960 align:middle line:84% But what I find I struggle with is articulating 02:15:24.960 --> 02:15:28.340 align:middle line:90% that as a problem statement. 02:15:28.340 --> 02:15:31.180 align:middle line:84% So the idea conceptually makes sense to me, 02:15:31.180 --> 02:15:33.520 align:middle line:84% But it's not really good enough to write down 02:15:33.520 --> 02:15:36.072 align:middle line:84% what other patterns of behavior might arise from it. 02:15:36.072 --> 02:15:37.280 align:middle line:90% HAZHIR RAHMANDAD: Absolutely. 02:15:37.280 --> 02:15:40.760 align:middle line:84% So in that memo also I kind of discussed these three types 02:15:40.760 --> 02:15:42.440 align:middle line:90% of problem definitions. 02:15:42.440 --> 02:15:44.520 align:middle line:90% One is reference-mode driven. 02:15:44.520 --> 02:15:47.260 align:middle line:90% One is policy-question driven. 02:15:47.260 --> 02:15:50.340 align:middle line:84% That was closer with what Hassam said. 02:15:50.340 --> 02:15:52.520 align:middle line:84% And the third is mechanism driven. 02:15:52.520 --> 02:15:54.240 align:middle line:84% That is, you have a set of mechanisms. 02:15:54.240 --> 02:15:58.280 align:middle line:84% You want to investigate what comes out of those 02:15:58.280 --> 02:16:00.000 align:middle line:90% and only those mechanisms. 02:16:00.000 --> 02:16:03.500 align:middle line:84% And in this case, we are saying we have two populations. 02:16:03.500 --> 02:16:06.260 align:middle line:84% They interact with each other, one eating the other one. 02:16:06.260 --> 02:16:08.490 align:middle line:90% That's a core mechanism. 02:16:08.490 --> 02:16:10.150 align:middle line:84% They have their deaths and births. 02:16:10.150 --> 02:16:12.670 align:middle line:90% That's kind of implied in this. 02:16:12.670 --> 02:16:16.130 align:middle line:84% If you don't have that, nothing works in this system. 02:16:16.130 --> 02:16:19.490 align:middle line:84% And then the one that is being eaten also 02:16:19.490 --> 02:16:23.090 align:middle line:84% eats some other resource that regenerates itself. 02:16:23.090 --> 02:16:27.170 align:middle line:84% That is grass or trees or shrubs or whatever 02:16:27.170 --> 02:16:33.770 align:middle line:84% it is, the food for the deer in this case example. 02:16:33.770 --> 02:16:37.250 align:middle line:84% So that's the set of mechanisms that are relevant. 02:16:37.250 --> 02:16:40.889 align:middle line:84% Now, how to formulate it in a robust manner? 02:16:40.889 --> 02:16:43.610 align:middle line:90% That's the primary task. 02:16:43.610 --> 02:16:47.610 align:middle line:84% And the second task is exploring what kinds of behaviors 02:16:47.610 --> 02:16:51.930 align:middle line:84% can come out of this combination or these set of mechanisms. 02:16:51.930 --> 02:16:55.650 align:middle line:84% So I think that is the problem definition close enough 02:16:55.650 --> 02:16:57.370 align:middle line:90% for what you need. 02:16:57.370 --> 02:16:59.650 align:middle line:90% What is stocks? 02:16:59.650 --> 02:17:00.389 align:middle line:90% What do we need? 02:17:00.389 --> 02:17:02.129 align:middle line:90% What are the sources of inertia? 02:17:02.129 --> 02:17:05.330 align:middle line:84% And what are good stock variables? 02:17:05.330 --> 02:17:07.309 align:middle line:90% Thoughts on that? 02:17:07.309 --> 02:17:09.950 align:middle line:90% Let's hear from somebody online. 02:17:09.950 --> 02:17:13.870 align:middle line:84% We have been keeping you too quiet. 02:17:13.870 --> 02:17:18.570 align:middle line:84% Anybody wants to take a stab on identifying the stock 02:17:18.570 --> 02:17:21.350 align:middle line:90% variables that are relevant? 02:17:21.350 --> 02:17:22.230 align:middle line:90% AUDIENCE: Predators. 02:17:22.230 --> 02:17:23.980 align:middle line:84% HAZHIR RAHMANDAD: Predators, there you go. 02:17:23.980 --> 02:17:25.350 align:middle line:90% You have one in your hands. 02:17:25.350 --> 02:17:26.790 align:middle line:90% Excellent. 02:17:26.790 --> 02:17:32.469 align:middle line:84% So this was a very good show-and-tell from Jake. 02:17:32.469 --> 02:17:34.990 align:middle line:90% So predators, for sure. 02:17:34.990 --> 02:17:37.330 align:middle line:84% Basically, that's the population that we care about. 02:17:37.330 --> 02:17:40.290 align:middle line:84% Now there is a question in the selection of stocks, 02:17:40.290 --> 02:17:43.549 align:middle line:84% whether we want to put everybody together 02:17:43.549 --> 02:17:47.670 align:middle line:84% as a single stock of predator or perhaps separate them 02:17:47.670 --> 02:17:51.709 align:middle line:90% based on age groups. 02:17:51.709 --> 02:17:56.889 align:middle line:84% I am OK with putting everybody into a single stock. 02:17:56.889 --> 02:18:01.510 align:middle line:84% That's what the traditional Lotka-Volterra does. 02:18:01.510 --> 02:18:04.070 align:middle line:84% Adding age groups may be relevant 02:18:04.070 --> 02:18:07.129 align:middle line:84% because it introduces some additional nuance delays that 02:18:07.129 --> 02:18:10.010 align:middle line:84% may actually contribute to more of the oscillatory mode 02:18:10.010 --> 02:18:11.250 align:middle line:90% of behavior. 02:18:11.250 --> 02:18:17.170 align:middle line:84% So if you have time or interest, feel free to explore that. 02:18:17.170 --> 02:18:22.010 align:middle line:84% But don't go more than two stock variables per species 02:18:22.010 --> 02:18:28.690 align:middle line:84% because you don't need that much resolution in terms of age here. 02:18:28.690 --> 02:18:30.430 align:middle line:90% So that's good. 02:18:30.430 --> 02:18:34.530 align:middle line:84% So for predators, one or maximum two. 02:18:34.530 --> 02:18:38.730 align:middle line:84% Similar thing for prey, that's also all you need. 02:18:38.730 --> 02:18:39.910 align:middle line:90% Anything else? 02:18:39.910 --> 02:18:42.250 align:middle line:90% Any other stocks? 02:18:42.250 --> 02:18:42.770 align:middle line:90% Kathy? 02:18:42.770 --> 02:18:45.889 align:middle line:84% AUDIENCE: I would put something about vegetation in there. 02:18:45.889 --> 02:18:48.629 align:middle line:84% HAZHIR RAHMANDAD: Yeah, something about the vegetation, 02:18:48.629 --> 02:18:52.889 align:middle line:84% the resource capacity, carrying capacity for the prey. 02:18:52.889 --> 02:18:59.209 align:middle line:84% So for that, you could also use a single stock 02:18:59.209 --> 02:19:03.549 align:middle line:84% or consider larger number of stocks, maybe two. 02:19:03.549 --> 02:19:07.790 align:middle line:84% Again, very much depends on what reproduction process 02:19:07.790 --> 02:19:09.990 align:middle line:90% the carrying capacity has. 02:19:09.990 --> 02:19:15.430 align:middle line:84% So for example, if kind of trees were the primary source 02:19:15.430 --> 02:19:20.670 align:middle line:84% of food for the deer, then breaking down into two 02:19:20.670 --> 02:19:21.730 align:middle line:90% would make sense. 02:19:21.730 --> 02:19:25.730 align:middle line:84% Because if you eat the smaller trees, 02:19:25.730 --> 02:19:28.030 align:middle line:84% they wouldn't grow to the age that they 02:19:28.030 --> 02:19:31.049 align:middle line:90% would be fruitful and so on. 02:19:31.049 --> 02:19:35.309 align:middle line:84% And that will have some interesting additional dynamics. 02:19:35.309 --> 02:19:40.309 align:middle line:84% Again, for your use case, feel free to go with one. 02:19:40.309 --> 02:19:42.430 align:middle line:90% Don't go more than two. 02:19:42.430 --> 02:19:47.309 align:middle line:84% And perhaps start with one anyway to keep things simple 02:19:47.309 --> 02:19:48.010 align:middle line:90% for yourself. 02:19:48.010 --> 02:19:53.310 align:middle line:84% And then if you have time and interest, explore having more. 02:19:53.310 --> 02:20:01.680 align:middle line:84% OK, so those are some of the stock conversations. 02:20:01.680 --> 02:20:07.760 align:middle line:84% Let's spend the last few minutes on what 02:20:07.760 --> 02:20:10.400 align:middle line:84% are the good tests for performance and robustness 02:20:10.400 --> 02:20:11.900 align:middle line:90% of the resulting model. 02:20:11.900 --> 02:20:17.200 align:middle line:84% What are the things that should happen in the model? 02:20:17.200 --> 02:20:20.560 align:middle line:84% What are the robustness conditions you can test? 02:20:20.560 --> 02:20:22.680 align:middle line:84% What are the key inputs to change and outputs 02:20:22.680 --> 02:20:29.560 align:middle line:84% to track for those tests to be well specified and useful? 02:20:29.560 --> 02:20:34.100 align:middle line:84% So what are your thoughts on that? 02:20:34.100 --> 02:20:41.460 align:middle line:84% I'm happy to write down your suggestions for tests. 02:20:41.460 --> 02:20:43.830 align:middle line:90% 02:20:43.830 --> 02:20:46.080 align:middle line:84% AUDIENCE: This might be kind of the thing we were just 02:20:46.080 --> 02:20:48.960 align:middle line:84% talking about of, can we actually 02:20:48.960 --> 02:20:53.080 align:middle line:84% create the expected reference mode behaviors we can 02:20:53.080 --> 02:20:55.582 align:middle line:84% by introducing shocks that we think will create them? 02:20:55.582 --> 02:20:56.540 align:middle line:90% HAZHIR RAHMANDAD: Good. 02:20:56.540 --> 02:21:06.900 align:middle line:84% Can we recreate the expected reference modes, e.g. 02:21:06.900 --> 02:21:08.240 align:middle line:90% oscillations? 02:21:08.240 --> 02:21:14.620 align:middle line:90% 02:21:14.620 --> 02:21:15.360 align:middle line:90% What else? 02:21:15.360 --> 02:21:19.100 align:middle line:90% 02:21:19.100 --> 02:21:22.940 align:middle line:84% Actually, thinking about inputs and outputs is also good. 02:21:22.940 --> 02:21:30.500 align:middle line:84% So what inputs would this model potentially take? 02:21:30.500 --> 02:21:33.020 align:middle line:84% AUDIENCE: The reproduction rate of each species. 02:21:33.020 --> 02:21:35.460 align:middle line:84% HAZHIR RAHMANDAD: So you would have various parameters 02:21:35.460 --> 02:21:37.200 align:middle line:90% that are potential inputs. 02:21:37.200 --> 02:21:44.860 align:middle line:90% 02:21:44.860 --> 02:21:46.340 align:middle line:90% AUDIENCE: Initial states. 02:21:46.340 --> 02:21:48.140 align:middle line:84% HAZHIR RAHMANDAD: And initial states, yeah. 02:21:48.140 --> 02:21:55.100 align:middle line:90% 02:21:55.100 --> 02:21:55.760 align:middle line:90% Good. 02:21:55.760 --> 02:21:58.800 align:middle line:90% 02:21:58.800 --> 02:22:01.860 align:middle line:84% So we haven't really introduced much else in this model. 02:22:01.860 --> 02:22:04.000 align:middle line:84% This is a very self-contained model the way 02:22:04.000 --> 02:22:09.160 align:middle line:84% we have conceptualized it so far. 02:22:09.160 --> 02:22:15.440 align:middle line:84% You could consider shocks from, OK, let's go and hunt the deer 02:22:15.440 --> 02:22:18.720 align:middle line:84% or hunt the wolf type of a situation. 02:22:18.720 --> 02:22:25.060 align:middle line:84% So hunting could very much be part of your most policy levers, 02:22:25.060 --> 02:22:28.740 align:middle line:84% but also shocks to the system if you want to consider that. 02:22:28.740 --> 02:22:32.440 align:middle line:84% And it kind of makes it closer to the policy application 02:22:32.440 --> 02:22:33.380 align:middle line:90% questions you have. 02:22:33.380 --> 02:22:42.720 align:middle line:84% So hunting of both species might be useful to consider. 02:22:42.720 --> 02:22:47.080 align:middle line:84% AUDIENCE: In the same line, you have changing land application. 02:22:47.080 --> 02:22:52.920 align:middle line:84% HAZHIR RAHMANDAD: Yes, changing land availability. 02:22:52.920 --> 02:22:55.160 align:middle line:90% Good. 02:22:55.160 --> 02:22:56.860 align:middle line:90% AUDIENCE: What is changing land? 02:22:56.860 --> 02:23:00.420 align:middle line:84% HAZHIR RAHMANDAD: So basically, build houses, cut the trees 02:23:00.420 --> 02:23:02.540 align:middle line:84% and build houses or something like that. 02:23:02.540 --> 02:23:04.827 align:middle line:84% AUDIENCE: Yeah, like environmental encroachment. 02:23:04.827 --> 02:23:06.660 align:middle line:84% HAZHIR RAHMANDAD: Environmental encroachment 02:23:06.660 --> 02:23:12.660 align:middle line:84% would be another relevant shock to the system. 02:23:12.660 --> 02:23:15.980 align:middle line:84% AUDIENCE: Should we also include the area available, 02:23:15.980 --> 02:23:16.980 align:middle line:90% like the size? 02:23:16.980 --> 02:23:19.720 align:middle line:84% HAZHIR RAHMANDAD: So that's a good question. 02:23:19.720 --> 02:23:22.740 align:middle line:84% If you want to try this alternative, 02:23:22.740 --> 02:23:27.260 align:middle line:84% then area becomes another stock variable rather than 02:23:27.260 --> 02:23:30.540 align:middle line:90% a parameter. 02:23:30.540 --> 02:23:33.400 align:middle line:84% Now, you could still deal with it as a parameter, 02:23:33.400 --> 02:23:38.380 align:middle line:84% but it is a messier system to do it as a parameter. 02:23:38.380 --> 02:23:41.260 align:middle line:84% It might be easier to think of it as a stock variable 02:23:41.260 --> 02:23:44.125 align:middle line:84% if you want to go down that road. 02:23:44.125 --> 02:23:45.500 align:middle line:84% AUDIENCE: Similar to hunting, you 02:23:45.500 --> 02:23:49.072 align:middle line:84% could think about disease killing one of the populations. 02:23:49.072 --> 02:23:50.780 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so basically this 02:23:50.780 --> 02:23:55.200 align:middle line:84% would be exogenous shocks that are reducing I think 02:23:55.200 --> 02:23:57.120 align:middle line:90% this is a good set of inputs. 02:23:57.120 --> 02:24:02.600 align:middle line:84% So outputs that you want to track, the obvious one is 02:24:02.600 --> 02:24:18.720 align:middle line:84% the populations of all species and carrying capacity 02:24:18.720 --> 02:24:24.000 align:middle line:84% is a pretty basic important thing. 02:24:24.000 --> 02:24:26.160 align:middle line:84% We don't have very clear policy questions 02:24:26.160 --> 02:24:29.760 align:middle line:84% so we don't need to define more KPIs. 02:24:29.760 --> 02:24:32.360 align:middle line:90% OK. 02:24:32.360 --> 02:24:41.400 align:middle line:84% Now, other robustness tests, tests that you would feel 02:24:41.400 --> 02:24:44.760 align:middle line:90% are worth considering? 02:24:44.760 --> 02:24:47.050 align:middle line:84% AUDIENCE: The extreme conditions of the population, 02:24:47.050 --> 02:24:48.800 align:middle line:84% like if I take out some of the population. 02:24:48.800 --> 02:24:52.420 align:middle line:84% HAZHIR RAHMANDAD: Yes, take out some population. 02:24:52.420 --> 02:25:01.410 align:middle line:90% 02:25:01.410 --> 02:25:03.170 align:middle line:90% Good. 02:25:03.170 --> 02:25:05.610 align:middle line:90% That's a good suggestion. 02:25:05.610 --> 02:25:11.610 align:middle line:84% AUDIENCE: Compliment is expanding one population. 02:25:11.610 --> 02:25:14.930 align:middle line:84% HAZHIR RAHMANDAD: Yeah, perhaps making 02:25:14.930 --> 02:25:18.230 align:middle line:84% carrying capacity not a binding constraint, for example. 02:25:18.230 --> 02:25:24.810 align:middle line:90% 02:25:24.810 --> 02:25:30.690 align:middle line:84% You could also consider adding one of the other species 02:25:30.690 --> 02:25:32.150 align:middle line:84% at the beginning of the simulation. 02:25:32.150 --> 02:25:35.690 align:middle line:84% So that's more playing with the initial states 02:25:35.690 --> 02:25:37.010 align:middle line:90% because that's more continuous. 02:25:37.010 --> 02:25:40.990 align:middle line:84% 0 is a qualitatively different thing for these models. 02:25:40.990 --> 02:25:45.170 align:middle line:90% 02:25:45.170 --> 02:25:46.770 align:middle line:84% AUDIENCE: Just a clarifying question, 02:25:46.770 --> 02:25:50.850 align:middle line:84% are we thinking we might have to figure this out on our own? 02:25:50.850 --> 02:25:56.390 align:middle line:84% Carrying capacity is a stock variable. 02:25:56.390 --> 02:26:01.270 align:middle line:84% HAZHIR RAHMANDAD: So you should decide how it works best. 02:26:01.270 --> 02:26:06.110 align:middle line:84% But conceptually, it is what your deer needs to survive. 02:26:06.110 --> 02:26:10.090 align:middle line:84% So that's what you need to model. 02:26:10.090 --> 02:26:10.590 align:middle line:90% Yeah. 02:26:10.590 --> 02:26:13.310 align:middle line:90% 02:26:13.310 --> 02:26:18.230 align:middle line:84% And the other general point for this model 02:26:18.230 --> 02:26:23.210 align:middle line:84% is, try actually doing it in more than one iteration. 02:26:23.210 --> 02:26:24.790 align:middle line:84% That is, don't try to put everything 02:26:24.790 --> 02:26:28.790 align:middle line:90% in the first iteration. 02:26:28.790 --> 02:26:30.850 align:middle line:84% You could even do it in three iterations. 02:26:30.850 --> 02:26:34.910 align:middle line:84% That is, build the part for deer, just the deer population 02:26:34.910 --> 02:26:41.750 align:middle line:84% in infinite, happy life, and then introduce the wolf, 02:26:41.750 --> 02:26:45.770 align:middle line:84% and have the two-species version without any carrying capacity. 02:26:45.770 --> 02:26:47.150 align:middle line:90% Then, add the carrying capacity. 02:26:47.150 --> 02:26:50.930 align:middle line:84% And at every step, test that your model 02:26:50.930 --> 02:26:52.970 align:middle line:90% does the right things. 02:26:52.970 --> 02:26:55.450 align:middle line:84% Make sure you have inputs and outputs. 02:26:55.450 --> 02:26:58.410 align:middle line:84% If you wanted, you felt more comfortable with jumping 02:26:58.410 --> 02:27:02.010 align:middle line:84% through these, you can build that deer 02:27:02.010 --> 02:27:07.890 align:middle line:84% and wolf at the same time, then add the carrying capacity. 02:27:07.890 --> 02:27:10.055 align:middle line:84% Make sure your models are unit consistent. 02:27:10.055 --> 02:27:12.430 align:middle line:84% Make sure you understand what is happening in your model. 02:27:12.430 --> 02:27:16.490 align:middle line:84% So we will probably do more simulations next time 02:27:16.490 --> 02:27:18.490 align:middle line:90% on this one. 02:27:18.490 --> 02:27:23.190 align:middle line:84% OK, I think this is a good coverage of the key items. 02:27:23.190 --> 02:27:28.410 align:middle line:90% So, go through iterations-- 02:27:28.410 --> 02:27:38.030 align:middle line:84% deer, then add wolf, then add carrying capacity. 02:27:38.030 --> 02:27:41.050 align:middle line:90% 02:27:41.050 --> 02:27:47.130 align:middle line:84% And that recommendation is based on where 02:27:47.130 --> 02:27:49.670 align:middle line:90% you stand modeling-wise. 02:27:49.670 --> 02:27:51.090 align:middle line:84% This is not a very complex model. 02:27:51.090 --> 02:27:53.470 align:middle line:84% So by the end of this course, you 02:27:53.470 --> 02:27:57.030 align:middle line:84% may feel comfortable that, OK, I just bring all of them 02:27:57.030 --> 02:28:00.950 align:middle line:84% together in one round and that's fair as well. 02:28:00.950 --> 02:28:05.310 align:middle line:84% Any questions for this assignment? 02:28:05.310 --> 02:28:09.150 align:middle line:90% AUDIENCE: I have question. 02:28:09.150 --> 02:28:11.430 align:middle line:84% When we talk about carrying capacity, 02:28:11.430 --> 02:28:15.990 align:middle line:84% we are talking about what the deer eats, right? 02:28:15.990 --> 02:28:18.953 align:middle line:90% So vegetables are what they eat. 02:28:18.953 --> 02:28:19.870 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:28:19.870 --> 02:28:20.950 align:middle line:90% Basically, that's it. 02:28:20.950 --> 02:28:24.090 align:middle line:90% 02:28:24.090 --> 02:28:26.790 align:middle line:84% The key thing we are focused on on carrying capacity 02:28:26.790 --> 02:28:28.830 align:middle line:90% is food for the deer. 02:28:28.830 --> 02:28:34.270 align:middle line:84% Now, that food itself is not a fixed amount that 02:28:34.270 --> 02:28:36.550 align:middle line:84% is out there in a form and the deer eat it 02:28:36.550 --> 02:28:39.610 align:middle line:90% and then everybody goes extinct. 02:28:39.610 --> 02:28:44.190 align:middle line:84% But it is a rejuvenating thing on its own. 02:28:44.190 --> 02:28:49.660 align:middle line:84% It can regrow when it is not fully eaten. 02:28:49.660 --> 02:28:54.720 align:middle line:84% So that has dynamics and that requires a stock variable, as we 02:28:54.720 --> 02:28:59.200 align:middle line:84% discussed, and perhaps even two stock variables if you want. 02:28:59.200 --> 02:29:04.247 align:middle line:84% AUDIENCE: Should we submit simulations with our models? 02:29:04.247 --> 02:29:05.580 align:middle line:90% HAZHIR RAHMANDAD: Good question. 02:29:05.580 --> 02:29:10.320 align:middle line:90% 02:29:10.320 --> 02:29:14.700 align:middle line:84% Actually, so let's do it this way. 02:29:14.700 --> 02:29:19.680 align:middle line:84% So analyze one interesting scenario. 02:29:19.680 --> 02:29:23.880 align:middle line:84% And you can pick it from your final model, whatever 02:29:23.880 --> 02:29:26.700 align:middle line:90% is your final model. 02:29:26.700 --> 02:29:29.880 align:middle line:84% Set the parameters so that it creates the scenario you think 02:29:29.880 --> 02:29:30.540 align:middle line:90% is interesting. 02:29:30.540 --> 02:29:33.960 align:middle line:84% It might include oscillations or some other behavior, overshoot 02:29:33.960 --> 02:29:36.820 align:middle line:84% and collapse or something, and analyze it. 02:29:36.820 --> 02:29:40.460 align:middle line:84% And by analyze it, I mean, be able to tell the story, 02:29:40.460 --> 02:29:42.600 align:middle line:84% what structures are generating that behavior 02:29:42.600 --> 02:29:45.900 align:middle line:90% at different points in time. 02:29:45.900 --> 02:29:50.140 align:middle line:90% And come prepared to share that. 02:29:50.140 --> 02:29:54.100 align:middle line:84% If you get a chance to write it down and copy and paste 02:29:54.100 --> 02:29:56.820 align:middle line:90% a few graphs, that's great. 02:29:56.820 --> 02:29:58.160 align:middle line:90% So that would be good. 02:29:58.160 --> 02:30:00.860 align:middle line:90% 02:30:00.860 --> 02:30:11.180 align:middle line:84% Analyze one key behavior out of the model 02:30:11.180 --> 02:30:14.580 align:middle line:90% and fully understand it. 02:30:14.580 --> 02:30:16.660 align:middle line:90% Excellent. 02:30:16.660 --> 02:30:17.680 align:middle line:90% Anything else? 02:30:17.680 --> 02:30:20.500 align:middle line:90% 02:30:20.500 --> 02:30:23.300 align:middle line:90% Online folks? 02:30:23.300 --> 02:30:25.100 align:middle line:90% OK, great. 02:30:25.100 --> 02:30:27.420 align:middle line:90% So enjoy your weekend. 02:30:27.420 --> 02:30:30.120 align:middle line:84% Enjoy, we have something here happening in a few minutes, 02:30:30.120 --> 02:30:32.580 align:middle line:90% I guess, some journal club. 02:30:32.580 --> 02:30:34.580 align:middle line:90% Yep, OK. 02:30:34.580 --> 02:30:37.900 align:middle line:84% Those online, have a good rest of your day or night. 02:30:37.900 --> 02:30:40.490 align:middle line:90% And we'll see you next week. 02:30:40.490 --> 02:30:44.000 align:middle line:90%