WEBVTT 00:00:00.000 --> 00:00:00.968 align:middle line:90% [SQUEAKING] 00:00:00.968 --> 00:00:02.420 align:middle line:90% 00:00:02.420 --> 00:00:03.388 align:middle line:90% [RUSTLING] 00:00:03.388 --> 00:00:04.356 align:middle line:90% 00:00:04.356 --> 00:00:05.324 align:middle line:90% [CLICKING] 00:00:05.324 --> 00:00:13.090 align:middle line:90% 00:00:13.090 --> 00:00:16.610 align:middle line:84% RICHARD DE NEUFVILLE: Now, given that you have a valuation 00:00:16.610 --> 00:00:21.090 align:middle line:84% model, given that you have uncertainties, 00:00:21.090 --> 00:00:25.620 align:middle line:84% you can see what the outcome, the performance of your system 00:00:25.620 --> 00:00:29.080 align:middle line:84% is when there's no flexibility-- simply saying, 00:00:29.080 --> 00:00:36.420 align:middle line:84% OK, if we build this plant and then see what the revenues are, 00:00:36.420 --> 00:00:39.330 align:middle line:84% we can think about, well, our production may 00:00:39.330 --> 00:00:42.960 align:middle line:84% go up and down because of mechanical problems 00:00:42.960 --> 00:00:44.130 align:middle line:90% or whatever. 00:00:44.130 --> 00:00:47.220 align:middle line:84% The demand may go up and down, depending 00:00:47.220 --> 00:00:49.660 align:middle line:90% upon competition or whatever. 00:00:49.660 --> 00:00:53.370 align:middle line:84% And all together, we may have the following results 00:00:53.370 --> 00:00:57.270 align:middle line:90% in terms of benefits and costs. 00:00:57.270 --> 00:01:00.000 align:middle line:84% To do this, you generate a dynamic scenario 00:01:00.000 --> 00:01:03.090 align:middle line:84% and apply it to the model period by period. 00:01:03.090 --> 00:01:05.970 align:middle line:84% That is, the demand starts at one level, 00:01:05.970 --> 00:01:10.030 align:middle line:84% goes up, goes up, goes down, up, down, whatever. 00:01:10.030 --> 00:01:12.390 align:middle line:84% And you do that for all the different demand 00:01:12.390 --> 00:01:16.530 align:middle line:84% possibilities that you simulate, and then you can think about-- 00:01:16.530 --> 00:01:19.900 align:middle line:84% that would also happen in terms of production possibilities. 00:01:19.900 --> 00:01:24.930 align:middle line:84% And for each of those scenarios, combination nation 00:01:24.930 --> 00:01:29.010 align:middle line:84% of the variables, you'll get a performance measure-- 00:01:29.010 --> 00:01:32.800 align:middle line:84% for example, the net present value for that. 00:01:32.800 --> 00:01:36.370 align:middle line:84% You go through the simulation-- we'll go through this process. 00:01:36.370 --> 00:01:40.960 align:middle line:84% 2,000 examples is a standard number a lot of people use. 00:01:40.960 --> 00:01:43.720 align:middle line:84% There's a way of saying-- of determining whether you think 00:01:43.720 --> 00:01:47.800 align:middle line:84% 2,000 is better than 1,000 or better than 10,000, 00:01:47.800 --> 00:01:49.120 align:middle line:90% what's the right balance. 00:01:49.120 --> 00:01:52.450 align:middle line:84% We won't get into that for the moment, but what I'm saying 00:01:52.450 --> 00:01:58.390 align:middle line:84% is that doing 2,000 is a reasonable first order 00:01:58.390 --> 00:02:01.190 align:middle line:84% approximation at least so that you 00:02:01.190 --> 00:02:04.820 align:middle line:84% have 2,000 measures of performance, 00:02:04.820 --> 00:02:07.700 align:middle line:84% such as the present value, and you 00:02:07.700 --> 00:02:10.010 align:middle line:90% can calculate the averages-- 00:02:10.010 --> 00:02:13.340 align:middle line:84% in particular, the ENPV, the expected-- 00:02:13.340 --> 00:02:14.455 align:middle line:90% the average. 00:02:14.455 --> 00:02:15.830 align:middle line:84% And you can then think about what 00:02:15.830 --> 00:02:17.180 align:middle line:90% the extremes are and so on. 00:02:17.180 --> 00:02:18.690 align:middle line:90% You can plot the distribution. 00:02:18.690 --> 00:02:25.330 align:middle line:84% So that's the basic result of a simulation. 00:02:25.330 --> 00:02:31.600 align:middle line:84% Now, it's important to recognize the nature of the product 00:02:31.600 --> 00:02:34.590 align:middle line:90% from a simulation analysis. 00:02:34.590 --> 00:02:39.670 align:middle line:84% A traditional discounted cash flow spreadsheet analysis 00:02:39.670 --> 00:02:44.940 align:middle line:84% to use for net present value is numbers in, numbers out. 00:02:44.940 --> 00:02:49.290 align:middle line:84% You use your best estimate for investment costs, production, 00:02:49.290 --> 00:02:50.940 align:middle line:90% sales, et cetera. 00:02:50.940 --> 00:02:54.550 align:middle line:84% You put the numbers in, you run the machine, you get a number. 00:02:54.550 --> 00:02:57.000 align:middle line:90% The net present value is such. 00:02:57.000 --> 00:03:01.070 align:middle line:84% The return on investment is such. 00:03:01.070 --> 00:03:04.040 align:middle line:84% In a simulation, in uncertainty analysis, 00:03:04.040 --> 00:03:05.270 align:middle line:90% don't put a number in. 00:03:05.270 --> 00:03:08.300 align:middle line:84% You put in a shape, a distribution in 00:03:08.300 --> 00:03:11.470 align:middle line:90% and you get a distribution out. 00:03:11.470 --> 00:03:15.610 align:middle line:84% And the target curve is a generic name 00:03:15.610 --> 00:03:18.550 align:middle line:84% to describe what that distribution is. 00:03:18.550 --> 00:03:21.230 align:middle line:84% Typically, it's either of two shapes. 00:03:21.230 --> 00:03:23.410 align:middle line:84% One is the one I personally prefer-- 00:03:23.410 --> 00:03:25.930 align:middle line:90% but it's a matter of choice-- 00:03:25.930 --> 00:03:28.270 align:middle line:90% is a cumulative distribution. 00:03:28.270 --> 00:03:32.620 align:middle line:84% It shows from-- there may be some chances things are really 00:03:32.620 --> 00:03:36.670 align:middle line:84% bad, more chances that things are better, and et cetera, 00:03:36.670 --> 00:03:39.160 align:middle line:84% It goes on up, a cumulative distribution 00:03:39.160 --> 00:03:41.270 align:middle line:90% to there's nothing-- 00:03:41.270 --> 00:03:45.220 align:middle line:84% it's not likely to be any better than a particular maximum. 00:03:45.220 --> 00:03:48.070 align:middle line:84% But you could also show it as a distribution. 00:03:48.070 --> 00:03:51.970 align:middle line:84% Think of it as a normal shape or something-- 00:03:51.970 --> 00:03:53.680 align:middle line:84% it could be or it could be bimodal, 00:03:53.680 --> 00:03:57.250 align:middle line:84% but a shape of a frequency or the cumulative. 00:03:57.250 --> 00:04:00.230 align:middle line:90% 00:04:00.230 --> 00:04:02.450 align:middle line:84% How do you create the target curve? 00:04:02.450 --> 00:04:07.200 align:middle line:84% Or how does the process create the target curve? 00:04:07.200 --> 00:04:10.450 align:middle line:84% So the simulation produces many files. 00:04:10.450 --> 00:04:13.480 align:middle line:84% Now, the probability of each scenario-- 00:04:13.480 --> 00:04:15.580 align:middle line:84% we've done the simulation correctly, 00:04:15.580 --> 00:04:17.050 align:middle line:90% the way it should be done-- 00:04:17.050 --> 00:04:20.470 align:middle line:84% is that each one is equally probable. 00:04:20.470 --> 00:04:21.459 align:middle line:90% Why? 00:04:21.459 --> 00:04:24.730 align:middle line:84% Because you sample from the underlying distribution 00:04:24.730 --> 00:04:26.860 align:middle line:90% according to probability. 00:04:26.860 --> 00:04:32.100 align:middle line:84% If the high value is 4 times more probable 00:04:32.100 --> 00:04:35.700 align:middle line:84% than the low value, you sample the high value 4 times 00:04:35.700 --> 00:04:43.020 align:middle line:84% and the low value 1 time so that you sampled it from the-- 00:04:43.020 --> 00:04:44.680 align:middle line:90% according to the distribution. 00:04:44.680 --> 00:04:49.200 align:middle line:84% So the consequence is that each of your 2,000 or however many 00:04:49.200 --> 00:04:52.520 align:middle line:84% simulations has the same probability. 00:04:52.520 --> 00:04:55.370 align:middle line:84% Given that, given your 2,000 results, 00:04:55.370 --> 00:04:58.400 align:middle line:84% the way that it proceeded mechanically 00:04:58.400 --> 00:05:00.410 align:middle line:90% is to bend the results. 00:05:00.410 --> 00:05:02.540 align:middle line:84% But as you look at outcome ranges-- 00:05:02.540 --> 00:05:05.450 align:middle line:90% the first 1%, 2%, 3%-- 00:05:05.450 --> 00:05:10.700 align:middle line:84% maybe 100 times, 100 bins, and that-- 00:05:10.700 --> 00:05:12.440 align:middle line:84% so the number of samples in each bin 00:05:12.440 --> 00:05:15.980 align:middle line:84% is that frequency, and that creates a histogram, 00:05:15.980 --> 00:05:17.765 align:middle line:90% if you want. 00:05:17.765 --> 00:05:21.830 align:middle line:84% If you have enough 1's, it is no longer a bar chart, 00:05:21.830 --> 00:05:23.780 align:middle line:90% but it's a distribution. 00:05:23.780 --> 00:05:27.650 align:middle line:84% And that can easily be calculated 00:05:27.650 --> 00:05:29.340 align:middle line:90% into a cumulative distribution. 00:05:29.340 --> 00:05:32.880 align:middle line:84% So this entire process is easily automated. 00:05:32.880 --> 00:05:35.300 align:middle line:84% And the garage case template, which 00:05:35.300 --> 00:05:40.710 align:middle line:84% is a very trivial spreadsheet-- but it does that for you. 00:05:40.710 --> 00:05:43.310 align:middle line:84% So if you wanted to do it yourself, you can do it, 00:05:43.310 --> 00:05:46.050 align:middle line:84% but it's not particularly necessary. 00:05:46.050 --> 00:05:49.310 align:middle line:84% It's all done for you for your projects, if you're using it, 00:05:49.310 --> 00:05:54.800 align:middle line:84% or for after class or later time. 00:05:54.800 --> 00:05:58.960 align:middle line:84% So here is an example of it, that there's 00:05:58.960 --> 00:06:02.830 align:middle line:84% all these individual bins have been put together, 00:06:02.830 --> 00:06:05.650 align:middle line:84% and here is the probability of each, 00:06:05.650 --> 00:06:08.470 align:middle line:84% and here is the cumulative distribution, the target 00:06:08.470 --> 00:06:11.640 align:middle line:90% curve-- a target curve. 00:06:11.640 --> 00:06:18.360 align:middle line:84% By the way, just to make it clear here, so this is the-- 00:06:18.360 --> 00:06:20.730 align:middle line:90% going from 0% to 100%. 00:06:20.730 --> 00:06:23.185 align:middle line:84% So there's nothing worse than this particular number 00:06:23.185 --> 00:06:24.060 align:middle line:90% in your distribution. 00:06:24.060 --> 00:06:25.590 align:middle line:90% That's the lowest one. 00:06:25.590 --> 00:06:27.690 align:middle line:90% This is the highest one, 100%. 00:06:27.690 --> 00:06:32.940 align:middle line:84% And this one, for example, here is that, at the 0 level, 00:06:32.940 --> 00:06:35.850 align:middle line:90% for some reason it's 50%. 00:06:35.850 --> 00:06:37.630 align:middle line:84% But it doesn't have to be that way, 00:06:37.630 --> 00:06:40.510 align:middle line:84% but it is in this particular case. 00:06:40.510 --> 00:06:44.234 align:middle line:84% So this is an example of a cumulative distribution. 00:06:44.234 --> 00:06:47.020 align:middle line:90% 00:06:47.020 --> 00:06:53.090 align:middle line:84% Now, the interesting aspect is, how do you look at flexibility? 00:06:53.090 --> 00:06:56.080 align:middle line:84% So the first question is, of course, well, what flexibility? 00:06:56.080 --> 00:06:58.040 align:middle line:90% What are we talking about? 00:06:58.040 --> 00:07:00.790 align:middle line:84% And the answer to that in general 00:07:00.790 --> 00:07:03.950 align:middle line:90% is the flexibility that is-- 00:07:03.950 --> 00:07:07.420 align:middle line:84% has the most impact regarding the uncertainty Is it high 00:07:07.420 --> 00:07:11.630 align:middle line:84% if you had a really bad case, what would you do about it? 00:07:11.630 --> 00:07:14.920 align:middle line:84% And what kind of flexibility would help you in the-- 00:07:14.920 --> 00:07:17.080 align:middle line:90% would be most impactful? 00:07:17.080 --> 00:07:20.920 align:middle line:84% In the case of the garage case, the uncertainty 00:07:20.920 --> 00:07:23.980 align:middle line:84% is in the demand, so what kind of flexibility 00:07:23.980 --> 00:07:26.590 align:middle line:84% is the capacity meet the demand, so it's a number 00:07:26.590 --> 00:07:28.630 align:middle line:90% of levels in the garage. 00:07:28.630 --> 00:07:31.150 align:middle line:84% In a particular case, you'd have to think 00:07:31.150 --> 00:07:34.030 align:middle line:84% about that for your problem and what kind of flexibility 00:07:34.030 --> 00:07:35.560 align:middle line:90% might be most impactful. 00:07:35.560 --> 00:07:38.320 align:middle line:84% And for those of you who are doing projects, 00:07:38.320 --> 00:07:40.420 align:middle line:90% we'll look at that in detail. 00:07:40.420 --> 00:07:42.320 align:middle line:84% That is one of the questions that you 00:07:42.320 --> 00:07:43.600 align:middle line:90% will want to wrestle with. 00:07:43.600 --> 00:07:46.640 align:middle line:90% 00:07:46.640 --> 00:07:51.100 align:middle line:84% So then the thing is, OK, I have this flexibility, for example, 00:07:51.100 --> 00:07:54.220 align:middle line:84% of building an extra floor on my garage. 00:07:54.220 --> 00:07:56.500 align:middle line:90% When should I exercise it? 00:07:56.500 --> 00:07:57.970 align:middle line:90% Should I do it right away? 00:07:57.970 --> 00:08:00.730 align:middle line:84% Should I do it in anticipation of future demand? 00:08:00.730 --> 00:08:02.620 align:middle line:84% Should I wait until demand is there? 00:08:02.620 --> 00:08:05.610 align:middle line:90% 00:08:05.610 --> 00:08:07.600 align:middle line:90% In simulation, we can't do this. 00:08:07.600 --> 00:08:09.330 align:middle line:84% We don't have a way of calculating 00:08:09.330 --> 00:08:11.830 align:middle line:90% when's the optimal time. 00:08:11.830 --> 00:08:13.570 align:middle line:84% There are some methods for dealing 00:08:13.570 --> 00:08:17.620 align:middle line:84% with that, such as dynamic programming, but it-- 00:08:17.620 --> 00:08:20.290 align:middle line:84% dynamic programming implies there's 00:08:20.290 --> 00:08:24.400 align:middle line:84% nothing you can do about it to affect future aspects. 00:08:24.400 --> 00:08:27.400 align:middle line:84% This is the so-called path independence function. 00:08:27.400 --> 00:08:30.160 align:middle line:84% And the whole point of having flexibility 00:08:30.160 --> 00:08:32.710 align:middle line:84% is precisely that you can do things 00:08:32.710 --> 00:08:41.429 align:middle line:84% so that that powerful method does not work for us. 00:08:41.429 --> 00:08:43.020 align:middle line:90% And there's so many paths. 00:08:43.020 --> 00:08:46.080 align:middle line:84% If we think about 2,000 samples of what may happen, 00:08:46.080 --> 00:08:48.240 align:middle line:84% that's only 2,000 samples of what 00:08:48.240 --> 00:08:51.000 align:middle line:84% may be a million possibility of paths 00:08:51.000 --> 00:08:53.520 align:middle line:84% as a combination of the different probabilities 00:08:53.520 --> 00:08:58.140 align:middle line:84% at different times of prices, and quantities, and so forth. 00:08:58.140 --> 00:09:01.060 align:middle line:84% It's much too large to be searched. 00:09:01.060 --> 00:09:06.770 align:middle line:84% So the procedure is to define what we know as decision rules. 00:09:06.770 --> 00:09:12.403 align:middle line:90%