15.060 | Fall 2014 | Graduate

# Data, Models, and Decisions

## Lecture Summaries

The table below contains descriptions of each lecture including materials and topics covered in the class. Lecture notes are not available for this course.

LEC # TOPICS LECTURES
1 Decision Analysis I - Kendall Crab & Lobster Case

In this session, we introduce decision trees and the decision tree methodology from an intuitive point of view without any formal theory of probability. This easy-to-grasp model helps students to structure a decision problem, and also helps students see the need for a theory of probability in order to model uncertainty.

In-class discussion of the Kendall Crab and Lobster case. Students prepare the following questions: What are the choices that Jeff Daniels faces? What are the sources of uncertainty in the case? What are the consequences of the various possible outcomes? What course of action would you recommend for Jeff Daniels?

2 Decision Analysis II – Conditional Probabilities

In this class session, we cover the laws of probability, including conditional probability and the arithmetic of conditional probability. We use probability tables instead of a “Bayes’ Theorem” formula in order to keep the concepts as intuitive as possible.

In-class discussion of the “Great Apps of Ann Arbor” case.

3 Discrete Probability Distributions

The next three classes lay the basic groundwork of probability distributions. We will see how data can be characterized as observed values of random variables, and we will study three important probability distributions: the uniform distribution, the binomial distribution, and the Normal distribution.

In this first session, we cover discrete random variables and probability distributions, including the binomial distribution.

4 Continuous Probability Distributions We cover linear functions of a random variable, covariance and correlation of two random variables, and sums of random variables. We show how these concepts lead to important use in finance and in operations. In the second part of this session, we introduce continuous random variables, the probability density function, and the cumulative distribution function. We cover the continuous uniform distribution and the Normal distribution in detail, showing how the Normal distribution arises in models of many management problems.
5 The Normal Distribution In this class we continue our coverage of the Normal distribution. We cover sums of Normally distributed random variables and we then cover the Central Limit Theorem. The Central Limit Theorem points the way to statistical inference.
6 Simulation I – The Gentle Lentil Case

In this session we return to constructing and using models, in this case simulation models based on random number generators. We develop the key ideas of simulation with a prototypical management decision problem that necessitates combining different random variables. We show how simulation models are constructed, used, and analyzed in a management context.

In-class discussion of the Gentle Lentil case.

7 Regression Models I Linear regression is introduced as a method of prediction. We cover all of the basics of simple and multiple linear regressions.
8 Simulation II – The Ontario Gateway Case In-class discussion of the Ontario Gateway case. Students perform the case analysis modeling assignment described at the end of the case and hand in a management memorandum.
9 Regression Models II This class is the second of three sessions on linear regression models. Particular care is taken to ensure that students learn how to evaluate and validate a regression model. We also discuss warnings and issues that arise in using linear regression, and we cover extended regression modeling techniques such as nonlinear transformations and the use of dummy variables.
10 Regression Illustrated

In this class session we present examples of how one goes about constructing, solving, and interpreting regression models.

Students prepare the analyses of two regression mini-cases, “Predicting Heating Oil Consumption at Oilplus” and “Executive Compensation” for in-class discussion.

11 Quiz The 1.5-hour quiz takes place during regular class time. The quiz covers all of the material we have considered so far in the course. The quiz will be closed-book with no notes allowed. Students may use a non-communications-type calculator, but no communications devices (cellphones, graphing calculators) are allowed. We provide a sheet of formulas that are pre-posted on the course website before the quiz.
12 Introduction to Linear Optimization Modeling In this session we will cover the basics of linear optimization, including formulations, key concepts, and graphical solution methods. We develop the basic concepts for constructing, solving, and interpreting the solution of a linear optimization model. We also present instructional material on using linear optimization in a spreadsheet.
13 Solving and Analyzing Linear Optimization Models We will cover computer solution methods for linear optimization, basic sensitivity and economic analysis of a linear optimization model, as well as extensions of linear optimization and applied optimization modeling in general. In addition to standard topics, we also focus on shadow prices and the importance of sensitivity analysis of a linear optimization model as an adjunct to informed decision-making. As an optional topic, we will show how to model uncertainty in linear optimization using two-stage linear optimization under uncertainty.
14 Filatoi Riuniti Case: Production Management In-class discussion of the Filatoi Riuniti case. We will see how to evaluate and interpret the solution output of a linear optimization model and to use this information to enhance informed decision-making.
15 Introduction to Nonlinear Optimization In this class we focus on the extension of the linear optimization model to nonlinear optimization, stressing the key similarities and key differences between linear and nonlinear optimization models. We present instructional material on solving a nonlinear optimization model in a spreadsheet. We also focus on portfolio optimization as an important application of nonlinear optimization modeling in management.
16 Introduction to Discrete Optimization In this class session we show how discrete optimization arises in the modeling of many management problems. We focus on binary optimization, integer optimization, and mixed-integer optimization models. We present instructional material on solving a discrete optimization model in a spreadsheet. We also illustrate how discrete optimization problems are solved, to give students a feel for the potential pros and cons of constructing large-scale discrete optimization models.
17 International Industries Case: Strategic Investment Management In-class discussion of the International Industries case. We will see how to “make sense” out of the solution to a discrete optimization model and use the model to make more informed and more efficient management decisions.
18 Integrative Case on the Financial Crisis In-class discussion of the integrative case on the Financial Crisis, “Money Tree Mortgage in Distress: Evaluating Alternative Funding Options.” We will see how such integrative modeling can clarify and improve understanding and ability to make better management decisions.
19 Dynamic Optimization for Retail Pricing

This session covers dynamic optimization models, whose uses are vast: from power system pricing, to revenue management for airlines, hotels, car rental companies, to retail pricing, and even including military wargame modeling.

We will have an in-class discussion and analysis of the case “Pricing Strategies for Power-Pro’s MBA Laptop Bag” case and we will build and then solve an optimization model for determining optimal retails pricing.

20 Summary and Look Ahead In this last class session, we will present some extensions of the concepts and modeling tools developed in the course. We will also discuss possible follow-on classes at Sloan and elsewhere on campus. Last but not least, we will reserve part of this session to provide guidance as you prepare for the Final Examination.
21 Final Exam Review One or two 3-hour course / exam reviews will take place. We will review the most important aspects of the course.
22 Final Exam The 3-hour final exam will cover the entire content of the course. The exam will be closed-book with no notes allowed. You may bring a calculator with you to the exam. You will also be given three pages of formulas that will be posted on the course website prior to the exam.

## Course Info

Fall 2014
##### Learning Resource Types
Problem Sets
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