MIME 4090, Operations Research II
Syllabus
Fall 2009
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Overview and Objectives: This course will teach you principles for making rational,
defensible decisions under uncertainty. These decisions do not guarantee a good
outcome but they improve the odds of a favorable outcome. You will learn a disciplined,
structured approach for rational decision-making under risk (this is what engineering
design is about). This approach beats intuitive approaches because the latter suffer from
human biases.
Objective probability, which views probability of an outcome as a long-term relative
frequency of an infinitely repeatable experiment is not useful for representing uncertainty
in risky decisions. The course will help you understand how to represent and elicit your
beliefs about the likelihood of uncertain events by subjective probability.
The class will present a scientific method for managing your company’s inventory to
maximize profit and maintain customer goodwill. Finally, the course will teach you how
to make choices when the actions of your competitors or collaborators affect the
outcomes of your choices.
Prerequisites by topic: Calculus, probability and statistics, and optimization
Instructor: Dr. Efstratios Nikolaidis
4035 Nitschke Hall, Phone 530-8216
Email: enikolai@eng.utoledo.edu
Web page: http://www.eng.utoledo.edu/~enikolai
Class time: T,Th 12:30-1:45 PM, Palmer Hall 3180
Office Hours: T, Th 10 AM-12 noon
Required text:
a) Notes on Decision Analysis and subjective probability. Dr. Nikolaidis will develop
these notes as the class progresses and post them on the course web page.
b) Hillier, F. S., and Lieberman, G. J., Introduction to Operation Research, 9th, (8th edition
is OK) McGraw-Hill, 2010
Material:
1. Decision Analysis and Subjective Probability
1.1 Introduction: Engineering and business decisions, examples
Elements of decision problems: Values and objectives, alternative course of
action (Choices or Options), uncertain events, predictive models, probabilities of
outcomes of uncertain events, decision criterion
Single-Step Decisions and Sequential Decisions, planning horizon
Overview of decision analysis process
Requirements for a good decision
1.2 Framing and structuring decisions
Framing
Determine what decisions to make now and what decisions to make later,
Identify the most important objectives to aim for,
Select to what aspects of the decision you should pay attention and what
aspects to ignore,
Determine your options (alternative course of action)
Fundamental vs. Means Objectives
Structuring Elements in a Logical Framework
Tools for Modeling Decisions
Influence Diagrams
Decision Trees
Decision Tables
Software: Tree Plan, Precision Tree
1.3 Modeling Uncertainty by Using Subjective Probability
Why we need subjective probability when making risky decisions
What subjective probability means and how we elicit it
Why subjective probability follows same rules as objective
Procedures for estimating probabilities and probability distributions from
expert judgment
Beware of heuristics and biases
1.4 Solving decision problems
Maximum expect monetary value criterion
Decisions based on existing information
Decisions based on additional information from experimentation
Preposterior analysis, value of additional information
Sensitivity analysis of decision
Sensitivity to problem parameters
Sensitivity to probabilities
1.5 Modeling Preferences
Motivation
Attitude toward risk, risk aversion
Inadequacy of expected monetary value, St. Petersburg or Bernouli
paradox
Max min, maximum likelihood and Max max criteria for making decisions
under uncertainty: critique;
Utility, Axioms of Utility, Elicitation, Paradoxes, Criticisms of Utility
Conflicting Objectives, Multi attribute Utility Models
2. Inventory theory
Introduction
Examples
Components of inventory models
Deterministic continuous review models
3. Game Theory
Concept of a game
Description of a game
Types of games
Example of games
Dominant strategies
Iterative dominance
Solution of two player’s games
Nash equilibrium
Min-max theorem
Exams, homework and grading: There will be approximately eight homework
assignments and a project. You can collaborate in the homework assignments and
projects but copying another student’s homework is unacceptable.
Your grade will be based on the homework (30%), project (20%) and final (50%). This
will be a take-home final.
Computer usage: Some homework problems can be solved efficiently using computer.
You can use any software program you like including FORTRAN, MATLAB, Excel, or
MathCad.
Email and Web page: Homework assignments, design problems, solutions, review
sessions, and exam prospectuses will be posted on the course web page or/and will be
emailed electronically.