IE5545 Decision Analysis
Assignment #1
Spring 2014
Due in class on 02/14/2014
This is an individual assignment. Each student must submit a separate set of the answers.
You may consult with other students in the class, but your answers should reect your
in
STRENLAR
In order to do a good job with the analysis, a number of assumptions must be made. Here is a reasonable set:
$8 million in profits is the present value of all profits to be realized over time.
$35 million in sales is also the present valu
IE5545 Decision Analysis
Assignment #3
Spring 2014
Due in class on 02/28/2014
Solve the following problems from C&R:
1 Problem 9.26
2 Problem 9.29
3 Overbooking Case Study Questions 13 (pp. 411)
4 A comptroller was preparing to analyze the distribution of
Modeling Uncertainty
Theoretical probability distributions
Updating (mixing subjective assessments and data)
Subjective probability encoding
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Common Theoretical Probability Models
Discrete Probability Distributions:
1
Binomial Distribution
2
Poisson
Probability Encoding in Decision Analysis
Sources:
Chapters 8 and 14.
Reading 1: Spetzler, C. S., and Von Holstein, C. S. (1975),
Probability Encoding in Decision Analysis."
Reading 2: Kahneman D., and Tversky, A. (1974) Judgment
under Uncertainty: Heu
IE 5545 Decision Analysis
Class 2: January 29, 2014
Instructor: Professor Diwakar Gupta
Room: ME 130B
Tel: 612-625-1810
Email: [email protected]
1
Recall
DM one who decides
Objectives fundamental and means
Formalism stages, states, actions,
outcomes
Uncertai
IE 5545 Decision Analysis
Stochastic Dominance
1.
2.
Further reading
Shaked, M. and Shanthikumar, J.G. 1994. Stochastic Orders
and their Applications, Academic Press, New York.
Muller, A. and Stoyan, D. 2002. Comparison Methods for
Stochastic Models and R
Value of Informa-on
C & R, Chapter 12
February 26, 2014
Measures of Correctness
P(informant says X will happen | X
happens); X could be one of mul-ple states
Perfect predictor correctly predicts X will
happen w
Problem 9.14 (Page 402)
a) Since E(TA) = 5 years and E(TB) = 10 years, choose B.
b) P(TA 5 | m = 0.2) = e-5(0.2) = 0.368
P(TB 10 | m = 0.1) = e-10(0.1) = 0.368.
For exponential random variables, the probability is
0.368 that the random variable will excee
IE5545 Decision Analysis
Assignment #1
Spring 2015
Due in class on 02/4/2014
This is an individual assignment.
Each student must submit a separate set of the answers. You may consult with other
students in the class, but your answers should reect your i
Dynamic Programming
IE 5455
Spring 2015
Professor: Phil Kim
ISyE, U of Minnesota
References
Markov Decision Processes: Discrete Stochastic
Dynamic Programing, by Martin L. Puterman
A Tutorial on Dynamic Programming Mike Trick
http:/mat.gsia.cmu.edu/classe
Game Theory
IE 5455
Spring 2015
Professor: Phil Kim
ISyE, U of Minnesota
Game ?
When one's payoff is not only a function of his/her
own decision but also a function of other's
decision, the decision problem is called a game.
History of Modern Game Theory
Outline
What do we want in a decision criterion?
Making decisions under ignorance
Making decisions under risk
IE 5545 Decision Analysis
Commonly Used Decision Criteria
January 29, 2014
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Outline
What do we want in a decision criterion?
Making decisio
IE 5545 Decision Analysis
Class 1 Part 2
1
Agenda
What is decision analysis (DA)?
Who uses it?
Will DA replace human decision makers?
Decision Analysis Framework
NPV calculations
2
Decision Analysis is
What you do when you do not know what to do.
A presc
A Probability Primer
Denitions of Terms
Experiment
Outcome
Event
Sample Space
Probability
An activity whose outcome is uncertain
but we know the set of all possible outcomes.
Result of an experiment.
Collection of one or more outcomes.
Collection of all p
IE5545 Decision Analysis
Assignment #2
Spring 2014
Due in class on 02/21/2014
1 Let A, B, C and D denote xed prizes. Suppose you nd yourself indifferent between
A for sure and a lottery that gives B with probability 0.9 and C with probability
0.1. You are
Question 1
Part a:
Neither option dominates the other on the basis of outcome
dominance. Therefore, we try probabilistic dominance. Using Yi to
denote the payo under option i , we have the following CDFs of
the two options.
P (Y1 x )
x
x < 600
0
600 x < 1
IE5545 Decision Analysis
Assignment #1 Solution
Spring 2014
Problem 1. (10 points)
Objectives are, of course, a matter of personal preferences, and so answers will vary
considerably.
a. Here is an objectives hierarchy for the decision context of going out
IE5545 Decision Analysis
Assignment #2 Solution
Spring 2014
Problem 1. (20 points)
Eu( L1 ) = 0.9u( B) + 0.1u(C ) = u( A),
Eu( L2 ) = 0.6u( B) + 0.4u( D ) = u( A).
1) Suppose B
D, show that D
C.
We can argue that because u( B) u( D ), u( A) = 0.6u( B) + 0
Chapter 14 Examples
1. 14.20
2. 14.21
3. 14.28
1/9
Problem 14.20
U (x ) = 1 e x /100 . It is easy to calculate the following
utilities of relevant payoffs.
U (50) = 0.393
U (100) = 0.632
U (150) = 0.777
Next, we calculate expected utilities.
EU (C ) = (1/
IE5545 Decision Analysis
Assignment #3 Solution
Spring 2014
Problem 1. (20 points)
Let X denote return (in percent), M = McDonalds, and S = US Steel. We have prior
probability P( M) = 0.80.
a.
P(6 < X < 18| M ) = PN (6 < X < 18| = 14, = 4)
6 14
18 14
<Z<
Outline Scales of Measurement The Problem Statement Utility Axioms Attitudes Towards Risk Types of Risk Aversion Absolute
IE 5545 Decision Analysis
Modeling Preferences
February 12, 2014
1 / 24
Outline Scales of Measurement The Problem Statement Utility A
University of Minnesota
IE5545 Decision Analysis
Midterm Examination
Instructor: Diwakar Gupta
Duration: 120 minutes
March 13, 2013
Maximum Marks: 70
This examination paper has 5 questions and 2 pages. You are responsible for ensuring
that your copy of th
Mark Connor, purchasing manager of a taco fast food chain, was
contacted by a salesperson for a food service company. The
salesperson claimed that his company had designed a new
container that reduced breakage of tacos during shipment to an
average rate o
Early Bird, Inc.
January 29, 2014
1
Goals
Identify the DM, his or her values and
objectives, and develop a hierarchy
Identify/generate alternatives
Decompose the model the problem
Problem structure
Uncertainty
Preferences
Identify the best alternative
Per
IE 5545 Decision Analysis
Instructor: Professor Diwakar Gupta
Office: ME 130B
Tel: 612-625-1810
Email: [email protected]
1
Administrative Matters
Midterm Exam March 12 during class
Moodle Site (https:/ay13.moodle.umn.edu)
Assignments (6) 30%, Midterm 35%, Fi
Decision Criteria
IE 5455
Spring 2015
Professor: Phil Kim
ISyE, U of Minnesota
Decision Environment
With Certainty
With Uncertainty
Without Probability
Environment in which it is impossible to assess the likelihood
of various possible future events
Wi