Homework Set 1
Due September 19, 2013
The focus of this homework is on linear programming models and methods. You may communicate with your fellow students about the questions in the homework but you must complete
and write up the homework on your own. Th
Homework Set 4
Due December 5, 2013
The focus of this homework is on Markov Chains and Queueing Theory. You may communicate with your fellow students about the questions in the homework but you must complete and
write up the homework on your own. The asso
Homework Set 2
Due October 10, 2013
1. (September 19) You are taking a trip by car to a town you have never visited before. Unfortunately, your cell phone and GPS are out of battery and you broke your laptop, so you
are studying a map to determine the sho
Introduction
Our First OR Problem
ISYE 4600/6610
Introduction to Operations Research and Linear
Programming
Thomas C. Sharkey
August 26, 2013
Sharkey
Introduction
Introduction
Our First OR Problem
Background
Some Applications
1
Introduction
Background
Som
Grey Cells are Unavailable.
Also, if it says `Group Meeting' then someone has already confirmed that spot.
Please provide 3 potential meeting times - in your order of preference. I will try to update this as I fill requests.
These meetings are optional an
1. The consumer price index (1983=100) was 209.44 on January 1, 2008 and 230.22 on Janaury 1, 2013
What was the total inflation rate over that time period and the average annual inflation rate over that period?
2. If the inflation rate is 4.5%, what is th
Demand
Retail Store
Month
January
February
March
April
May
June
July
August
September
October
November
December
Total per Facility
Pittsburgh
Cleveland
200
150
225
250
250
180
180
200
150
150
200
300
2435
Buffalo
100
125
150
200
175
175
200
150
100
100
75
Portfolio Optimization Video Module: Follow-up Questions
In order to receive credit for viewing the advanced video module on the portfolio optimization
problem, it is necessary for you to complete the following questions. You must complete these
questions
n
P_nq
L = customers in system
W = wait time in system
Lq = customers in queue
Wq = wait time in queue
lambda
1/mu
1
0.034
2
0.04
3
0.05
Lower Bound on Lq
9.719
4.8595
7.719
3.8595
2
1
4
0.05
5
6
7
8
9
0.07 0.095 0.145 0.145 0.095
Upper Bound on Lq
9.744
Discussing Steady-State Probabilities
Calculating and Applying Steady-State Probabilities
A Tougher Example to Model
ISYE 4600/6610
Markov Chains: Steady-State Probabilities
Thomas C. Sharkey
November 7, 2014
Sharkey
MC - Steady State Probs
Discussing Ste
A Motivating Example: Planning Your Week
Solution Approaches
Another Application
ISYE 4600/6610
Multi-Objective Optimization: Goal Programming
Thomas C. Sharkey
October 21, 2014
Sharkey
MOO - Goal
A Motivating Example: Planning Your Week
Solution Approach
A Small Example
Mathematical Formulation and Definitions
Computing n-step Transition Probabilities
ISYE 4600/6610
Markov Chains: Introduction and Definitions
Thomas C. Sharkey
November 7, 2014
Sharkey
MC - Introduction
A Small Example
Mathematical Formula
First Passage Times
Probabilities of Absorbtion
ISYE 4600/6610
Markov Chains: First Passage Times and
Absorbtion Probabilities
Thomas C. Sharkey
November 18, 2014
Sharkey
MC - Assorted Analysis
First Passage Times
Probabilities of Absorbtion
A Common Them
Some Motivating Applications
A Framework and Solution Method for MDPs
An Example: Machine Replacement
ISYE 4600/6610
Markov Chains: Markov Decision Processes
Thomas C. Sharkey
November 18, 2014
Sharkey
MC - MDP
Some Motivating Applications
A Framework and
Probability of Max Payoff To Be Indifferent `Utility'
0
1
Neutral
0
0
0
0
0
0
0
0
0
0
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.4
0.5
0.75
1
1
0.8
0.6
U t ili t y
Minimum Payoff (0)
0
50000
100000
150000
200000
250000
300000
400000
500000
750000
1000000
Maximum Pa
Introducing a New Variable
Changing the Objective Function Coecients of Variables
Changing the Right-Hand Side of the Constraints
Other Types of Sensitivity Analysis
ISYE 4600/6610
Linear Programming: Sensitivity Analysis and
Duality, Part 3 - Sensitivity
Sensitivity Analysis
Duality
ISYE 4600/6610
Linear Programming: Introduction to Sensitivity
Analysis and Duality
Thomas C. Sharkey
September 12, 2013
Sharkey
LP - Sensitivity Analysis
Sensitivity Analysis
Duality
1
Sensitivity Analysis
2
Duality
Sharkey
L
Special Considerations and Implications
Conversion Techniques
Considerations for Converted LPs
ISYE 4600/6610
Linear Programming: The Simplex Method Special Considerations and Conversion Techniques
Thomas C. Sharkey
September 9, 2013
Sharkey
Simplex-Consi
Primer: Logic and Denitions
The Simplex Method: An Example
Algorithmic Denitions
ISYE 4600/6610
Linear Programming: The Simplex Method
Thomas C. Sharkey
September 5, 2013
Sharkey
LP - The Simplex Method
Primer: Logic and Denitions
The Simplex Method: An E
Homework Set 3
Due November 14, 2013
The focus of this homework is on integer programming methods, multi-objective optimization,
and decision analysis. You may communicate with your fellow students about the questions in the
homework but you must complete
Linear Programming: List of Denitions and Notation
As an example for many of the denitions, we consider the following linear program.
maximize 3x1 + 2x2
subject to
(Workshop)
2x1 + x2 100
(1)
x1 + x2 80
(2)
x1 40
(3)
x1 , x2 0
(4)
Decision Variables: Mat
Motivating Example: Locating an EMT Station
Solution Method
ISYE 4600/6610
Multi-Objective Optimization: Efficient Solutions
and Frontier
Thomas C. Sharkey
October 24, 2014
Sharkey
MOO - Efficient
Motivating Example: Locating an EMT Station
Solution Metho