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
Note that I have modified some of these problems to better reflect the focus of how we
covered material. There are also problems in italics that we wouldnt have on the final (we
either covered them on the midterm or approached the material differently)
IS
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
Lecture 16. Queuing Theory
Introduction & Littles Law
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Review of Markov Decision Processes
An MDP has four components:
1. A set o
Lecture 18. Queuing Theory Birth
and Death Processes
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
We will use an exponential distribution to model the
interarrival tim
Lecture 13. Markov Chains
Steady-State Probabilities
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
A stochastic process is a collection of random variables indexed
on t
Lecture 08. Network Optimization
Shortest Path Problems
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
The field of Network Optimization concerns optimization problems o
Lecture 17. Queuing Theory
Exponential Distributions
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
Queuing theory is the study of waiting lines.
To model an applicatio
Final Exam Review
ISYE 4600/6610 OPERATIONS RESEARCH
METHOD
SYSTEMS MODELING IN DSES
Jennifer Pazour, Ph.D.
1
ISYE 4600/6610 1 OPERATIONS
RESEARCH METHOD/SYSTEMS
MODELING IN DSES
Wed. May 10, 3-6pm Sage 3704
2
Exam Format
Open Book
Closed notes
You are
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
Homework 4 on Markov Chains (100 Points)
ISYE 4600/ISYE 6610
This homework covers the lecture materials on Markov Chains, which is chapter 17, and Markov
Decision Processes, which is chapter 19, in the Winston text.
Below you will find the homework questi
Homework 3 on Integer Programming (100 Points)
ISYE 4600/ISYE 6610, Jennifer Pazour, Ph.D.
This homework covers the lecture materials on Integer Programming, which is
chapter 9 in the Winston text.
Below you will find the homework questions for this assig
Homework 1 on Linear Programming (100 Points)
ISYE 4600/ISYE 6610, Jennifer Pazour, Ph.D.
This homework covers the lecture materials on Linear Programming. This material
is found in Chapters 3-6 in the Winston text.
Below you will find the homework questi
Homework 5 on Queuing (100 Points)
ISYE 4600/ISYE 6610
This homework covers the lecture materials on Queuing Theory, which is chapter 20 in the Winston.
You may discuss the assignment with other student, but each student must complete and turn in an
assig
Homework 2 on Linear Programming (100 Points)
ISYE 4600/ISYE 6610, Jennifer Pazour, Ph.D.
This homework covers the lecture materials on Linear Programming Sensitivity
Analysis and Duality (from Hwk1), and Network Optimization. Network optimization
is in C
Lecture 20. Queuing Theory
Cost Analysis
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture
M/M/s queue has exponential interarrivals
and service times, and s parallel servers.
W
Computer Software to Solve
Optimization Models
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision
Sciences
Jennifer Pazour, Ph.D.
ISYE 4600 Operations Research Method Pazour
1
Computer Solution of LPs
You are welcome to use an
Lecture 13. Markov Chains
Steady-State Probabilities
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
A stochastic process is a collection of random variables indexed
on t
Lecture 14. Markov Chains
First Passage Times and Absorbtion Probabilities
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
Ifa Markov Chain is irreducible (i.e., all stat
Lecture 06. Linear Programming
Sensitivity Analysis and Duality
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Recap from Last Lecture:
SIMPLEX method starts at a basic feasible solution (a
Lecture 11. Integer Programming
Solution Approaches
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap: Formulating Integer
Programs (IP)
Integer Programs have linear constr
Lecture 11. Integer Programming
Solution Approaches
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap: Formulating Integer
Programs (IP)
Integer Programs have linear constr
Lecture 15. Markov Decision Processes
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap
We
have seen how to calculate first passage
time probabilities and expected first p
Lecture 07. Network Optimization
Assignment Problems
and Transportation Problems
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap: Shadow/Dual Price
The shadow/dual price
Lecture 10. Integer Programming
Modeling and Applications
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Last Lecture Recap: Network Optimization
Models
For special cases, network structur
Lecture 03. Linear Programming
Graphical Solution Approach
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Review from Last Lecture
Linear Programming, which is a prescriptive modeling
tech
Lecture 05. Simplex method to Solve
Linear Programming
ISYE 4600: Operations Research Methods
ISYE 6610: Systems Modeling in Decision Sciences
Jennifer Pazour, Ph.D.
1
Review from Last Lecture
Graphical solution method to LPs gave us good intuition about