Schedule: Monday, Wednesday, 4:10pm-5:50pm, Room 155, Russ Center
Professor: Dr. Xinhui Zhang
Email: xinhui.zhang@wright.edu
Office: 234 Russ Center
Office Hour: Monday, Wednesday, 1:30 p.m. – 2:30 p.m.
Website: http://www.wright.edu/~xinhui.zhang/
Course Description
Any realistic model of a real-world system must take into account the possibilities of randomness. Example systems include the congestions on the highway, the number of customers in a checkout line, the number of items in a warehouse, the price of a financial security, to name a few. Such a model is usually referred to as a probabilistic model. This course focuses on the probabilistic models to study these systems and understand how these systems evolve over time. Topics include stochastic systems, discrete and continuous Markov chains, queue models, simulation and their applications such as inventory theory as well as in operations management, economics, and finance. This is the second of the two-term introductory course on Operations Research and Industrial Engineering. The same textbook will be used in both these two courses. While the deterministic operations research model course covers the mathematical or linear and integer programming models, this second course focuses more on the probabilistic part, such as Markov chains and queuing theory.
Textbooks
P.A. Jensen and J.F. Bard, Operations Research Models and Methods, John Wiley & Sons, 2003 ISBN: 0-471-38004-0
References
W. L. Winston, Operations Research: Applications and Algorithms, Fourth Edition, Duxbury Press, 2003. ISBN: 0-534-38058-1
S. Ross, Introduction to Probability Models, Eighth Edition, Academic Press, 2000. ISBN: 0-12-598055-8
Prerequisites: an understanding of a) random variables, b) probability and c) conditional probability.
The grade will be based on homework (30%), one midterms (30%), and the final exam (40%).
Course Outline(Tentative)
1. Introduction
and Review of Probability Theory (Chapter 11)
Introduction to stochastic models and a few examples. Review of
topics in probability theory which should be known: probability sample space,
conditional probability, independence, random variables, distributions, mean and
variance, limit laws.
2. Discrete Time
Markov Chains (Chapter 12, 13)
Definition and formulation of a Markov chain, examples,
classification of states, first passage times, recurrence and transience,
stationary distributions, limit theorems, costs and rewards.
3. Continuous
Time Markov Chains (Chapter 14, 15)
Formulating continuous time Markov chains, embedded discrete time
Markov chain, Poisson process, birth and death processes, stationary
distributions, limit theorems, costs and rewards.
4. Queuing
Theory (Chapter 16 and 17)
Little's Law,
Markovian Queues, networks of queues, general single server queue, multiserver
queues.
5. Inventory
Theory (Chapter 16, Winston, 2003)
Single and multi-period inventory models, the newsvendor
problem
6. Other
Applications of Probabilistic OR Models (Multiple references to be determined)
Maintenance problems, manufacturing flow lines and dynamic job shops
from Edelmand Prize Project.
Class Policy:
a) I expect to see you in class and be active in class. If you are going to miss class, drop me an email and please spend time to make up material missed.
b) If you miss an exam without prior coordination with your instructor, you will receive a zero. Quizzes will be given periodically throughout the quarter (4-5).
c) You are encouraged to solve the problems in the exercise especially if you want to get an A in the class. It is inadequate to rely solely on homework!!