SIE 321 - Probabilistic Models in Operations Research

SIE 321 - Probabilistic Models in Operations Research (3) Probability, Markov chains, Poisson processes, queuing models, reliability models. 3ES. P, 230.

Ross, S. M., Introduction to Probability Models

Feldman, R. M. and C. Valdez-Flores, Applied Probability and Stochastic Processes.

Hillier, F. S. and G. J. Lieberman, Introduction to Operations Research.

J. L. Higle, Associate Professor of Systems and Industrial Engineering

1. Axioms of probability
2. Common discrete and continuous distributions
3. Independence
4. Conditional probability
5. Expectations

On the first day of class, an assignment designed to test facility with prerequisite material will be distributed. Results will be evaluated and the instructor will consult with individual students, if necessary.

The objective of SIE 321 is to familiarize students with some of the probabilistic models available for the solution of stochastic industrial and engineering problems.

1. Be able to develop an appropriate probabilistic model from a verbal description of a problem.
2. Have an understanding of the restrictions associated with various modeling assumptions.
3. Be able to extract relevant information from various types of models.

1. Review Of Basic Probability: Axioms of Probability
2. Discrete Distributions, Continuous Distributions (6 classes)
3. Computing Probabilities And Expectations by Conditioning (5 classes)
4. Introduction to Stochastic Processes (1 class)
5. Markov Chains: Transition Probabilities, Chapman-Kolmogorov Equations, Limiting Distributions, Examples (8 classes)
6. Poisson Processes: Definition, Properties, Examples (9 classes)
7. Queuing Theory: Poisson Queues, Little’s Result, Networks of Queues (13 classes)

Class Requirements:

1. Three lecture sections per week
2. Approximately 10 homework assignments per semester
3. Two examinations and a final

Limited to calculation simplification

Laboratory Projects: None

1. Class examinations
2. Homework evaluation

Contribution to program objectives: Goals 1

Prepared by: J. L. Higle   Date: April 14, 1998