## Probability Models in Operations Research

Series:
Published:
Author(s):

Hardback
\$113.95
ISBN 9781420054897
Cat# 54899

### Features

• Addresses probability modeling concepts, including probability distributions and conditioning
• Explores issues related to single and multiple random variables
• Covers the use of stochastic processes to model the time evolution of a random variable
• Includes Poisson processes, discrete-time Markov chains, and continuous-time Markov chains
• Presents queuing models that can be applied to waiting lines, manufactured parts in an assembly process, and calls in a telephone network Textbook Features
• Includes homework problems at the end of each chapter
• Concludes each of the first six chapters with an extended homework problem

Solutions manual available upon qualifying course adoption

### Summary

Industrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive overview of the probabilistic and stochastic modeling approaches commonly used to capture the randomness in industrial and systems engineering.

Probability Modeling Fundamentals
Random Experiments and Events
Probability
Conditional Probability
Homework Problems
Application: Basic Reliability Theory
Analysis of Random Variables
Introduction to Random Variables
Discrete Random Variables
Continuous Random Variables
Expectation
Generating Functions
Common Applications of Random Variables
Homework Problems
Application: Basic Warranty Modeling
Analysis of Multiple Random Variables
Two Random Variables
Common Applications of Multiple Random Variables
Computing Expectations by Conditioning
Computing Probabilities by Conditioning
Homework Problems
Application: Bivariate Warranty Modeling
Introduction to Stochastic Processes
Introduction to Stochastic Processes
Introduction to Counting Processes
Introduction to Renewal Processes
Bernoulli Processes
Homework Problems
Application: Acceptance Sampling
Poisson Processes
Introduction to Poisson Processes
Interarrival Times
Arrival Times
Decomposition and Superposition of Poisson Processes
Competing Poisson Processes
Nonhomogeneous Poisson Processes
Homework Problems
Application: Repairable Equipment
Discrete-Time Markov Chains
Introduction
Manipulating the Transition Probability Matrix
Classification of States
Limiting Behavior
Absorbing States
Homework Problems
Application: Inventory Management
Continuous-Time Markov Chains
Introduction
Birth and Death Processes
Limiting Probabilities
Time-Dependent Behavior
Semi-Markov Processes
Homework Problems
Markovian Queuing Systems
Queuing Basics
The M/M/1 Queue
The M/M/1/c Queue
The M/M/s
The M/M/s/c Queue
The M/G/1 Queue
Networks of Queues
Homework Problems
Bibliography

### Editorial Reviews

The authors used a subset of the homework problems as in-class examples and another subset for homework–an excellent idea. Each of the six chapters also contains an application illustrating how the principles discussed can be applied in real life ... another very good idea. Overall, this clearly written work is a useful resource ... Summing Up: Highly recommended.
– R. Bharath, Emeritus, Northern Michigan University, in Choice: Current Reviews for Academic Libraries, Vol. 47, No. 1