Introduction to the Mathematics of Operations Research with Mathematica®: 2nd Edition (Hardback) book cover

Introduction to the Mathematics of Operations Research with Mathematica®

2nd Edition

By Kevin J. Hastings

Chapman and Hall/CRC

592 pages

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Hardback: 9781574446128
pub: 2006-05-30
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The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance.

The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving.

Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.

Table of Contents

Graph Theory and Network Analysis

Definitions and Examples

Spanning Trees

Minimal Cost Networks

Critical Path Algorithm

Maximal Flow Problems

Maximum Matching Problems

Other Problems of Graph Theory

Linear Programming

Two-Variable Problems

Geometry of Linear Programming

Simplex Algorithm for the Standard Maximum Problem

Duality and the Standard Minimum Problem

Further Topics in Linear Programming

Non-Standard Problems

Transportation Problem

Sensitivity Analysis

Markov Chains

Definitions and Examples

Short-Run Distributions

First Passage Times

Classification of States

Limiting Probabilities

Absorption Probabilities

Continuous Time Processes

Poisson Processes

Birth and Death Processes

Renewal Processes

Queueing Theory

Brownian Motion

Dynamic Programming

The Markovian Decision Model

The Finite Horizon Problem

The Discounted Reward Problem

Policy Improvement

Optimal Stopping of a Markov Chain

Extended Applications

Appendix A - Probability Review

Appendix B - Answers to Selected Exercises

Appendix C - Glossary of Mathematica Commands

Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
MATHEMATICS / Probability & Statistics / General
TECHNOLOGY & ENGINEERING / Operations Research