Introduction To The Mathematics Of Operations Research With Mathematica

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ISBN:9781574446128
Editorial: Crc Press Inc.
Fecha de la edición:2006
Número de la edición: 2
Colección: Pure and Applied Mathematics nº 279
Encuadernación:Tapa dura
Dimensiones: 0 cm x 0 cm
Nº Pág.:592
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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/re execute 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.

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