Integrates suggestions and self-check questions throughout the text, making the book much more interactiveEmploys a software package, Mathematica, in order to expose new issues and possibilities, enhance users' desire to experiment, and reduce the computational burdenIntroduces the Traveling Salesman problem and other famous graph theory problems, and covers Brownian motionIncludes longer investigations that promote the development of problem-solving techniques Deploys Mathematica tools to execute probabilistic computations regarding Poisson processes and queuesApplies Mathematica's symbolic algebra ability to solve dynamic programming problems, refocusing attention on the modeling aspect of these problems
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
Minimal Cost Networks
Critical Path Algorithm
Maximal Flow Problems
Maximum Matching Problems
Other Problems of Graph Theory
Geometry of Linear Programming
Simplex Algorithm for the Standard Maximum Problem
Duality and the Standard Minimum Problem
Further Topics in Linear Programming
Definitions and Examples
First Passage Times
Classification of States
Continuous Time Processes
Birth and Death Processes
The Markovian Decision Model
The Finite Horizon Problem
The Discounted Reward Problem
Optimal Stopping of a Markov Chain
Appendix A - Probability Review
Appendix B - Answers to Selected Exercises
Appendix C - Glossary of Mathematica Commands
||September 27, 2016
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