Introduction to Mathematical Programming, 1/e
Russell C. Walker, Carnegie Mellon University
Published January, 1999 by Prentice Hall Engineering/Science/Mathematics
Copyright 1999, 560 pp.
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Intended for Mathematical Programming courses at the undergraduate level. Course can be found in business schoolsespecially MBA programsas Management Science and Operations Research. Providing the background in mathematics departments, the course may also be called Linear Programming or Optimization. Necessary to begin using mathematical programming as a tool for managerial applications and beyond, this empowering guide helps students learn to recognize when a mathematical model can be useful and helps them develop an appreciation and understanding of the mathematics associated with the applied techniques. Formatted in a flexible framework to suit individual course needs, it presents self-contained chapters later in the book which are designed to work in the order an instructor deems most suitable.
Presents students with a comprehensive survey of problem types and discusses various ways to use specific mathematical tools they will be studying.
Chapters are organized so that many of the later topics are largely independent to allow variety in the selection of course content.
Develops the ideas needed to treat linear problems.
Treats four network problems: the transportation problem, the critical path method, the shortest path problem, and minimal spanning trees - with discussions on the special structures of these problems.
- Contains the prerequisite material for the study of linear programming, and offers a brief introduction to matrix algebra.
An introduction to the use of Maple is given to solve optimization problems.
Includes an important and insightful chapter on compound interest which explores the financial aspects of some of the problems considered throughout the text.
Provides open-ended problems suitable for longer assignments and group projects. Chapter 9 (Case Studies).
Offers additional material for instructors wishing to tailor their course more towards pure mathematics (vs. applications).
Comes with an extensive appendix section that includes answers to many problems, an introduction to the linear programming packages and LINGO, an overview of the symbolic computation package Maple, and brief introductions to the TI-82 and TI-92 calculators and their applications.
- Integrates some proofs throughout the presentation and occasionally delves into such topics as basic graph theory, linear algebra, analysis, properties of algorithms, and combinatorics.
Solutions to the Case Studies in Chapter 9 are also available.
A detailed Table of Contents and chapter abstracts can be found at the author's website:
A tenth chapter devoted to compound interest is also available at the website above.
1. Introduction to the Problems.
2. Vectors and Matrices.
3. Linear Programming.
4. Network Models.
5. Unconstrained Extrema.
6. Constrained Extrema.
7. Integer Programming.
8. Introduction to Dynamic Programming.
9. Case Studies.
Appendix A. A Brief Introduction to Maple.
Appendix B. Introduction to Texas Instrument Calculators.
Appendix C. Selected Answers and Hints.
Appendix D. Brief Introductions to LINDO and LINGO.