Elementary Linear Programming with Applications

By

  • Bernard Kolman
  • Robert Beck

Linear programming finds the least expensive way to meet given needs with available resources. Its results are used in every area of engineering and commerce: agriculture, oil refining, banking, and air transport. Authors Kolman and Beck present the basic notions of linear programming and illustrate how they are used to solve important common problems. The software on the included disk leads students step-by-step through the calculations.
The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications.
The companion website on www.elsevierdirect.com contains the student-oriented linear programming code SMPX, written by Professor Evar Nering of Arizona State University. The authors also recommend inexpensive linear programming software for personal computers.

Please note the previous printing included a disk attached to the back of the book.

The material is now only available on the companion website -

http://www.elsevierdirect.com/product.jsp?isbn=9780124179103

Audience
Students in one-term undergraduate course on linear programming. Focused on students in quantitative fields who need some business-related skills, or for business students who need to develop quantitative methods for decision-making.

Hardbound, 449 Pages Pages

Published: June 1995

Imprint: Academic Press

Reviews

  • "The book presents the basic ideas of linear programming and related areas by not using a rigorous approach. The main objective, to provide a textbook that is readable by students in business, engineering, and computer science, seems to have been achieved....A rich set of more than 280 exercises, real-life projects and further reading suggestions successfully stimulates learning." --MATHEMATICAL REVIEWS "...The book is very clearly written with many illustrative examples and exercises. The proofs of theoretical results are kept to a minimum so that the book is easy to read even for non mathematics students. It is an excellent textbook on linear programming at an introductory level." --ZENT. FUR MATHEMATIK UNDIHRE GRENZGEBIETE

Contents

  • Prologue: Introduction to Operations Research. Review of Linear Algebra: Matrices. Gauss-Jordan Reduction. The Inverse of a Matrix. Subspaces. Linear Independence and Basis. Introduction to Linear Programming: The Linear Programming Problem. Matrix Notation. Geometry of Linear Programming Problems. The Extreme Point Theorem. Basic Solutions. The Simplex Method: The Simplex Method for Problems in Standard Form. Degeneracy and Cycling. Artificial Variables.Further Topics in Linear Programming: Duality. The Duality Theorem. Computational Relations between the Primal and Dual Problems. The Dual Simplex Method. The Revised Simplex Method. Sensitivity Analysis. Computer Aspects. Integer Programming: Examples. Cutting Plane Methods. Branch and Bound Methods. Computer Aspects. Special Types of Linear Programming Problems: The Transportation Problem. The Assignment Problem. Graphs and Networks (Basic Definitions). The Maximal Flow Problem. The Shortest Route Problem. The Critical Path Method. Computer Aspects. Appendices: Karmarkar's Algorithm. Microcomputer Software. SMPX. Answers to Odd-Numbered Exercises. Index.

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