Linear Programming Methods and Applications: Fifth Edition

by Gass, Saul I.

• ISBN13: 9780486432847
• ISBN10: 048643284X
• Edition: 5th
• Format: Paperback
• Copyright: 2010-11-18
• Publisher: Dover Publications

Summary

Clear and comprehensive, this volume introduces theoretical, computational, and applied concepts and is useful both as text and as a reference book. Considerations of theoretical and computational methods include the general linear programming problem, the simplex computational procedure, the revised simplex method, the duality problems of linear programming degeneracy procedures, parametric linear programming and sensitivity analysis, and additional computational techniques. The treatment of applications covers the transportation problem and general linear programming applications, and a final part examines nonlinear programming. Numerical examples and exercises with selected answers appear in every chapter. 1995 ed.

Author Biography

Saul I. Gass has been a leading contributor to operations research.

Table of Contents

Preface	vii
Part 1 INTRODUCTION
General Discussion	3	(14)
Linear-Programming Problems	3	(4)
Examples of Linear-Programming Problems	7	(10)
Mathematical Background	17	(50)
Matrices	17	(11)
Vectors and Vector Spaces	28	(4)
Convex Sets	32	(5)
Linear Inequalities	37	(6)
Solution of a Set of Linear Equations	43	(24)
Part 2 Methods: Theoretical and Computational
The Geneeral Linear-Programming Problem	67	(19)
The Linear-Programming Problem	67	(2)
Properties of a Solution to the Linear-Programming Problem	69	(8)
Generating Extreme-Point Solutions	77	(9)
The Simplex Computational Procedure	86	(37)
Development of a Minimum Feasible Solution	88	(6)
Computational Procedure	94	(12)
The Artificial-Basis Technique	106	(7)
A First Feasible Solution Using Slack Variables	113	(1)
Geometric Interpretation of the Simplex Procedure	114	(9)
The Revised Simplex Method	123	(34)
The General Form of the Inverse	123	(16)
The Product Form of the Inverse	139	(3)
Computational Considerations	142	(15)
The Duality Problems of Linear Programming	157	(24)
The Unsymmetric Primal-Dual Problems	157	(9)
The Symmetric Primal-Dual Problems	166	(7)
Economic Interpretation of the Primal-Dual Problems	173	(8)
Degeneracy and Anticycling Procedures	181	(14)
Perturbation Techniques	183	(3)
The Lowest-Index Anticycling Rules	186	(4)
Example of Cycling	190	(5)
Parametric Linear Programming and Sensitivity Analysis	195	(43)
The Parametric Objective Function	196	(11)
The Parametric Dual Problem	207	(6)
Sensitivity Analysis	213	(11)
Multiobjective Linear Programming	224	(14)
Additional Computational Techniques	238	(81)
Determining a First Feasible Solution	240	(5)
The Dual Simplex Method	245	(4)
Integer Programming	249	(17)
The Decomposition of Large-Scale Systems	266	(16)
Bounded-Variable Problems	282	(21)
The Simplex Algorithm and Computational Efficiency	303	(16)
Part 3 APPLICATIONS
The Transportation Problem	319	(32)
The General Transportation Problem	319	(9)
Computational Procedure for Solving the Transportation Problem	328	(15)
Variations of the Transportation Problem	343	(8)
General Linear-Programming Application	351	(80)
Production-Scheduling and Inventory-Control Problems	353	(9)
Interindustry Problems	362	(6)
Diet Problems	368	(4)
Network-Flow Problems	372	(18)
Sample of Applications	390	(16)
Linear Programming and the Theory of Games	406	(25)
Part 4 Nonlinear Programming
Nonlinear Programming	431	(38)
The General Problem of Mathematical Programming	432	(3)
Mathematical Background	435	(7)
The Convex-Programming Problem	442	(9)
Quadratic Programming	451	(7)
Separable Programming	458	(11)
Bibliography of Linear-Programming Applications	469	(22)
References	491	(34)
Index	525