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E-raamat: Introductory Operations Research: Theory and Applications

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  • Ilmumisaeg: 14-Mar-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662080115
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  • Formaat: PDF+DRM
  • Ilmumisaeg: 14-Mar-2013
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Keel: eng
  • ISBN-13: 9783662080115
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This introductory text provides undergraduate and graduate students with a concise and practical introduction to the primary concepts and techniques of optimization. Practicing engineers and managers will also find useful its concentration on problems and examples relevant to them. With a strong emphasis on basic concepts and techniques throughout, the book explains the theory behind each technique as simply as possible, along with illustrations and worked examples. It gives a balanced treatment of both the linear and nonlinear programming, plus search techniques, geometric programming, and game theory. Some typical problems varying in difficulty level are solved so readers can appreciate intricacies of the underlying concepts useful for practical problem solving. Suitable for individual or group learning, the book also includes numerous end-of-chapter problems for study and review.

Arvustused

From the reviews: "The book has a very wide scope, including linear, integer, nonlinear, dynamic and geometric programming, 2-person zero-sum games, networks, goal programming , project management, and numerical techniques for unconstrained optimization in one and several dimensions. Another strength is the large number of numerical examples in the text, worked in great detail." (David Griffel, The Mathematical Gazette, Vol. 90 (518), 2006) "The textbook is aimed to 'provide undergraduate and graduate students with a concise and practical introduction to the primary concepts and techniques of optimization', as it is stated at the back cover, It is also promised there that practicing engineers and managers will find the book useful because it gives a balanced treatment of both linear and nonlinear programming and their extensions. ... The appendices contain the objective type questions, and the solutions to the problems presented at the end of all chapters." (Antana Zilinskas, Zentralblatt MATH, Vol. 1099 (1), 2007) "The focus in this textbook is on deterministic problems in operations research. Besides the respective models the reader will be informed about solution algorithms illustrated by a large number of examples and he is encouraged to solve many exercises. Throughout the textbook the results are often outlined using illustrative examples. ... It may be helpful ... for the students who have a good and precise knowledge in operations research and want to see other problems in this field." (Stephan Dempe, OR News, Issue 25, 2005)

Preface v
Formulation
1(32)
The Scope of Optimization
1(3)
Introduction
4(5)
Formulation of Models
9(24)
Geometry of Linear Programming
33(30)
Geometric Interpretation
33(12)
Extreme Points and Basic Feasible Solutions
45(10)
Fundamental Theorem of Linear Programming
55(1)
Graphical Method
56(7)
The Simplex Algorithm
63(44)
Introduction
63(1)
The Simplex Algorithm
64(16)
The Big-M Method
80(3)
Two Phase Method
83(6)
Exceptional Cases in LPP
89(18)
Duality Theory
107(24)
Dual Linear Program
107(5)
Duality Theorems
112(2)
Complementary Slackness Theorem
114(4)
An Economic Interpretation of Duality
118(1)
The Dual Simplex Method
119(12)
Advanced Linear Programming
131(38)
The Revised Simplex Algorithm
131(12)
Complexity of The Simplex Algorithm
143(1)
Bounded Variable Technique
144(7)
Decomposition Principle
151(5)
Karmarkar Interior Point Algorithm
156(13)
Sensitivity Analysis
169(36)
Introduction
169(1)
Change in the Cost Vector
170(5)
Changes in the Right-hand Side Vector
175(4)
Change in the Constraint Matrix
179(11)
Special Cases
190(2)
Parametric Programming
192(13)
Transportation Problems
205(48)
Introduction
205(8)
Optimal Solution from BFS
213(8)
Unbalanced Transportation Problem
221(5)
Transshipment
226(6)
Assignment Problems
232(2)
Hungarian Method
234(19)
Network Analysis
253(24)
Introduction to Networks
253(1)
Minimal Spanning Tree Algorithm
254(5)
Shortest Path Problem
259(8)
Maximal Flow Problem
267(10)
Project Management
277(30)
Introduction
277(1)
Critical Path Method
278(3)
Critical Path Determination
281(2)
Optimal Scheduling by CPM
283(10)
Project Evaluation and Review Technique
293(14)
Sequencing Problems
307(18)
Introduction
307(1)
Problem of n Jobs and 2 Machines
308(5)
Problem of n Jobs and m Machines
313(4)
Two Jobs on Ordered m Machines
317(8)
Integer Programming
325(24)
Introduction
325(1)
Branch and Bound Algorithm
326(5)
Traveling Salesman Problem
331(9)
Cargo Loading Problem
340(9)
Dynamic Programming
349(28)
Introduction
349(1)
Formulation
350(5)
Recursive Relations
355(3)
Continuous Cases
358(3)
Discrete Cases
361(8)
Forward Recursions
369(1)
Linear Programming vs Dynamic Programming
370(7)
Nonlinear Programming
377(36)
Introduction
377(4)
Lagrange Multipliers Method
381(5)
Convex Nonlinear Programming Problem
386(4)
Kuhn Tucker Theory
390(3)
Quadratic Programming
393(5)
Separable Programming
398(7)
Duality in Nonlinear Programming
405(8)
Search Techniques
413(20)
Unimodal function
413(2)
Dichotomous Search Method
415(2)
Fibonacci Search Method
417(4)
Golden Section Method
421(1)
Steepest Descent Method
422(3)
Conjugate Gradient Method
425(8)
Geometric Programming
433(24)
Introduction
433(5)
Unconstrained Posynomial Optimization
438(8)
Constrained Posynomial Optimization
446(11)
Goal Programming
457(38)
Introduction
457(2)
Standard form of LGPP
459(1)
Partitioning Algorithm
460(8)
Grouping Algorithm
468(27)
Games Theory
495(14)
Introduction
495(1)
Two Person Zero Sum Game (Pure Strategies)
496(3)
Two Person Zero Sum Game (Mixed Strategies)
499(2)
Games Theory vs Linear Programming
501(8)
Special Topics
509(20)
Extremum Difference Method
509(2)
Generalized Transportation Problem
511(6)
Generalized Assignment Problem
517(3)
Multiobjective Transportation Problem
520(9)
Appendix: Objective Type Questions 529(20)
Bibliography 549(4)
Answers 553(24)
Index 577