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Optimization in Operations Research

by: Rardin, Ronald L.

Optimization in Operations Research

by: Rardin, Ronald L.

ISBN 13:
9780023984150
ISBN 10:
0023984155
Edition: 1st
Format: Paperback
Copyright: 08/05/1997
Publisher: Pearson
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Summary

This book is specifically designed to change the way deterministic optimization is taught to introductory students.Toward this end, it exposes students to the broad scope of the topic, reinforces the basic principles, sparks students'enthusiasm about the field, provides tools of immediate relevance and develops the skills necessary to use those tools.

PREFACE

(7)

ABOUT THE AUTHOR

XVI

CHAPTER 1 PROBLEM SOLVING WITH MATHEMATICAL MODELS

(22)

1.1 OR Application Stories

(2)

1.2 Optimization and the Operations Research Process

(5)

1.3 System Boundaries, Sensitivity Analysis, Tractability and Validity

(3)

1.4 Descriptive Models and Simulation

(3)

1.5 Numerical Search and Exact versus Heuristic Solutions

(2)

1.6 Deterministic versus Stochastic Models

(3)

1.7 Perspectives

(1)

Exercises

(3)

CHAPTER 2 DETERMINISTIC OPTIMIZATION MODELS IN OPERATIONS RESEARCH

(54)

2.1 Decision Variables, Constraints, and Objective Functions

(4)

2.2 Graphic Solution and Optimization Outcomes

(12)

2.3 Large-Scale Optimization Models and Indexing

(7)

2.4 Linear and Nonlinear Programs

(6)

2.5 Discrete or Integer Programs

(7)

2.6 Multiobjective Optimization Models

(4)

2.7 Classification Summary

(1)

Exercises

(13)

CHAPTER 3 IMPROVING SEARCH

(54)

3.1 Improving Search, Local and Global Optima

(11)

3.2 Search with Improving and Feasible Directions

(11)

3.3 Algebraic Conditions for Improving and Feasible Directions

(10)

3.4 Unimodel and Convex Model Forms Tractable for Improving Search

109

(9)

3.5 Searching and Starting Feasible Solutions

118

(9)

Exercises

127

(4)

CHAPTER 4 LINEAR PROGRAMMING MODELS

131

(44)

4.1 Allocation Models

131

(4)

4.2 Blending Models

135

(4)

4.3 Operations Planning Models

139

(9)

4.4 Shift Scheduling and Staff Planning Models

148

(5)

4.5 Time-Phased Models

153

(4)

4.6 Models with Linearizable Nonlinear Objectives

157

(7)

Exercises

164

(11)

CHAPTER 5 SIMPLEX SEARCH FOR LINEAR PROGRAMMING

175

(76)

5.1 LP Optimal Solutions and Standard Form

175

(11)

5.2 Extreme-Point Search and Basic Solutions

186

(11)

5.3 The Simplex Algorithm

197

(10)

5.4 Dictionary and Tableau Representations of Simplex

207

(4)

5.5 Two Phase Simplex

211

(9)

5.6 Degeneracy and Zero-Length Simplex Steps

220

(4)

5.7 Convergence and Cycling with Simplex

224

(1)

5.8 Doing It Efficiently: Revised Simplex

225

(20)

Exercises

245

(6)

CHAPTER 6 INTERIOR POINT METHODS FOR LINEAR PROGRAMMING

251

(48)

6.1 Searching through the Interior

251

(11)

6.2 Scaling with the Current Solution

262

(7)

6.3 Affine Scaling Search

269

(6)

6.4 Log Barrier Methods for Interior Point Search

275

(12)

6.5 Dual and Primal-Dual Extensions

287

(6)

Exercises

293

(6)

CHAPTER 7 DUALITY AND SENSITIVITY IN LINEAR PROGRAMMING

299

(74)

7.1 Generic Activities versus Resources Perspective

299

(5)

7.2 Qualitative Sensitivity to Changes in Model Coefficients

304

(11)

7.3 Quantifying Sensitivity to Changes in LP Model Coefficients: A Dual Model

315

(9)

7.4 Formulating Linear Programming Duals

324

(5)

7.5 Primal-to-Dual Relationships

329

(9)

7.6 Computer Outputs and What If Changes of Single Parameters

338

(16)

7.7 Bigger Model Changes, Reoptimization, and Parametric Programming

354

(9)

Exercises

363

(10)

CHAPTER 8 MULTIOBJECTIVE OPTIMIZATION AND GOAL PROGRAMMING

373

(36)

8.1 Multiobjective Optimization Models

373

(5)

8.2 Efficient Points and the Efficient Frontier

378

(6)

8.3 Preemptive Optimization and Weighted Sums of Objectives

384

(5)

8.4 Goal Programming

389

(11)

Exercises

400

(9)

CHAPTER 9 SHORTEST PATHS AND DISCRETE DYNAMIC PROGRAMMING

409

(66)

9.1 Shortest Path Models

409

(8)

9.2 Dynamic Programming Approach to Shortest Paths

417

(9)

9.3 Shortest Paths From One Node to All Others: Bellman-Ford

426

(7)

9.4 Shortest Paths From All Nodes to All Others: Floyd-Warshall

433

(7)

9.5 Shortest Path From One Node to All Others With Costs Nonnegative: Dijkstra

440

(6)

9.6 Shortest Paths From One Node to All Others in Acyclic Digraphs

446

(4)

9.7 CPM Project Scheduling and Longest Paths

450

(8)

9.8 Discrete Dynamic Programming Models

458

(10)

Exercises

468

(7)

CHAPTER 10 NETWORK FLOWS

475

(80)

10.1 Graphs, Networks, and Flows

475

(8)

10.2 Cycle Directions for Network Flow Search

483

(11)

10.3 Rudimentary Cycle Direction Search Algorithms for Network Flows

494

(6)

10.4 Integrality of Optimal Network Flows

500

(2)

10.5 Transportation and Assignment Models

502

(9)

10.6 Other Single-Commodity Network Flow Models

511

(8)

10.7 Network Simplex Algorithm for Optimal Flows

519

10.8 Cycle Canceling Algorithms for Optimal Flows

000

10.9 Multicommodity and Gain/Loss Flows

536

(7)

Exercises

543

(12)

CHAPTER 11 DISCRETE OPTIMIZATION MODELS

555

(72)

11.1 Lumpy Linear Programs and Fixed Charges

555

(5)

11.2 Knapsack and Capital Budgeting Models

560

(6)

11.3 Set Packing, Covering, and Partitioning Models

566

(8)

11.4 Assignment and Matching Models

574

(10)

11.5 Traveling Salesman and Routing Models

584

(29)

Exercises

613

(14)

CHAPTER 12 DISCRETE OPTIMIZATION METHODS

627

(88)

12.1 Solving by Total Enumeration

627

(3)

12.2 Relaxations of Discrete Optimization Models and Their Uses

630

(11)

12.3 Stronger LP relaxations, Valid Inequalities, and Lagrangian Relaxations

641

(10)

12.4 Branch and Bound Search

651

(13)

12.5 Rounding, Parent Bounds, Enumerations Sequences, and Stopping Early in Branch and Bound

664

(16)

12.6 Improving Search Heuristics for Discrete Optimization INLPs

680

(7)

12.7 Tabu, Simulated Annealing, and Genetic Algorithm Extensions of Improving Search

687

(11)

12.8 Constructive Heuristics

698

(7)

Exercises

705

(10)

CHAPTER 13 UNCONSTRAINED NONLINEAR PROGRAMMING

715

(72)

13.1 Unconstrained Nonlinear Programming Models

715

(11)

13.2 One-Dimensional Search

726

(11)

13.3 Derivatives, Taylor Series, and Conditions for Local Optima

737

(12)

13.4 Convex Concave Functions and Global Optimality

749

(8)

13.5 Gradient Search

757

(4)

13.6 Newton's Method

761

(5)

13.7 Quasi-Newton Methods and BFGS Search

766

(8)

13.8 Optimization without Derivatives and Nelder-Mead

774

(7)

Exercises

781

(6)

CHAPTER 14 CONSTRAINED NONLINEAR PROGRAMMING

787

(100)

14.1 Constrained Nonlinear Programming Models

787

(8)

14.2 Convex, Separable, Quadratic and Posynomial Geometric Programming Special NLP Forms

795

(15)

14.3 Lagrange Multiplier Methods

810

(7)

14.4 Karush-Kuhn-Tucker Optimality Conditions

817

(10)

14.5 Penalty and Barrier Methods

827

(10)

14.6 Reduced Gradient Algorithms

837

(12)

14.7 Quadratic Programming Methods

849

(9)

14.8 Separable Programming Methods

858

(8)

14.9 Posynomial Programming Methods

866

(9)

Exercises

875

(12)

SELECTED ANSWERS

887

(18)

INDEX

905

Amazon no longer offers textbook rentals. We do!

Optimization in Operations Research

Optimization in Operations Research

9780023984150

0023984155

Summary

Table of Contents

Supplemental Materials

Write a Review

Amazon no longer offers textbook rentals. We do!

Optimization in Operations Research

Optimization in Operations Research

9780023984150

0023984155

Summary

Table of Contents

Supplemental Materials

Write a Review

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