Operations Research: An Introduction / Edition 9

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Operations Research: An Introduction, 9/e is ideal for or junior/senior undergraduate and first-year graduate courses in Operations Research in departments of Industrial Engineering, Business Administration, Statistics, Computer Science, and Mathematics.

This text streamlines the coverage of the theory, applications, and computations of operations research. Numerical examples are effectively used to explain complex mathematical concepts. A separate chapter of fully analyzed applications aptly demonstrates the diverse use of OR. The popular commercial and tutorial software AMPL, Excel, Excel Solver, and Tora are used throughout the book to solve practical problems and to test theoretical concepts.

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Editorial Reviews

From the Publisher

“Dr. Taha is an excellent author and presents materials in his book very well in terms of readability and clarity. The topics within every chapter are presented in a cohesive and logical manner.”


“The book is very clear and readable. Figures do a good job of illustrating Dr. Taha’s points. It is very useful to have the Solver & TORA output shown in the chapter with discussion of how to interpret results.”


From The Critics
This textbook introduces deterministic models, probabilistic models, and nonlinear models of decision making and problem solving. Example applications of the Tora, Excel, Lingo, and Ampl programs are integrated throughout the book. The seventh edition adds sections on the generalized simplex method, PERT networks, and solution of the traveling salesperson problem. Annotation c. Book News, Inc., Portland, OR
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Product Details

  • ISBN-13: 9780132555937
  • Publisher: Prentice Hall
  • Publication date: 9/15/2010
  • Edition description: New Edition
  • Edition number: 9
  • Pages: 832
  • Sales rank: 358,636
  • Product dimensions: 7.10 (w) x 9.20 (h) x 1.30 (d)

Meet the Author

Hamdy A. Taha is a University Professor Emeritus of Industrial Engineering with the University of Arkansas, where he taught and conducted research in operations research and simulation.¿ He is the author of three other books on integer programming and simulation, and his works have been translated to numerous languages.¿ He is also the author of several book chapters, and his technical articles have appeared in European Journal of Operations Research, IEEE Transactions on Reliability, IIE Transactions, Interfaces, Management Science, Naval Research Logistics Quarterly, Operations Research, and Simulation.¿


Professor Taha was the recipient of the Alumni Award for excellence in research and the university-wide Nadine Baum Award for excellence in teaching, both from the University of Arkansas, and numerous other research and teaching awards from the College of Engineering, University of Arkansas.¿ He was also named a Senior Fulbright Scholar to Carlos III University, Madrid, Spain.¿ He is fluent in three languages and has held teaching and consulting positions in Europe, Mexico, and the Middle East.


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Table of Contents

Chapter 1: What Is Operations Research?

1.1 Operations Research Models

1.2 Solving the OR Model

1.3 Queuing and Simulation Models

1.4 Art of Modeling

1.5 More Than Just Mathematics …

1.6 Phases of an OR Study

1.7 About This Book


Chapter 2: Modeling with Linear Programming

2.1 Two-Variable LP Model

2.1.1 Properties of the LP Model

2.2 Graphical LP Solution

2.2.1 Solution of a Maximization Model

2.2.2 Solution of a Minimization Model

2.3 Computer Solution with Excel Solver and AMPL

2.3.1 LP Solution with Excel Solver

2.3.2 LP Solution with AMPL

2.4 Linear Programming Applications

2.4.1 Investment

2.4.2 Production Planning and Inventory Control

2.4.3 Manpower Planning

2.4.4 Urban Development Planning

2.4.5 Blending and Refining

2.4.6 Additional LP Applications


Chapter 3: The Simplex Method and Sensitivity Analysis

3.1 LP Solution Space in Equation Form

3.2 Transition from Graphical to Algebraic Solution

3.3 The simplex Method

3.3.1 Iterative Nature of the Simplex Method

3.3.2 Computational Details of the Simplex Algorithm

3.4 Artificial Starting Solution

3.4.1 M-Method

3.4.2 Two-Phase Method

3.5 Special Cases in Simplex Method Application

3.5.1 Degeneracy

3.5.2 Alternative Optima

3.5.3 Unbounded Solution

3.5.4 Infeasible Solution

3.6 Sensitivity Analysis

3.6.1 Graphical Sensitivity Analysis

3.6.2 Algebraic Sensitivity Analysis–Right-hand Side of the Constraints

3.6.3 Algebraic Sensitivity Analysis–Objective-Function Coefficients

3.6.4 Sensitivity Analysis with TORA, Excel Solver, and AMPL

3.7 Computational Issue in Linear Programming


Chapter 4: Duality and Post-Optimal Analysis

4.1 Definition of the Dual Problem

4.2 Primal-Dual Relationships

4.2.1 Review of Simple Matrix Operations

4.2.2 Simplex Tableau Layout

4.2.3 Optimal Dual Solution

4.2.4 Simplex Tableau Computations

4.3 Economic Interpretation of Duality

4.3.1 Economic Interpretation of Dual Variables

4.3.2 Economic Interpretation of Dual Constraints

4.4 Additional Simplex Algorithms for LP

4.4.1 Dual Simplex Algorithm

4.4.2 Generalized Simplex Algorithm

4.5 Post-optimal Analysis

4.5.1 Changes Affecting Feasibility

4.5.2 Changes Affecting Optimality


Chapter 5: Transportation Model and Its Variants

5.1 Definition of the Transportation Model

5.2 Nontraditional transportation models

5.3 The transportation Algorithm

5.3.1 Determination of the Starting Solution

5.3.2 Iterative Computations of the Transportation Algorithm

5.4 The Assignment Model

5.4.1 The Hungarian Method

5.4.2 Simplex Explanation of the Hungarian Method


Chapter 6: Network Models

6.1 Network definitions

6.2 Minimal Spanning tree Algorithm

6.3 Shortest-Route Problem

6.3.1 Examples of the Shortest-Route Applications

6.3.2 Shortest-Route Algorithms

6.3.3 Linear Programming Formulation of the Shortest-Route Problem

6.4 Maximal flow model

6.4.1 Enumeration of Cuts

6.4.2 Maximal-Flow Algorithm

6.4.3 Linear Programming Formulation of the Maximal Flow Model

6.5 CPM and PERT

6.5.1 Network Representation

6.5.2 Critical Path Computations

6.5.3 Construction of the Time Schedule

6.5.4 Linear Programming Formulation of CPM

6.5.5 PERT Calculations


Chapter 7: Advanced Linear Programming

7.1 Fundamentals of the Simplex Method

7.1.1 From Extreme Points to Basic Solutions

7.1.2 Generalized Simplex Tableau in Matrix Form

7. 2 Revised Simplex Algorithm

7.3 Bounded-Variables Algorithm

7.4 Duality

7.4.1 Matrix Definition of the Dual Problem

7.4.2 Optimal Dual Solution

7.5 Parametric Linear Programming

7.5.1 Parametric Changes in C

7.5.2 Parametric Changes in b

7.6 More Linear Programming Topics


Chapter 8: Goal Programming

8.1 A Goal Programming Formulation

8.2 Goal Programming Algorithms

8.2.1 The Weights Method

8.2.2 The Preemptive Method


Chapter 9: Integer Linear Programming

9.1 Illustrative Applications

9.2 Integer Programming Algorithms

9.2.1 Branch-and-Bound (B&B) Algorithm

9.2.2 Cutting-Plane Algorithm


Chapter 10: Heuristic and Constraint Programming

10.1 Introduction

10.2 Greedy (local Search) Heuristics

10.2.1 Discrete Variable Heuristi

10.2.2 Continuous Variable Heuristic

10.3 Metaheuristics

10.3.1 Tabu Search Algorithm

10.3.2 Simulated Annealing Algorithm

10.3.3 Genetic Algorithm

10.4 Application of metaheuristics to Integer Linear Programs

10.4.1 ILP Tabu Algorithm

10.4.2 ILP Simulated Annealing Algorithm

10.4.3 ILP Genetic Algorithm

10.5 Introduction to Constraint Programming


Chapter 11: Traveling Salesperson Problem (TSP)

11.1 Example Applications of TSP

11.2 TSP Mathematical Model

11.3 Exact TSP Algorithm

11.3.1 B&B Algorithm

11.3.2 Cutting-plane Algorithm

11.4 Local Search Heuristics

11.4.1 Nearest-neighbor Heuristic

11.4.2 Sub-tour Reversal heuristic

11.5 Metaheuristic

11.5.1 TSP Tabu Algorithm

11.5.2 TSP Simulated Annealing Algorithm

11.5.3 TSP Genetic Algorithm


Chapter 12: Deterministic Dynamic Programming

12.1 Recursive Nature of Computations in DP

12.2 Forward and Backward Recursion

12.3 Selected DP Applications

12.3.1 Knapsack/Flyaway Kit/Cargo-Loading Model

12.3.2 Workforce Size Model

12.3.3 Equipment Replacement Model

12.3.4 Investment Model

12.3.5 Inventory Models

12.4 Problem of Dimensionality


Chapter 13: Deterministic Inventory Models

13.1 General Inventory Model

13.2 Role of Demand in the Development of Inventory Models

13.3 Static Economic-Order-Quantity (EOQ) Models

13.3.1 Classic EOQ model

13.3.2 EOQ with Price Breaks

13.3.3 Multi-Item EOQ with Storage Limitation

13.4 Dynamic EOQ Models

13.4.1 No-Setup EOQ Model

13.4.2 Setup EOQ Model


Chapter 14: Review of Basic Probability

14.1 Laws of Probability

14.1.1 Addition Law of Probability

14.1.2 Conditional Law of Probability

14.2 Random Variables and Probability Distributions

14.3 Expectation of a Random Variable

14.3.1 Mean and Variance (Standard Deviation) of a Random Variable

14.3.2 Mean and Variance of Joint Random Variables

14.4 Four Common Probability Distributions

14.4.1 Binomial Distribution

14.4.2 Poisson Distribution

14.4.3 Negative Exponential Distribution

14.4.4 Normal Distribution

14.5 Empirical Distributions


Chapter 15: Decision Analysis and Games

15.1 Decision Making under Certainty–Analytic Hierarchy Process (AHP)

15.2 Decision Making under Risk

15.2.1 Expected Value Criterion

15.2.2 Variations of the Expected Value Criterion

15.3 Decision under Uncertainty

15.4 Game Theory

15.4.1 Optimal Solution of Two-Person Zero-Sum Games

15.4.2 Solution of Mixed Strategy Games


Chapter 16: Probabilistic Inventory Models

16.1 Continuous Review Models

16.1.1 “Probabilitized” EOQ Model

16.1.2 Probabilistic EOQ Model

16.2 Single-Period Models

16.2.1 No Setup Model

16.2.2 Setup Model (s-S Policy)

16.3 Multiperiod Model


Chapter 17: Markov Chains

17.1 Definition of a Markov Chain

17.2 Absolute and n-Step Transition Probabilities

17.3 Classification of the States in a Markov Chain

17.4Steady-State Probabilities and Mean Return Times of Ergodic Chains

17.5 First Passage Time

17.6 Analysis of Absorbing States


Chapter 18: Queuing Systems

18.1 Why Study Queues?

18.2 Elements of a Queuing Model

18.3 Role of Exponential Distribution

18.4 Pure Birth and Death Models (Relationship Between the Exponential and Poisson Distributions)

18.4.1 Pure Birth Model

18.4.2 Pure Death Model

18.5 Generalized Poisson Queuing Model

18.6 Specialized Poisson Queues

18.6.1 Steady-State Measures of Performance

18.6.2 Single-Server Models

18.6.3 Multiple-Server Models

18.6.4 Machine Servicing Model–(M/M/R) : (GD/K/K),R K

18.7 –Pollaczek-Khintchine (P-K) Formula

18.8 Other Queuing Models

18.9 Queuing Decision Models

18.9.1 Cost Models

18.9.2 Aspiration Level Model


Chapter 19: Simulation Modeling

19.1 Monte Carlo Simulation

19.2 Types of Simulation

19.3 Elements of Discrete-Event Simulation

19.3.1 Generic Definition of Events

19.3.2 Sampling from Probability Distributions

19.4 Generation of Random Numbers

19.5 Mechanics of Discrete Simulation

19.5.1 Manual Simulation of a Single-Server Model

19.5.2 Spreadsheet-Based Simulation of the Single-Server Model

19.6 Methods for Gathering Statistical Observations

19.6.1 Subinterval Method

19.6.2 Replication Method

19.7 Simulation Languages


Chapter 20: Classical Optimization Theory

20.1 Unconstrained Problems

20.1.1 Necessary and Sufficient Conditions

20.1.2 The Newton-Raphson Method

20.2 Constrained Problems

20.2.1 Equality Constraints

20.2.2 Inequality ConstraintsKarush-Kuhn-Tucker (KKT) Conditions


Chapter 21: Nonlinear Programming Algorithms

21.1 Unconstrained Algorithms

21.1.1 Direct Search Method

21.1.2 Gradient Method

21.2 Constrained Algorithms

21.2.1 Separable Programming

21.2.2 Quadratic Programming

21.2.3 Chance-Constrained Programming

21.2.4 Linear Combinations Method

21.2.5 SUMT Algorithm


Appendix A: Statistical Tables

Appendix B: Partial Answers to Selected Problems

On the CD-ROM

Chapter 22-CD: Additional Network and LP algorithms

22.1 Minimum-Cost Capacitated Flow Problem

22.1.1 Network Representatio

22.1.2 Linear Programming Formulation

22.1.3 Capacitated Network Simplex Algorithm Model

22.2 Decomposition Algorithm

22.3 Karmarkar Interior-Point Method

22.3.1 Basic Idea of the Interior-Point Algorithm

22.3.2 Interior-Point Algorithm


Chapter 23-CD: Forecasting Models

23.1 Moving Average Technique

23.2 Exponential Smoothing

23.3 Regression


Chapter 24-CD: Probabilistic Dynamic Programming

24.1 A Game of Chance

24.2 Investment Problem

24.3 Maximization of the Event of Achieving a Goal


Chapter 25-CD: Markovian Decision Process

25.1 Scope of the Markovian Decision Problem

25.2 Finite-Stage Dynamic Programming Model

25.3 Infinite-Stage Model

25.3.1 Exhaustive Enumeration Method

25.3.2 Policy Iteration Method Without Discounting

25.3.3 Policy Iteration Method with Discounting

25.4 Linear Programming Solution


Chapter 26-CD: Case Analysis

Case 1: Airline Fuel Allocation Using Optimum Tankering

Case 2: Optimization of Heart Valves Production

Case 3: Scheduling Appointments at Australian Tourist Commission Trade Events

Case 4: Saving Federal Travel Dollars

Case 5: Optimal Ship Routing and Personnel Assignment for Naval Recruitment in Thailand

Case 6: Allocation of Operating Room Time in Mount Sinai Hospital

Case 7: Optimizing Trailer Payloads at PFG Building Glass

Case 8: Optimization of Crosscutting and Log Allocation at Weyerhaeuser

Case 9: Layout Planning for a Computer Integrated Manufacturing (CIM) Facility

Case 10: Booking Limits in Hotel Reservations

Case 11: Casey’s Problem: Interpreting and Evaluating a New Test

Case 14: Ordering Golfers on the Final Day of Ryder Cup Matches

Case 13: Inventory Decisions in Dell’s Supply Chain

Case 14: Analysis of an Internal Transport System in a Manufacturing Plant

Case 15: Telephone Sales Manpower Planning at Qantas Airways

Appendix C-CD: AMPL Modeling Language

C.1 Rudimentary AMPL Model

C.2 Components of AMPL Model

C.3 Mathematical Expressions and Computed Parameters

C.4 Subsets and Indexed Sets

C.5 Accessing External Files

C.5.1 Simple Read Files

C.5.2 Using Print or Printf to Retrieve Output

C.5.3 Input Table Files

C.5.4 Output Table Files

C.5.5 Spreadsheet Input/Output Tables

C.6 Interactive Commands

C.7 Iterative and Conditional Execution of AMPL Commands

C.8 Sensitivity Analysis using AMPL

C.9 Selected AMPL Models


Appendix D-CD: Review of Vectors and Matrices

D.1 Vectors

D.1.1 Definition of a Vector

D.1.2 Addition (Subtraction) of Vectors

D.1.3 Multiplication of Vectors by Scalars

D.1.4 Linearly Independent Vectors

D.2 Matrices

D.2.1 Definition of a Matrix

D.2.2 Types of Matrices

D.2.3 Matrix Arithmetic Operations

D.2.4 Determinant of a Square Matrix

D.2.5 Nonsingular Matrix

D.2.6 Inverse of a Nonsingular Matrix

D.2.7 Methods of Computing the Inverse of Matrix

D.2.8 Matrix Manipulations Using Excel

D.3 Quadratic Forms

D.4 Convex and Concave Functions



Appendix E: Case Studies


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It is gratifying that, for over 30 years, hundreds of thousands of students worldwide have been introduced to operations research through the various editions of this book. This success carries with it the responsibility of meeting the needs of future generations of students. The seventh edition is the result of a dedicated effort to live up to this responsibility.

The main thrust of the seventh edition is the extensive software support used throughout the book:

  1. Windows-based TORA.
  2. Excel spreadsheet templates.
  3. Examples of LINGO and AMPL applications.

The TORA software offers modules for matrix inversion, solution of simultaneous linear equations, linear programming, transportation models, network models, integer programming, queuing models, project planning with CPM and PERT, and game theory. TORA can be executed in automated or tutorial mode. The automated mode reports the final solution of the problem, usually in the standard format followed in commercial packages. The tutorial mode is a unique feature that provides immediate feedback to test the reader's understanding of the computational details of each algorithm. As with its DOS predecessor, the different screens in TORA are accessed in a logical and unambiguous manner, essentially eliminating the need for a user's manual.

Excel spreadsheet templates complement TORA's modules. These templates include linear programming, dynamic programming, analytical hierarchy process (AHP), inventory models, histogramming of raw data, decision theory, Poisson queues, P-K formula, simulation, and nonlinear models. Some of the templates are direct spreadsheets. Others use Excel Solveror VBA macros. Regardless of the design, all templates offer the unique feature of being equipped with an input data section that allows solving different problems without the need to modify the formulas or the layout of the spreadsheet. In this manner, the user can experiment with, test, and compare different sets of input data in a convenient manner. Where possible, the formulas and the layout of the spreadsheets have been protected to minimize the chance of inadvertently corrupting them.

The book includes examples of the commercial packages LINGO and AMPL for solving linear programming problems. The objective is to familiarize the reader with how very large mathematical programming models are solved in practice.

TORA software and the Excel spreadsheets are integrated into the text in a manner that facilitates introducing and testing concepts that otherwise could not be presented effectively. From my personal experience, I have found TORA's tutorial module and Excel spreadsheets to be highly effective in classroom presentations. Many concepts can be demonstrated instantly, simply by changing the data of the problem. To cite a few examples, TORA can be used to demonstrate the bizarre behavior of the branch-and-bound algorithm by applying it to a (small) integer programming problem, where the solution is found in nine iterations but its optimality verified in more than 25,000 iterations. Without the software and the special design of TORA, it would be impossible to demonstrate this situation in an effective manner. Another example is the unique design of the dynamic programming and the AHP spreadsheets, where the user interactive input is designed to enhance effective understanding of the details of these two topics. A third example deals with explaining the congruential method for generating 0-1 pseudo-random numbers. With the spreadsheet, one can instantly demonstrate the effect of selecting the seed (and the parameters) on the "quality" of the generator, particularly with regard to the cycle length of the random number sequence and, hence, warn the student about the danger of a "causal" implementation of the congruential method within a simulation model.

In addition to the software support in the book, all chapters have been streamlined (many rewritten) to present the material in a concise manner. New material includes a new introduction to operations research (Chapter 1); the generalized simplex method (Chapter 4); representation of all network models, including CPM, as linear programs (Chapter 6); PERT networks (Chapter 6); solution of the traveling sales Person problem (Chapter 9); and the golden section method (Chapter 21).

As in the sixth edition, the book is organized into three parts: deterministic models, probabilistic models, and nonlinear models. Appendices A through D include a review of matrix algebra, a TORA primer (though TORA's design makes a user's manual unnecessary), basic statistical tables, and partial answers to selected problems.

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