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More About This Textbook
Overview
Operations Research: An Introduction, 9/e is ideal for or junior/senior undergraduate and firstyear 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.
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.”
M. Jeya Chandra, PENN STATE UNIVERSITY
“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.”
Marc E. Posner, THE OHIO STATE UNIVERSITY
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, ORProduct Details
Related Subjects
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 universitywide 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.
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
References
Chapter 2: Modeling with Linear Programming
2.1 TwoVariable 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
References
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 MMethod
3.4.2 TwoPhase 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–Righthand Side of the Constraints
3.6.3 Algebraic Sensitivity Analysis–ObjectiveFunction Coefficients
3.6.4 Sensitivity Analysis with TORA, Excel Solver, and AMPL
3.7 Computational Issue in Linear Programming
References
Chapter 4: Duality and PostOptimal Analysis
4.1 Definition of the Dual Problem
4.2 PrimalDual 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 Postoptimal Analysis
4.5.1 Changes Affecting Feasibility
4.5.2 Changes Affecting Optimality
References
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
References
Chapter 6: Network Models
6.1 Network definitions
6.2 Minimal Spanning tree Algorithm
6.3 ShortestRoute Problem
6.3.1 Examples of the ShortestRoute Applications
6.3.2 ShortestRoute Algorithms
6.3.3 Linear Programming Formulation of the ShortestRoute Problem
6.4 Maximal flow model
6.4.1 Enumeration of Cuts
6.4.2 MaximalFlow 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
References
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 BoundedVariables 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
References
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
References
Chapter 9: Integer Linear Programming
9.1 Illustrative Applications
9.2 Integer Programming Algorithms
9.2.1 BranchandBound (B&B) Algorithm
9.2.2 CuttingPlane Algorithm
References
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
References
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 Cuttingplane Algorithm
11.4 Local Search Heuristics
11.4.1 Nearestneighbor Heuristic
11.4.2 Subtour Reversal heuristic
11.5 Metaheuristic
11.5.1 TSP Tabu Algorithm
11.5.2 TSP Simulated Annealing Algorithm
11.5.3 TSP Genetic Algorithm
References
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/CargoLoading 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
References
Chapter 13: Deterministic Inventory Models
13.1 General Inventory Model
13.2 Role of Demand in the Development of Inventory Models
13.3 Static EconomicOrderQuantity (EOQ) Models
13.3.1 Classic EOQ model
13.3.2 EOQ with Price Breaks
13.3.3 MultiItem EOQ with Storage Limitation
13.4 Dynamic EOQ Models
13.4.1 NoSetup EOQ Model
13.4.2 Setup EOQ Model
References
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
References
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 TwoPerson ZeroSum Games
15.4.2 Solution of Mixed Strategy Games
References
Chapter 16: Probabilistic Inventory Models
16.1 Continuous Review Models
16.1.1 “Probabilitized” EOQ Model
16.1.2 Probabilistic EOQ Model
16.2 SinglePeriod Models
16.2.1 No Setup Model
16.2.2 Setup Model (sS Policy)
16.3 Multiperiod Model
References
Chapter 17: Markov Chains
17.1 Definition of a Markov Chain
17.2 Absolute and nStep Transition Probabilities
17.3 Classification of the States in a Markov Chain
17.4SteadyState Probabilities and Mean Return Times of Ergodic Chains
17.5 First Passage Time
17.6 Analysis of Absorbing States
References
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 SteadyState Measures of Performance
18.6.2 SingleServer Models
18.6.3 MultipleServer Models
18.6.4 Machine Servicing Model–(M/M/R) : (GD/K/K),R K
18.7 –PollaczekKhintchine (PK) Formula
18.8 Other Queuing Models
18.9 Queuing Decision Models
18.9.1 Cost Models
18.9.2 Aspiration Level Model
References
Chapter 19: Simulation Modeling
19.1 Monte Carlo Simulation
19.2 Types of Simulation
19.3 Elements of DiscreteEvent 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 SingleServer Model
19.5.2 SpreadsheetBased Simulation of the SingleServer Model
19.6 Methods for Gathering Statistical Observations
19.6.1 Subinterval Method
19.6.2 Replication Method
19.7 Simulation Languages
References
Chapter 20: Classical Optimization Theory
20.1 Unconstrained Problems
20.1.1 Necessary and Sufficient Conditions
20.1.2 The NewtonRaphson Method
20.2 Constrained Problems
20.2.1 Equality Constraints
20.2.2 Inequality Constraints–KarushKuhnTucker (KKT) Conditions
References
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 ChanceConstrained Programming
21.2.4 Linear Combinations Method
21.2.5 SUMT Algorithm
References
Appendix A: Statistical Tables
Appendix B: Partial Answers to Selected Problems
On the CDROM
Chapter 22CD: Additional Network and LP algorithms
22.1 MinimumCost 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 InteriorPoint Method
22.3.1 Basic Idea of the InteriorPoint Algorithm
22.3.2 InteriorPoint Algorithm
References
Chapter 23CD: Forecasting Models
23.1 Moving Average Technique
23.2 Exponential Smoothing
23.3 Regression
References
Chapter 24CD: Probabilistic Dynamic Programming
24.1 A Game of Chance
24.2 Investment Problem
24.3 Maximization of the Event of Achieving a Goal
References
Chapter 25CD: Markovian Decision Process
25.1 Scope of the Markovian Decision Problem
25.2 FiniteStage Dynamic Programming Model
25.3 InfiniteStage 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
References
Chapter 26CD: 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 CCD: 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
Reference
Appendix DCD: 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
Problems
References
Appendix E: Case Studies
Index
Introduction
The main thrust of the seventh edition is the extensive software support used throughout the book:
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, PK 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 branchandbound 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 01 pseudorandom 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.