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Operations Research : An Introduction

ISBN: 9780131889231 | 0131889230
Edition: 9th
Format: Nonspecific Binding
Publisher: Prentice Hall
Pub. Date: 1/1/2003

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SummaryTable of Contents
Significantly revised, this book provides balanced coverage of the theory, applications, and computations of operations research. The applications and computations in operations research are emphasized. Explains complex mathematical concepts effectively using carefully designed numerical examples, virtually eliminating the need for formal mathematical proofs. Introduces practical applications of software, enabling readers to test concepts. Presents complete integration throughout of the powerful programming language AMPL, using numerous example... MORE
Prefacexvii
About the Authorxix
Trademarksxx
What Is Operations Research?
1(10)
... MORE
Operations Research Models
1(3)
Solving the OR Model
4(1)
Queuing and Simulation Models
5(1)
Art of Modeling
5(2)
More Than Just Mathematics
7(1)
Phases of an OR Study
8(2)
About This Book
10(1)
References
10(1)
Modeling with Linear Programming
11(70)
Two-Variable LP Model
12(3)
Graphical LP Solution
15(12)
Solution of a Maximization Model
16(7)
Solution of a Minimization Model
23(4)
Selected LP Applications
27(41)
Urban Planning
27(5)
Currency Arbitrage
32(5)
Investment
37(5)
Production Planning and Inventory Control
42(9)
Blending and Refining
51(6)
Manpower Planning
57(3)
Additional Applications
60(8)
Computer Solution with Excel Solver and AMPL
68(13)
LP Solution with Excel Solver
69(4)
LP Solution with AMPL
73(7)
References
80(1)
The Simplex Method and Sensitivity Analysis
81(70)
LP Model in Equation Form
82(3)
Converting Inequalities into Equations with Nonnegative Right-Hand Side
82(2)
Dealing with Unrestricted Variables
84(1)
Transition from Graphical to Algebraic Solution
85(5)
The Simplex Method
90(13)
Iterative Nature of the Simplex Method
90(3)
Computational Details of the Simplex Algorithm
93(6)
Summary of the Simplex Method
99(4)
Artificial Starting Solution
103(10)
M-Method
104(4)
Two-Phase Method
108(5)
Special Cases in the Simplex Method
113(10)
Degeneracy
113(3)
Alternative Optima
116(3)
Unbounded Solution
119(2)
Infeasible Solution
121(2)
Sensitivity Analysis
123(28)
Graphical Sensitivity Analysis
123(6)
Algebraic Sensitivity Analysis---Changes in the Right-Hand Side
129(10)
Algebraic Sensitivity Analysis---Objective Function
139(7)
Sensitivity Analysis with TORA, Solver, and AMPL
146(4)
References
150(1)
Duality and Post-Optimal Analysis
151(42)
Definition of the Dual Problem
151(5)
Primal-Dual Relationships
156(13)
Review of Simple Matrix Operations
156(2)
Simplex Tableau Layout
158(1)
Optimal Dual Solution
159(6)
Simplex Tableau Computations
165(4)
Economic Interpretation of Duality
169(5)
Economic Interpretation of Dual Variables
170(2)
Economic Interpretation of Dual Constraints
172(2)
Additional Simplex Algorithms
174(7)
Dual Simplex Method
174(6)
Generalized Simplex Algorithm
180(1)
Post-Optimal Analysis
181(12)
Changes Affecting Feasibility
182(5)
Changes Affecting Optimality
187(4)
References
191(2)
Transportation Model and Its Variants
193(42)
Definition of the Transportation Model
194(7)
Nontraditional Transportation Models
201(5)
The Transportation Algorithm
206(15)
Determination of the Starting Solution
207(4)
Iterative Computations of the Transportation Algorithm
211(9)
Simplex Method Explanation of the Method of Multipliers
220(1)
The Assignment Model
221(8)
The Hungarian Method
222(6)
Simplex Explanation of the Hungarian Method
228(1)
The Transshipment Model
229(6)
References
234(1)
Network Models
235(62)
Scope and Definition of Network Models
236(3)
Minimal Spanning Tree Algorithm
239(4)
Shortest-Route Problem
243(20)
Examples of the Shortest-Route Applications
243(5)
Shortest-Route Algorithms
248(9)
Linear Programming Formulation of the Shortest-Route Problem
257(6)
Maximal flow model
263(12)
Enumeration of Cuts
263(1)
Maximal-Flow Algorithm
264(9)
Linear Programming Formulation of Maximal Flow Mode
273(2)
CPM and PERT
275(22)
Network Representation
277(5)
Critical Path (CPM) Computations
282(3)
Construction of the Time Schedule
285(7)
Linear Programming Formulation of CPM
292(1)
PERT Calculations
293(3)
References
296(1)
Advanced Linear Programming
297(36)
Simplex Method Fundamentals
298(8)
From Extreme Points to Basic Solutions
300(3)
Generalized Simplex Tableau in Matrix Form
303(3)
Revised Simplex Method
306(9)
Development of the Optimality and Feasibility Conditions
307(2)
Revised Simplex Algorithm
309(6)
Bounded-Variables Algorithm
315(6)
Duality
321(5)
Matrix Definition of the Dual Problem
322(1)
Optimal Dual Solution
322(4)
Parametric Linear Programming
326(7)
Parametric Changes in C
327(3)
Parametric Changes in b
330(2)
References
332(1)
Goal Programming
333(16)
A Goal Programming Formulation
334(4)
Goal Programming Algorithms
338(11)
The Weights Method
338(3)
The Preemptive Method
341(7)
References
348(1)
Integer Linear Programming
349(50)
Illustrative Applications
350(19)
Capital Budgeting
350(4)
Set-Covering Problem
354(6)
Fixed-Charge Problem
360(4)
Either-Or and If-Then Constraints
364(5)
Integer Programming Algorithms
369(16)
Branch-and-Bound (B&B) Algorithm
370(9)
Cutting-Plane Algorithm
379(5)
Computational Considerations in ILP
384(1)
Traveling Salesperson Problem (TSP)
385(14)
Heuristic Algorithms
389(3)
B&B Solution Algorithm
392(3)
Cutting-Plane Algorithm
395(2)
References
397(2)
Deterministic Dynamic Programming
399(28)
Recursive Nature of Computations in DP
400(3)
Forward and Backward Recursion
403(2)
Selected DP Applications
405(19)
Knapsack/Fly-Away/Cargo-Loading Model
405(8)
Work-Force Size Model
413(3)
Equipment Replacement Model
416(4)
Investment Model
420(3)
Inventory Models
423(1)
Problem of Dimensionality
424(3)
References
426(1)
Deterministic Inventory Models
427(36)
General Inventory Model
427(1)
Role of Demand in the Development of Inventory Models
428(2)
Static Economic-Order-Quantity (EOQ) Models
430(13)
Classic EOQ model
430(6)
EOQ with Price Breaks
436(4)
Multi-Item EOQ with Storage Limitation
440(3)
Dynamic EOQ Models
443(20)
No-Setup Model
445(4)
Setup Model
449(12)
References
461(2)
Review of Basic Probability
463(26)
Laws of Probability
463(4)
Addition Law of Probability
464(1)
Conditional Law of Probability
465(2)
Random Variables and Probability Distributions
467(2)
Expectation of a Random Variable
469(6)
Mean and Variance (Standard Deviation) of a Random Variable
470(2)
Mean and Variance of Joint Random Variables
472(3)
Four Common Probability Distributions
475(6)
Binomial Distribution
475(1)
Poisson Distribution
476(1)
Negative Exponential Distribution
477(1)
Normal Distribution
478(3)
Empirical Distributions
481(8)
References
488(1)
Decision Analysis and Games
489(42)
Decision Making under Certainty---Analytic Hierarchy Process (AHP)
490(10)
Decision Making under Risk
500(15)
Decision Tree-Based Expected Value Criterion
500(6)
Variations of the Expected Value Criterion
506(9)
Decision under Uncertainty
515(5)
Game Theory
520(11)
Optimal Solution of Two-Person Zero-Sum Games
521(3)
Solution of Mixed Strategy Games
524(6)
References
530(1)
Probabilistic Inventory Models
531(18)
Continuous Review Models
532(7)
``Probabilitized'' EOQ Model
532(2)
Probabilistic EOQ Model
534(5)
Single-Period Models
539(6)
No-Setup Model (Newsvendor Model)
539(4)
Setup Model (s-S Policy)
543(2)
Multiperiod Model
545(4)
References
548(1)
Queuing Systems
549(56)
Why Study Queues?
550(1)
Elements of a Queuing Model
551(2)
Role of Exponential Distribution
553(3)
Pure Birth and Death Models (Relationship Between the Exponential and Poisson Distributions)
556(7)
Pure Birth Model
556(4)
Pure Death Model
560(3)
Generalized Poisson Queuing Model
563(5)
Specialized Poisson Queues
568(27)
Steady-State Measures of Performance
569(4)
Single-Server Models
573(9)
Multiple-Server Models
582(10)
Machine Servicing Model---(M/M/R): (GD/K/K), R > K
592(3)
(M/G/1):(GD/ ∞ / ∞)---Pollaczek-Khintchine (P-K) Formula
595(2)
Other Queuing Models
597(1)
Queuing Decision Models
597(8)
Cost Models
598(4)
Aspiration Level Model
602(2)
References
604(1)
Simulation Modeling
605(36)
Monte Carlo Simulation
605(5)
Types of Simulation
610(1)
Elements of Discrete-Event Simulation
611(11)
Generic Definition of Events
611(2)
Sampling from Probability Distributions
613(9)
Generation of Random Numbers
622(2)
Mechanics of Discrete Simulation
624(9)
Manual Simulation of a Single-Server Model
624(6)
Spreadsheet-Based Simulation of the Single-Server Model
630(3)
Methods for Gathering Statistical Observations
633(5)
Subinterval Method
634(1)
Replication Method
635(1)
Regenerative (Cycle) Method
636(2)
Simulation Languages
638(3)
References
640(1)
Markov Chains
641(24)
Definition of a Markov Chain
641(3)
Absolute and n-Step Transition Probabilities
644(2)
Classification of the States in a Markov Chain
646(3)
Steady-State Probabilities and Mean Return Times of Ergodic Chains
649(5)
First Passage Time
654(4)
Analysis of Absorbing States
658(7)
References
663(2)
Classical Optimization Theory
665(26)
Unconstrained Problems
665(7)
Necessary and Sufficient Conditions
676
The Newton-Raphson Method
670(2)
Constrained Problems
672(19)
Equality Constraints
673(12)
Inequality Constraints---Karush-Kuhn-Tucker (KKT) Conditions
685(5)
References
690(1)
Nonlinear Programming Algorithms
691(32)
Unconstrained Algorithms
691(8)
Direct Search Method
691(4)
Gradient Method
695(4)
Constrained Algorithms
699(24)
Separable Programming
699(9)
Quadratic Programming
708(5)
Chance-Constrained Programming
713(5)
Linear Combinations Method
718(3)
SUMT Algorithm
721(1)
References
722(1)
Appendix A AMPL Modeling Language
723(26)
A Rudimentary AMPL Model
723(1)
Components of AMPL Model
724(8)
Mathematical Expressions and Computed Parameters
732(3)
Subsets and Indexed Sets
735(2)
Accessing External Files
737(7)
Simple Read Files
737(2)
Using Print and Printf to Retrieve Output
739(1)
Input Table Files
739(3)
Output Table Files
742(2)
Spreadsheet Input/Output Tables
744(1)
Interactive Commands
744(2)
Iterative and Conditional Execution of AMPL Commands
746(2)
Sensitivity Analysis Using AMPL
748(1)
References
748(1)
Appendix B Statistical Tables
749(4)
Appendix C Partial Solutions to Selected Problems
753(50)
Index803

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