Operations research: an introduction
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Upper Saddle River, NJ
Pearson, Prentice Hall
2007
|
| Ausgabe: | 8. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | XX, 813 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0131889230 0131360140 |
Internformat
MARC
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| 100 | 1 | |a Taha, Hamdy A. |d 1937- |e Verfasser |0 (DE-588)133779432 |4 aut | |
| 245 | 1 | 0 | |a Operations research |b an introduction |c Hamdy A. Taha |
| 250 | |a 8. ed. | ||
| 264 | 1 | |a Upper Saddle River, NJ |b Pearson, Prentice Hall |c 2007 | |
| 300 | |a XX, 813 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Investigación operacional |2 lemb | |
| 650 | 4 | |a Operations Research | |
| 650 | 7 | |a Pesquisa operacional |2 larpcal | |
| 650 | 7 | |a Programación (Matemáticas) |2 lemb | |
| 650 | 4 | |a Operations research | |
| 650 | 4 | |a Programming (Mathematics) | |
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| 650 | 0 | 7 | |a Operations Research |0 (DE-588)4043586-6 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804135409384423424 |
|---|---|
| adam_text | Contents
Preface
xvii
About the Author
xix
Trademarks
xx
Chapter
1
What Is Operations Research?
1
1.1
Operations Research Models
1
1.2
Solving the OR Model
4
1.3
Queuing and Simulation Models
5
1.4
Art of Modeling
5
1.5
More Than Just Mathematics
7
1.6
Phases of an OR Study
8
1.7
About This Book
10
References
10
Chapter
2
Modeling with Linear Programming
11
2.1
Two-Variable LP Model
12
2.2
Graphical LP Solution
15
2.2.1
Solution of a Maximization Model
16
2.2.2
Solution of a Minimization Model
23
12.3
Selected LP Applications
27
2.3.1
Urban Planning
27
2.3.2
Currency Arbitrage
32
2.3.3
Investment
37
2.3.4
Production Planning and Inventory Control
42
2.3.5
Blending and Refining
51
2.3.6
Manpower Planning
57
2.3.7
Additional Applications
60
2.4
Computer Solution with Excel Solver and AMPL
68
2.4.1
LP Solution with Excel Solver
69
2.4.2
LP Solution with AMPL
73
References
80
Chapter
3
The Simplex Method and Sensitivity Analysis
81
3.1
LP Model in Equation Form
82
3.1.1
Converting Inequalities into Equations
with
Nonnegative Right-Hand
Side
82
3.1.2
Dealing with Unrestricted Variables
84
3.2
Transition from Graphical to Algebraic Solution
85
VII
viii Contents
3.3
The Simplex Method
90
3.3.1
Iterative Nature of the Simplex Method
90
3.3.2
Computational Details of the Simplex Algorithm
93
3.3.3
Summary of the Simplex Method
99
3.4
Artificial Starting Solution
103
3.4.1
M-Method
704
3.4.2
Two-Phase Method
108
3.5
Special Cases in the Simplex Method
113
3.5.1
Degeneracy
113
3.5.2
Alternative Optima
116
3.5.3
Unbounded Solution
119
3.5.4
Infeasible Solution
121
3.6
Sensitivity Analysis
723
3.6.1
Graphical Sensitivity Analysis
123
3.6.2
Algebraic Sensitivity Analysis
—
Changes in the Right-
Hand Side
729
3.6.3
Algebraic Sensitivity Analysis
—
Objective Function
739
3.6.4
Sensitivity Analysis with
TORA,
Solver, and AMPL
746
References
750
Chapter
4
Duality and Post-Optimal Analysis
151
4.1
Definition of the Dual Problem
757
4.2
Primal-Dual Relationships
756
4.2.1
Review of Simple Matrix Operations
756
4.2.2
Simplex Tableau Layout
758
4.2.3
Optimal Dual Solution
759
4.2.4
Simplex Tableau Computations
765
4.3
Economic Interpretation of Duality
769
4.3.1
Economic Interpretation of Dual Variables
770
4.3.2
Economic Interpretation of Dual Constraints
772
4.4
Additional Simplex Algorithms
774
4.4.1
Dual Simplex Method
774
4.4.2
Generalized Simplex Algorithm
780
4.5
Post-Optimal Analysis
787
4.5.1
Changes Affecting Feasibility
782
4.5.2
Changes Affecting Optimality
787
References
797
Chapter
5
Transportation Model and Its Variants
193
5.1
Definition of the Transportation Model
794
5.2
Nontraditional
Transportation Models
207
5.3
The Transportation Algorithm
206
5.3.1
Determination of the Starting Solution
207
5.3.2
Iterative Computations of the Transportation
Algorithm
277
Contents
¡χ
5.3.3 Simplex
Method Explanation of the Method
of Multipliers
220
5.4
The Assignment Model
221
5.4.1
The Hungarian Method
222
5.4.2
Simplex Explanation of the Hungarian Method
228
5.5
The Transshipment Model
229
References
234
Chapter
6
Network Models
235
6.1
Scope and Definition of Network Models
236
6.2
Minimal Spanning Tree Algorithm
239
6.3
Shortest-Route Problem
243
6.3.1
Examples of the Shortest-Route Applications
243
6.3.2
Shortest-Route Algorithms
248
6.3.3
Linear Programming Formulation
of the Shortest-Route Problem
257
6.4
Maximal flow model
263
6.4.1
Enumeration of Cuts
263
6.4.2
Maximal-Flow Algorithm
264
6.4.3
Linear Programming Formulation of Maximal
Flow Mode
273
6.5
CPM and PERT
275
6.5.1
Network Representation
277
6.5.2
Critical Path (CPM) Computations
282
6.5.3
Construction of the Time Schedule
285
6.5.4
Linear Programming Formulation of CPM
292
6.5.5
PERT Calculations
293
References
296
Chapter
7
Advanced Linear Programming
297
7.1
Simplex Method Fundamentals
298
7.1.1
From Extreme Points to Basic Solutions
300
7.1.2
Generalized Simplex Tableau in Matrix Form
303
7.2
Revised Simplex Method
306
7.2.1
Development of the Optimality and Feasibility
Conditions
307
7.2.2
Revised Simplex Algorithm
309
7.3
Bounded-Variables Algorithm
315
7.4
Duality
321
7.4.1
Matrix Definition of the Dual Problem
322
7.4.2
Optimal Dual Solution
322
7.5
Parametric Linear Programming
326
7.5.1
Parametric Changes
¡n C
327
7.5.2
Parametric Changes in
b
330
References
332
Contents
Chapter
8
Coal Programming
333
8.1
A Goal Programming Formulation
334
8.2
Goal Programming Algorithms
338
8.2.1
The Weights Method
338
8.2.2
The Preemptive Method
341
References
348
Chapter
9
Integer Linear Programming
349
9.1
Illustrative Applications
350
9.1.1
Capital Budgeting
350
9.1.2
Set-Covering Problem
354
9.1.3
Fixed-Charge Problem
360
9.1.4
Either-Or and If-Then Constraints
364
9.2
Integer Programming Algorithms
369
9.2.1
Branch-and-Bound (B&B) Algorithm
370
9.2.2
Cutting-Plane Algorithm
379
9.2.3
Computational Considerations in ILP
384
9.3
Traveling Salesperson Problem (TSP)
385
9.3.1
Heuristic Algorithms
389
9.3.2
B&B Solution Algorithm
392
9.3.3
Cutting-Plane Algorithm
395
References
397
Chapter 1O Deterministic Dynamic Programming
399
400
10.1
Recursive Nature of Computations in DP
10.2
Forward and Backward Recursion
403
10.3
Selected DP Applications
405
10.3.1
Knapsack/Fly-Away/Cargo-Loading Model
405
10.3.2
Work-Force Size Model
413
10.3.3
Equipment Replacement Model
476
10.3.4
Investment Model
420
10.3.5
Inventory Models
423
10.4
Problem of Dimensionality
424
References
426
Chapter
11
Deterministic Inventory Models
427
11.1
General Inventory Model
427
11.2
Role of Demand in the Development of Inventory
Models
428
11.3
Static Economic-Order-Quantity (EOQ) Models
430
11.3.1
Classic EOQ model
430
11.3.2
EOQ with Price Breaks
436
11.3.3
Multi-Item EOQ with Storage Limitation
440
11.4
Dynamic EOQ Models
443
11.4.1
No-Setup Model
445
11.4.2
Setup Model
449
References
467
Contents xi
Chapter
12 Review
of
Basic
Probability
463
12.1
Laws of Probability
463
12.1.1
Addition Law of Probability
464
12.1.2
Conditional Law of Probability
465
12.2
Random Variables and Probability Distributions
467
12.3
Expectation of a Random Variable
469
12.3.1
Mean and Variance (Standard Deviation) of a Random
Variable
470
12.3.2
Mean and Variance of Joint Random Variables
472
12.4
Four Common Probability Distributions
475
12.4.1
Binomial Distribution
475
12.4.2
Poisson
Distribution
476
МАЗ
Negative Exponential Distribution
477
12.4.4
Normal Distribution
478
12.5
Empirical Distributions
481
References
488
Chapter
13
Decision Analysis and Games
489
13.1
Decision Making under Certainty
—
Analytic Hierarchy
Process
(ΑΗΡ)
490
13.2
Decision Making under Risk
500
13.2.1
Decision Tree-Based Expected Value Criterion
500
13.2.2
Variations of the Expected Value Criterion
506
13.3
Decision under Uncertainty
515
13.4
Game Theory
520
13.4.1
Optimal Solution of Two-Person Zero-Sum Games
521
13.4.2
Solution of Mixed Strategy Games
524
References
530
Chapter
14
Probabilistic Inventory Models
531
14.1
Continuous Review Models
532
14.1.1
Probabilitized EOQ Model
532
14.1.2
Probabilistic EOQ Model
534
14.2
Single-Period Models
539
14.2.1
No-Setup Model (Newsvendor Model)
539
14.2.2
Setup Model (s-S Policy)
543
14.3
Multiperiod Model
545
References
548
Chapter
15
Queuing Systems
549
15.1
Why Study Queues?
550
15.2
Elements of a Queuing Model
557
15.3
Role of Exponential Distribution
553
15.4
Pure Birth and Death Models (Relationship Between
the Exponential and
Poisson
Distributions)
556
15.4.1
Pure Birth Model
556
15.4.2
Pure Death Model
560
xii
Table
of Contents
15.5
Generalized
Poisson
Queuing Model
563
15.6
Specialized
Poisson
Queues
568
15.6.1
Steady-State Measures of Performance
569
15.6.2
Single-Server Models
573
15.6.3
Multiple-Server Models
582
15.6.4
Machine Servicing Model—{M/MfR): (GD/KIK),
R>
К
592
15.7
(M/G/1):(GD/ oo/ oo)—Pollaczek-Khintchine (P-K)
Formula
595
15.8
Other Queuing Models
597
15.9
Queuing Decision Models
597
15.9.1
Cost Models
598
15.9.2
Aspiration Level Model
602
References
604
Chapter
16
Simulation Modeling
6О5
16.1
Monte Carlo Simulation
605
16.2
Types of Simulation
610
16.3
Elements of Discrete-Event Simulation
611
16.3.1
Generic Definition of Events
611
16.3.2
Sampling from Probability Distributions
613
16.4
Generation of Random Numbers
622
16.5
Mechanics of Discrete Simulation
624
16.5.1
Manual Simulation of a Single-Server Model
624
16.5.2
Spreadsheet-Based Simulation of the Single-Server
Model
630
16.6
Methods for Gathering Statistical Observations
633
16.6.1
Subinterval Method
634
16.6.2
Replication Method
635
16.6.3
Regenerative (Cycle) Method
636
16.7
Simulation Languages
638
References
640
Chapter
17
Markov Chains
641
17.1
Definition of a Markov Chain
641
17.2
Absolute and
η
-Step
Transition Probabilities
644
17.3
Classification of the States in a Markov Chain
646
17.4
Steady-State Probabilities and Mean Return Times
of Ergodic Chains
649
17.5
First Passage Time
654
17.6
Analysis of Absorbing States
658
References
663
Chapter
18
Classical Optimization Theory
665
18.1
Unconstrained Problems
665
18.1.1
Necessary and Sufficient Conditions
676
18.1.2
The Newton-Raphson Method
670
Table
of Contents
xiii
18.2
Constrained Problems
672
18.2.1
Equality Constraints
673
18.2.2
Inequality Constraints
—
Karush-Kuhn-Tucker
(KKT) Conditions
685
References
690
Chapter
19
Nonlinear Programming Algorithms
691
19.1
Unconstrained Algorithms
691
19.1.1
Direct Search Method
697
19.1.2
Gradient Method
695
19.2
Constrained Algorithms
699
19.2.1
Separable Programming
699
19.2.2
Quadratic Programming
708
19.2.3
Chance-Constrained Programming
713
19.2.4
Linear Combinations Method
778
19.2.5
SUMT Algorithm
727
References
722
Appendix A AMPL Modeling Language
723
A.1 A Rudimentary AMPL Model
723
A.2 Components of AMPL Model
724
A.3 Mathematical Expressions and Computed Parameters
732
A.4 Subsets and Indexed Sets
735
A.5 Accessing External Files
737
A.5.1 Simple Read Files
737
A.5.2 Using Print and Printf to Retrieve Output
739
A.5.3 Input Table Files
739
A.5.4 Output Table Files
742
A.5.5 Spreadsheet Input/Output Tables
744
A.6 Interactive Commands
744
A.7 Iterative and Conditional Execution
of AMPL Commands
746
A.8 Sensitivity Analysis Using AMPl
748
References
748
Appendix
В
Statistical Tables
749
Appendix
С
Partial Solutions to Selected Problems
753
Index
803
This eighth edition continues to build on the strength
of the first seven editions, providing balanced coverage of
the theory, applications, and computations of operations
research. This is a major revision, one that streamlines
the presentation of the text material with emphasis on
the applications and computations in operations
research. Complex mathematical concepts are effectively
explained by means of carefully designed numerical
examples, essentially eliminating the need for formal
mathematical proofs. The integration of practical applica¬
tions of software allows students to test concepts that
otherwise could not be presented effectively. The book
includes fully analyzed practical situations and each
chapter concludes with summary applications borrowed
from published case studies.
Four supplemental chapters plus two additional
appendices
TORA:
the easy-to-use, menu-driven optimization
system
Over
20
general and ready-to-use Excel
spreadsheet templates
Several Excel Solver templates
AMPI®
language (student version) with numerous
fully developed models.
New for the Eighth Edition:
•
AMPL, the powerful commercial modeling language, has been
integrated throughout the book using numerous examples
ranging from linear and network to integer and nonlinear
programming. The syntax of AMPL is given and the content
is cross-referenced within the examples in the book.
•
Chapter
2
is dedicated to linear program modeling, with
applications in the areas of urban renewal, currancy arbitrage,
investment, production planning, blending, scheduling, and
trim loss. This chapter includes end-of-section problems that
deal with topics ranging from water quality management and
traffic control to warfare.
•
Chapter
3
presents the general LP sensitivity analysis in a
simple and straightforward manner as a direct extension of
the simplex tableau computations.
•
Chapter
4
is now dedicated to LP post-optimal analysis based
on duality.
•
An Excel-based combined nearest neighbor-reversal heuristic
is presented for the traveling salesperson problem.
•
Markov chains treatment has been expanded in a new
Chapter
17.
•
Approximately
50
end-of chapter mini-cases of real-life
situations are included. There are more than
1000
end-of-
section problems in the book.
•
Each chapter starts with a study guide that facilitates the
understanding of the material and the effective use of the
accompanying software.
•
Excel spreadsheet implementations are used extensively
throughout the book. The interactive user input in some
spreadsheets is designed to promote a better understanding
of the underlying techniques.
•
The use of Excel Solver has been expanded significantly
throughout the book, particularly in the areas of linear,
network, Integer, and nonlinear programming.
•
The totally new Chapter
24,
on the CD, presents
15
fully
developed real-life applications. The analysis, which often
cuts across more than one OR technique, deals with the
modeling, data collection, and computational aspects of
solving the problem. These applications are cross-referenced
in pertinent chapters to provide an appreciation of the use of
OR techniques in practice.
• TORA
continues to play the key role of tutorial software.
•
All computer-related material has been deliberately
compartmentalized either in separate sections or as
AMPL/Excel/Sofve^ORA moment subsections to minimize
disruptions in the main presentation in the book.
|
| adam_txt |
Contents
Preface
xvii
About the Author
xix
Trademarks
xx
Chapter
1
What Is Operations Research?
1
1.1
Operations Research Models
1
1.2
Solving the OR Model
4
1.3
Queuing and Simulation Models
5
1.4
Art of Modeling
5
1.5
More Than Just Mathematics
7
1.6
Phases of an OR Study
8
1.7
About This Book
10
References
10
Chapter
2
Modeling with Linear Programming
11
2.1
Two-Variable LP Model
12
2.2
Graphical LP Solution
15
2.2.1
Solution of a Maximization Model
16
2.2.2
Solution of a Minimization Model
23
12.3
Selected LP Applications
27
2.3.1
Urban Planning
27
2.3.2
Currency Arbitrage
32
2.3.3
Investment
37
2.3.4
Production Planning and Inventory Control
42
2.3.5
Blending and Refining
51
2.3.6
Manpower Planning
57
2.3.7
Additional Applications
60
2.4
Computer Solution with Excel Solver and AMPL
68
2.4.1
LP Solution with Excel Solver
69
2.4.2
LP Solution with AMPL
73
References
80
Chapter
3
The Simplex Method and Sensitivity Analysis
81
3.1
LP Model in Equation Form
82
3.1.1
Converting Inequalities into Equations
with
Nonnegative Right-Hand
Side
82
3.1.2
Dealing with Unrestricted Variables
84
3.2
Transition from Graphical to Algebraic Solution
85
VII
viii Contents
3.3
The Simplex Method
90
3.3.1
Iterative Nature of the Simplex Method
90
3.3.2
Computational Details of the Simplex Algorithm
93
3.3.3
Summary of the Simplex Method
99
3.4
Artificial Starting Solution
103
3.4.1
M-Method
704
3.4.2
Two-Phase Method
108
3.5
Special Cases in the Simplex Method
113
3.5.1
Degeneracy
113
3.5.2
Alternative Optima
116
3.5.3
Unbounded Solution
119
3.5.4
Infeasible Solution
121
3.6
Sensitivity Analysis
723
3.6.1
Graphical Sensitivity Analysis
123
3.6.2
Algebraic Sensitivity Analysis
—
Changes in the Right-
Hand Side
729
3.6.3
Algebraic Sensitivity Analysis
—
Objective Function
739
3.6.4
Sensitivity Analysis with
TORA,
Solver, and AMPL
746
References
750
Chapter
4
Duality and Post-Optimal Analysis
151
4.1
Definition of the Dual Problem
757
4.2
Primal-Dual Relationships
756
4.2.1
Review of Simple Matrix Operations
756
4.2.2
Simplex Tableau Layout
758
4.2.3
Optimal Dual Solution
759
4.2.4
Simplex Tableau Computations
765
4.3
Economic Interpretation of Duality
769
4.3.1
Economic Interpretation of Dual Variables
770
4.3.2
Economic Interpretation of Dual Constraints
772
4.4
Additional Simplex Algorithms
774
4.4.1
Dual Simplex Method
774
4.4.2
Generalized Simplex Algorithm
780
4.5
Post-Optimal Analysis
787
4.5.1
Changes Affecting Feasibility
782
4.5.2
Changes Affecting Optimality
787
References
797
Chapter
5
Transportation Model and Its Variants
193
5.1
Definition of the Transportation Model
794
5.2
Nontraditional
Transportation Models
207
5.3
The Transportation Algorithm
206
5.3.1
Determination of the Starting Solution
207
5.3.2
Iterative Computations of the Transportation
Algorithm
277
Contents
¡χ
5.3.3 Simplex
Method Explanation of the Method
of Multipliers
220
5.4
The Assignment Model
221
5.4.1
The Hungarian Method
222
5.4.2
Simplex Explanation of the Hungarian Method
228
5.5
The Transshipment Model
229
References
234
Chapter
6
Network Models
235
6.1
Scope and Definition of Network Models
236
6.2
Minimal Spanning Tree Algorithm
239
6.3
Shortest-Route Problem
243
6.3.1
Examples of the Shortest-Route Applications
243
6.3.2
Shortest-Route Algorithms
248
6.3.3
Linear Programming Formulation
of the Shortest-Route Problem
257
6.4
Maximal flow model
263
6.4.1
Enumeration of Cuts
263
6.4.2
Maximal-Flow Algorithm
264
6.4.3
Linear Programming Formulation of Maximal
Flow Mode
273
6.5
CPM and PERT
275
6.5.1
Network Representation
277
6.5.2
Critical Path (CPM) Computations
282
6.5.3
Construction of the Time Schedule
285
6.5.4
Linear Programming Formulation of CPM
292
6.5.5
PERT Calculations
293
References
296
Chapter
7
Advanced Linear Programming
297
7.1
Simplex Method Fundamentals
298
7.1.1
From Extreme Points to Basic Solutions
300
7.1.2
Generalized Simplex Tableau in Matrix Form
303
7.2
Revised Simplex Method
306
7.2.1
Development of the Optimality and Feasibility
Conditions
307
7.2.2
Revised Simplex Algorithm
309
7.3
Bounded-Variables Algorithm
315
7.4
Duality
321
7.4.1
Matrix Definition of the Dual Problem
322
7.4.2
Optimal Dual Solution
322
7.5
Parametric Linear Programming
326
7.5.1
Parametric Changes
¡n C
327
7.5.2
Parametric Changes in
b
330
References
332
Contents
Chapter
8
Coal Programming
333
8.1
A Goal Programming Formulation
334
8.2
Goal Programming Algorithms
338
8.2.1
The Weights Method
338
8.2.2
The Preemptive Method
341
References
348
Chapter
9
Integer Linear Programming
349
9.1
Illustrative Applications
350
9.1.1
Capital Budgeting
350
9.1.2
Set-Covering Problem
354
9.1.3
Fixed-Charge Problem
360
9.1.4
Either-Or and If-Then Constraints
364
9.2
Integer Programming Algorithms
369
9.2.1
Branch-and-Bound (B&B) Algorithm
370
9.2.2
Cutting-Plane Algorithm
379
9.2.3
Computational Considerations in ILP
384
9.3
Traveling Salesperson Problem (TSP)
385
9.3.1
Heuristic Algorithms
389
9.3.2
B&B Solution Algorithm
392
9.3.3
Cutting-Plane Algorithm
395
References
397
Chapter 1O Deterministic Dynamic Programming
399
400
10.1
Recursive Nature of Computations in DP
10.2
Forward and Backward Recursion
403
10.3
Selected DP Applications
405
10.3.1
Knapsack/Fly-Away/Cargo-Loading Model
405
10.3.2
Work-Force Size Model
413
10.3.3
Equipment Replacement Model
476
10.3.4
Investment Model
420
10.3.5
Inventory Models
423
10.4
Problem of Dimensionality
424
References
426
Chapter
11
Deterministic Inventory Models
427
11.1
General Inventory Model
427
11.2
Role of Demand in the Development of Inventory
Models
428
11.3
Static Economic-Order-Quantity (EOQ) Models
430
11.3.1
Classic EOQ model
430
11.3.2
EOQ with Price Breaks
436
11.3.3
Multi-Item EOQ with Storage Limitation
440
11.4
Dynamic EOQ Models
443
11.4.1
No-Setup Model
445
11.4.2
Setup Model
449
References
467
Contents xi
Chapter
12 Review
of
Basic
Probability
463
12.1
Laws of Probability
463
12.1.1
Addition Law of Probability
464
12.1.2
Conditional Law of Probability
465
12.2
Random Variables and Probability Distributions
467
12.3
Expectation of a Random Variable
469
12.3.1
Mean and Variance (Standard Deviation) of a Random
Variable
470
12.3.2
Mean and Variance of Joint Random Variables
472
12.4
Four Common Probability Distributions
475
12.4.1
Binomial Distribution
475
12.4.2
Poisson
Distribution
476
МАЗ
Negative Exponential Distribution
477
12.4.4
Normal Distribution
478
12.5
Empirical Distributions
481
References
488
Chapter
13
Decision Analysis and Games
489
13.1
Decision Making under Certainty
—
Analytic Hierarchy
Process
(ΑΗΡ)
490
13.2
Decision Making under Risk
500
13.2.1
Decision Tree-Based Expected Value Criterion
500
13.2.2
Variations of the Expected Value Criterion
506
13.3
Decision under Uncertainty
515
13.4
Game Theory
520
13.4.1
Optimal Solution of Two-Person Zero-Sum Games
521
13.4.2
Solution of Mixed Strategy Games
524
References
530
Chapter
14
Probabilistic Inventory Models
531
14.1
Continuous Review Models
532
14.1.1
"Probabilitized" EOQ Model
532
14.1.2
Probabilistic EOQ Model
534
14.2
Single-Period Models
539
14.2.1
No-Setup Model (Newsvendor Model)
539
14.2.2
Setup Model (s-S Policy)
543
14.3
Multiperiod Model
545
References
548
Chapter
15
Queuing Systems
549
15.1
Why Study Queues?
550
15.2
Elements of a Queuing Model
557
15.3
Role of Exponential Distribution
553
15.4
Pure Birth and Death Models (Relationship Between
the Exponential and
Poisson
Distributions)
556
15.4.1
Pure Birth Model
556
15.4.2
Pure Death Model
560
xii
Table
of Contents
15.5
Generalized
Poisson
Queuing Model
563
15.6
Specialized
Poisson
Queues
568
15.6.1
Steady-State Measures of Performance
569
15.6.2
Single-Server Models
573
15.6.3
Multiple-Server Models
582
15.6.4
Machine Servicing Model—{M/MfR): (GD/KIK),
R>
К
592
15.7
(M/G/1):(GD/ oo/ oo)—Pollaczek-Khintchine (P-K)
Formula
595
15.8
Other Queuing Models
597
15.9
Queuing Decision Models
597
15.9.1
Cost Models
598
15.9.2
Aspiration Level Model
602
References
604
Chapter
16
Simulation Modeling
6О5
16.1
Monte Carlo Simulation
605
16.2
Types of Simulation
610
16.3
Elements of Discrete-Event Simulation
611
16.3.1
Generic Definition of Events
611
16.3.2
Sampling from Probability Distributions
613
16.4
Generation of Random Numbers
622
16.5
Mechanics of Discrete Simulation
624
16.5.1
Manual Simulation of a Single-Server Model
624
16.5.2
Spreadsheet-Based Simulation of the Single-Server
Model
630
16.6
Methods for Gathering Statistical Observations
633
16.6.1
Subinterval Method
634
16.6.2
Replication Method
635
16.6.3
Regenerative (Cycle) Method
636
16.7
Simulation Languages
638
References
640
Chapter
17
Markov Chains
641
17.1
Definition of a Markov Chain
641
17.2
Absolute and
η
-Step
Transition Probabilities
644
17.3
Classification of the States in a Markov Chain
646
17.4
Steady-State Probabilities and Mean Return Times
of Ergodic Chains
649
17.5
First Passage Time
654
17.6
Analysis of Absorbing States
658
References
663
Chapter
18
Classical Optimization Theory
665
18.1
Unconstrained Problems
665
18.1.1
Necessary and Sufficient Conditions
676
18.1.2
The Newton-Raphson Method
670
Table
of Contents
xiii
18.2
Constrained Problems
672
18.2.1
Equality Constraints
673
18.2.2
Inequality Constraints
—
Karush-Kuhn-Tucker
(KKT) Conditions
685
References
690
Chapter
19
Nonlinear Programming Algorithms
691
19.1
Unconstrained Algorithms
691
19.1.1
Direct Search Method
697
19.1.2
Gradient Method
695
19.2
Constrained Algorithms
699
19.2.1
Separable Programming
699
19.2.2
Quadratic Programming
708
19.2.3
Chance-Constrained Programming
713
19.2.4
Linear Combinations Method
778
19.2.5
SUMT Algorithm
727
References
722
Appendix A AMPL Modeling Language
723
A.1 A Rudimentary AMPL Model
723
A.2 Components of AMPL Model
724
A.3 Mathematical Expressions and Computed Parameters
732
A.4 Subsets and Indexed Sets
735
A.5 Accessing External Files
737
A.5.1 Simple Read Files
737
A.5.2 Using Print and Printf to Retrieve Output
739
A.5.3 Input Table Files
739
A.5.4 Output Table Files
742
A.5.5 Spreadsheet Input/Output Tables
744
A.6 Interactive Commands
744
A.7 Iterative and Conditional Execution
of AMPL Commands
746
A.8 Sensitivity Analysis Using AMPl
748
References
748
Appendix
В
Statistical Tables
749
Appendix
С
Partial Solutions to Selected Problems
753
Index
803
This eighth edition continues to build on the strength
of the first seven editions, providing balanced coverage of
the theory, applications, and computations of operations
research. This is a major revision, one that streamlines
the presentation of the text material with emphasis on
the applications and computations in operations
research. Complex mathematical concepts are effectively
explained by means of carefully designed numerical
examples, essentially eliminating the need for formal
mathematical proofs. The integration of practical applica¬
tions of software allows students to test concepts that
otherwise could not be presented effectively. The book
includes fully analyzed practical situations and each
chapter concludes with summary applications borrowed
from published case studies.
Four supplemental chapters plus two additional
appendices
TORA:
the easy-to-use, menu-driven optimization
system
Over
20
general and ready-to-use Excel
spreadsheet templates
Several Excel Solver templates
AMPI®
language (student version) with numerous
fully developed models.
New for the Eighth Edition:
•
AMPL, the powerful commercial modeling language, has been
integrated throughout the book using numerous examples
ranging from linear and network to integer and nonlinear
programming. The syntax of AMPL is given and the content
is cross-referenced within the examples in the book.
•
Chapter
2
is dedicated to linear program modeling, with
applications in the areas of urban renewal, currancy arbitrage,
investment, production planning, blending, scheduling, and
trim loss. This chapter includes end-of-section problems that
deal with topics ranging from water quality management and
traffic control to warfare.
•
Chapter
3
presents the general LP sensitivity analysis in a
simple and straightforward manner as a direct extension of
the simplex tableau computations.
•
Chapter
4
is now dedicated to LP post-optimal analysis based
on duality.
•
An Excel-based combined nearest neighbor-reversal heuristic
is presented for the traveling salesperson problem.
•
Markov chains treatment has been expanded in a new
Chapter
17.
•
Approximately
50
end-of chapter mini-cases of real-life
situations are included. There are more than
1000
end-of-
section problems in the book.
•
Each chapter starts with a study guide that facilitates the
understanding of the material and the effective use of the
accompanying software.
•
Excel spreadsheet implementations are used extensively
throughout the book. The interactive user input in some
spreadsheets is designed to promote a better understanding
of the underlying techniques.
•
The use of Excel Solver has been expanded significantly
throughout the book, particularly in the areas of linear,
network, Integer, and nonlinear programming.
•
The totally new Chapter
24,
on the CD, presents
15
fully
developed real-life applications. The analysis, which often
cuts across more than one OR technique, deals with the
modeling, data collection, and computational aspects of
solving the problem. These applications are cross-referenced
in pertinent chapters to provide an appreciation of the use of
OR techniques in practice.
• TORA
continues to play the key role of tutorial software.
•
All computer-related material has been deliberately
compartmentalized either in separate sections or as
AMPL/Excel/Sofve^ORA moment subsections to minimize
disruptions in the main presentation in the book. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Taha, Hamdy A. 1937- |
| author_GND | (DE-588)133779432 |
| author_facet | Taha, Hamdy A. 1937- |
| author_role | aut |
| author_sort | Taha, Hamdy A. 1937- |
| author_variant | h a t ha hat |
| building | Verbundindex |
| bvnumber | BV021618778 |
| callnumber-first | T - Technology |
| callnumber-label | T57 |
| callnumber-raw | T57.6 |
| callnumber-search | T57.6 |
| callnumber-sort | T 257.6 |
| callnumber-subject | T - General Technology |
| classification_rvk | QH 400 |
| ctrlnum | (OCoLC)68626787 (DE-599)BVBBV021618778 |
| dewey-full | 658.4/034 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 658 - General management |
| dewey-raw | 658.4/034 |
| dewey-search | 658.4/034 |
| dewey-sort | 3658.4 234 |
| dewey-tens | 650 - Management and auxiliary services |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| edition | 8. ed. |
| format | Book |
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| illustrated | Illustrated |
| index_date | 2024-07-02T14:52:58Z |
| indexdate | 2024-07-09T20:40:03Z |
| institution | BVB |
| isbn | 0131889230 0131360140 |
| language | English |
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| spelling | Taha, Hamdy A. 1937- Verfasser (DE-588)133779432 aut Operations research an introduction Hamdy A. Taha 8. ed. Upper Saddle River, NJ Pearson, Prentice Hall 2007 XX, 813 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Investigación operacional lemb Operations Research Pesquisa operacional larpcal Programación (Matemáticas) lemb Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd rswk-swf Operations Research (DE-588)4043586-6 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Operations Research (DE-588)4043586-6 s DE-604 Verhaltensforschung (DE-588)4062862-0 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833874&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833874&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Taha, Hamdy A. 1937- Operations research an introduction Investigación operacional lemb Operations Research Pesquisa operacional larpcal Programación (Matemáticas) lemb Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd Operations Research (DE-588)4043586-6 gnd |
| subject_GND | (DE-588)4062862-0 (DE-588)4043586-6 (DE-588)4151278-9 |
| title | Operations research an introduction |
| title_auth | Operations research an introduction |
| title_exact_search | Operations research an introduction |
| title_exact_search_txtP | Operations research an introduction |
| title_full | Operations research an introduction Hamdy A. Taha |
| title_fullStr | Operations research an introduction Hamdy A. Taha |
| title_full_unstemmed | Operations research an introduction Hamdy A. Taha |
| title_short | Operations research |
| title_sort | operations research an introduction |
| title_sub | an introduction |
| topic | Investigación operacional lemb Operations Research Pesquisa operacional larpcal Programación (Matemáticas) lemb Operations research Programming (Mathematics) Verhaltensforschung (DE-588)4062862-0 gnd Operations Research (DE-588)4043586-6 gnd |
| topic_facet | Investigación operacional Operations Research Pesquisa operacional Programación (Matemáticas) Operations research Programming (Mathematics) Verhaltensforschung Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833874&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014833874&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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