Operations Research: Applications and Algorithms

1434 Pages·2016·2.23 MB·English

by  Wayne L. Winston

Operations
Research
APPLICATIONS
AND ALGORITHMS
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Operations
Research
AP P LI CATI O N S
AN D ALG O R ITH M S
F O U RTH E D ITI O N
Wayne L. Winston
INDIANA UNIVERSITY
WITH CASES BY
Jeffrey B. Goldberg
UNIVERSITY OF ARIZONA
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Brief Contents
1 An Introduction to Model Building 1
2 Basic Linear Algebra 11
3 Introduction to Linear Programming 49
4 The Simplex Algorithm and Goal Programming 127
5 Sensitivity Analysis:An Applied Approach 227
6 Sensitivity Analysis and Duality 262
7 Transportation, Assignment, and Transshipment Problems 360
8 Network Models 413
9 Integer Programming 475
10 Advanced Topics in Linear Programming 562
11 Nonlinear Programming 610
12 Review of Calculus and Probability 707
13 Decision Making under Uncertainty 737
14 Game Theory 803
15 Deterministic EOQ Inventory Models 846
16 Probabilistic Inventory Models 880
17 Markov Chains 923
18 Deterministic Dynamic Programming 961
19 Probabilistic Dynamic Programming 1016
20 Queuing Theory 1051
21 Simulation 1145
22 Simulation with Process Model 1191
23 Spreadsheet Simulation with the Excel Add-in @Risk 1212
24 Forecasting Models 1275
v
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Contents
Preface xii 3.3 Special Cases 63
About the Author xvi 3.4 A Diet Problem 68
3.5 A Work-Scheduling Problem 72
3.6 A Capital Budgeting Problem 76
An Introduction to 3.7 Short-Term Financial Planning 82
1
3.8 Blending Problems 85
Model-Building
1
3.9 Production Process Models 95
1.1 An Introduction to Modeling 1 3.10 Using Linear Programming to Solve
1.2 The Seven-Step Model-Building Multiperiod Decision Problems: An
Process 5 Inventory Model 100
1.3 CITGO Petroleum 6 3.1l Multiperiod Financial Models 105
1.4 San Francisco Police Department 3.12 Multiperiod Work Scheduling 109
Scheduling 7
1.5 GE Capital 9
The Simplex Algorithm and Goal
4
Programming
127
Basic Linear Algebra
2 11
4.1 How to Convert an LP to Standard
2.1 Matrices and Vectors 11 Form 127
2.2 Matrices and Systems of Linear 4.2 Preview of the Simplex Algorithm 130
Equations 20
4.3 Direction of Unboundedness 134
2.3 The Gauss-Jordan Method for Solving 4.4 Why Does an LP Have an
Systems of Linear Equations 22
Optimal bfs? 136
2.4 Linear Independence and Linear 4.5 The Simplex Algorithm 140
Dependence 32
4.6 Using the Simplex Algorithm to Solve
2.5 The Inverse of a Matrix 36 Minimization Problems 149
2.6 Determinants 42 4.7 Alternative Optimal Solutions 152
4.8 Unbounded LPs 154
4.9 The LINDO Computer Package 158
Introduction to Linear Programming
3 49
4.10 Matrix Generators, LINGO, and Scaling
of LPs 163
3.1 What Is a Linear Programming
Problem? 49 4.11 Degeneracy and the Convergence of the
Simplex Algorithm 168
3.2 The Graphical Solution of Two-Variable
Linear Programming Problems 56 4.12 The Big M Method 172
vi
4.13 The Two-Phase Simplex Method 178
Transportation, Assignment, and
4.14 Unrestricted-in-Sign Variables 184 7
4.15 Karmarkar's Method for Solving LPs 190 Transshipment Problems 360
4.16 Multiattribute Decision Making in the
7.1 Formulating Transportation Problems 360
Absence of Uncertainty: Goal
Programming 191 7.2 Finding Basic Feasible Solutions for
Transportation Problems 373
4.l7 Using the Excel Solver to Solve LPs 202
7.3 The Transportation Simplex Method 382
7.4 Sensitivity Analysis for Transportation
Sensitivity Analysis: Problems 390
5
7.5 Assignment Problems 393
An Applied Approach
227
7.6 Transshipment Problems 400
5.1 A Graphical Introduction to Sensitivity
Analysis 227
5.2 The Computer and Sensitivity 8 Network Models 413
Analysis 232
8.1 Basic Definitions 413
5.3 Managerial Use of Shadow Prices 246
8.2 Shortest-Path Problems 414
5.4 What Happens to the Optimal z-Value
If the Current Basis Is No Longer 8.3 Maximum-Flow Problems 419
Optimal? 248 8.4 CPM and PERT 431
8.5 Minimum-Cost Network Flow
Problems 450
Sensitivity Analysis and Duality
6 262 8.6 Minimum Spanning Tree Problems 456
8.7 The Network Simplex Method 459
6.1 A Graphical Introduction to Sensitivity
Analysis 262
6.2 Some Important Formulas 267
Integer Programming
9 475
6.3 Sensitivity Analysis 275
6.4 Sensitivity Analysis When More Than 9.1 Introduction to Integer Programming 475
One Parameter Is Changed: The 100%
9.2 Formulating Integer Programming
Rule 289
Problems 477
6.5 Finding the Dual of an LP 295
9.3 The Branch-and-Bound Method for
6.6 Economic Interpretation of the Dual Solving Pure Integer Programming
Problem 302 Problems 5l2
6.7 The Dual Theorem and Its 9.4 The Branch-and-Bound Method for
Consequences 304 Solving Mixed Integer Programming
6.8 Shadow Prices 313 Problems 523
6.9 Duality and Sensitivity Analysis 323 9.5 Solving Knapsack Problems by the
Branch-and-Bound Method 524
6.10 Complementary Slackness 325
9.6 Solving Combinatorial Optimization
6.11 The Dual Simplex Method 329
Problems by the Branch-and-Bound
6.12 Data Envelopment Analysis 335
Method 527
9.7 Implicit Enumeration 540
9.8 The Cutting Plane Algorithm 545
Contents vii
Advanced Topics in Linear Decision Making
10 13
Programming under Uncertainty
562 737
10.1 The Revised Simplex Algorithm 562 13.1 Decision Criteria 737
10.2 The Product Form of the Inverse 567 13.2 Utility Theory 741
10.3 Using Column Generation to Solve 13.3 Flaws in Expected Maximization
Large-Scale LPs 570 of Utility:Prospect Theory and
10.4 The Dantzig-Wolfe Decomposition Framing Effects 755
Algorithm 576 13.4 Decision Trees 758
10.5 The Simplex Method for Upper-Bounded 13.5 Bayes’Rule and Decision Trees 767
Variables 593
13.6 Decision Making with
10.6 Karmarkar's Method for Solving LPs 597 Multiple Objectives 773
13.7 The Analytic Hierarchy Process 785
Nonlinear Programming
11 610
Game Theory
14 803
11.1 Review of Differential Calculus 610
11.2 Introductory Concepts 616 14.1 Two-Person Zero-Sum and Constant-Sum
11.3 Convex and Concave Functions 630 Games: Saddle Points 803
11.4 Solving NLPs with One Variable 637 14.2 Two-Person Zero-Sum Games:
Randomized Strategies, Domination, and
11.5 Golden Section Search 649
Graphical Solution 807
11.6 Unconstrained Maximization and
14.3 Linear Programming and Zero-Sum
Minimization with Several Variables 655
Games 816
11.7 The Method of Steepest Ascent 660
14.4 Two-Person Nonconstant-Sum
11.8 Lagrange Multipliers 663 Games 827
11.9 The Kuhn–Tucker Conditions 670 14.5 Introduction to n-Person Game
11.10 Quadratic Programming 680 Theory 832
11.11 Separable Programming 688 14.6 The Core of an n-Person Game 834
11.12 The Method of Feasible Directions 693 14.7 The Shapley Value 837
11.13 Pareto Optimality and Tradeoff
Curves 695
Deterministic EOQ
15
Inventory Models
846
Review of Calculus
12
and Probability 15.1 Introduction to Basic
707
Inventory Models 846
12.1 Review of Integral Calculus 707 15.2 The Basic Economic Order
Quantity Model 848
12.2 Differentiation of Integrals 710
15.3 Computing the Optimal Order
12.3 Basic Rules of Probability 710
Quantity When Quantity
12.4 Bayes’Rule 713 Discounts Are Allowed 859
12.5 Random Variables, Mean, Variance, 15.4 The Continuous Rate EOQ Model 865
and Covariance 715
15.5 The EOQ Model with Back
12.6 The Normal Distribution 722 Orders Allowed 868
12.7 z-Transforms 730
viii Contents
15.6 When to Use EOQ Models 872 18.6 Formulating Dynamic
15.7 Multiple-Product EOQ Models 873 Programming Recursions 989
18.7 The Wagner–Whitin Algorithm
and the Silver–Meal Heuristic 1001
Probabilistic Inventory Models 18.8 Using Excel to Solve Dynamic
16 880
Programming Problems 1006
16.1 Single-Period Decision Models 880
16.2 The Concept of Marginal Analysis 880
Probabilistic Dynamic
16.3 The News Vendor Problem: 19
Discrete Demand 881 Programming
1016
16.4 The News Vendor Problem:
Continuous Demand 886 19.1 When Current Stage Costs Are
16.5 Other One-Period Models 888 Uncertain, but the Next Period’s
State Is Certain 1016
16.6 The EOQ with Uncertain Demand:
The (r, q) and (s, S) Models 890 19.2 A Probabilistic Inventory Model 1019
16.7 The EOQ with Uncertain Demand: 19.3 How to Maximize the Probability of a
The Service Level Approach to Favorable Event Occurring 1023
Determining Safety Stock Level 898 19.4 Further Examples of Probabilistic
16.8 (R, S) Periodic Review Policy 907 Dynamic Programming Formulations 1029
16.9 The ABCInventory 19.5 Markov Decision Processes 1036
Classification System 911
16.10 Exchange Curves 913
Queuing Theory
20 1051
Markov Chains 20.1 Some Queuing Terminology 1051
17 923
20.2 Modeling Arrival and Service
17.1 What Is a Stochastic Process? 923 Processes 1053
17.2 What Is a Markov Chain? 924 20.3 Birth–Death Processes 1053
17.3 n-Step Transition Probabilities 928 20.4 The M/M/1/GD/∞/∞Queuing System
and the Queuing Formula L(cid:2) (cid:3)W1072
17.4 Classification of States
in a Markov Chain 931 20.5 The M/M/1/GD/c/∞Queuing System 1083
17.5 Steady-State Probabilities and Mean 20.6 The M/M/s/GD/∞/∞Queuing
First Passage Times 934 System 1087
17.6 Absorbing Chains 942 20.7 The M/G/∞/GD/∞/∞and
GI/G/∞/GD/∞/∞Models 1095
17.7 Work-Force Planning Models 950
20.8 The M/G/1/GD/∞/∞Queuing System 1097
20.9 Finite Source Models:The Machine
Repair Model 1099
Deterministic Dynamic
18
20.10 Exponential Queues in Series and
Programming
961 Open Queuing Networks 1104
20.11 The M/G/s/GD/s/∞System (Blocked
18.1 Two Puzzles 961
Customers Cleared) 1112
18.2 ANetwork Problem 962
20.12 How to Tell Whether Interarrival Times
18.3 An Inventory Problem 969
and Service Times Are Exponential 1115
18.4 Resource-Allocation Problems 974
20.13 Closed Queuing Networks 1119
18.5 Equipment-Replacement Problems 985
Contents ix
20.14 An Approximation for the G/G/m 23.5 The RISKGENERAL Function 1244
Queuing System 1124
23.6 The RISKCUMULATIVE
20.15 Priority Queuing Models 1126 Random Variable 1248
20.16 Transient Behavior of 23.7 The RISKTRIGEN Random Variable 1249
Queuing Systems 1131
23.8 Creating a Distribution Based
on a Point Forecast 1250
23.9 Forecasting the Income of a
21 Simulation 1145 Major Corporation 1252
23.10 Using Data to Obtain Inputs for New
21.1 Basic Terminology 1145
Product Simulations 1256
21.2 An Example of a Discrete-Event
23.11 Simulation and Bidding 1267
Simulation 1146
23.12 Playing Craps with @Risk 1269
21.3 Random Numbers and Monte Carlo
23.13 Simulating the NBAFinals 1271
Simulation 1153
21.4 An Example of Monte Carlo
Simulation 1158
Forecasting Models
21.5 Simulations with Continuous 24 1275
Random Variables 1162
24.1 Moving-Average Forecast Methods 1275
21.6 An Example of a Stochastic
24.2 Simple Exponential Smoothing 1281
Simulation 1173
24.3 Holt’s Method:Exponential Smoothing
21.7 Statistical Analysis in Simulations 1180
with Trend 1283
21.8 Simulation Languages 1183
24.4 Winter’s Method:Exponential Smoothing
21.9 The Simulation Process 1184
with Seasonality 1286
24.5 Ad Hoc Forecasting 1292
24.6 Simple Linear Regression 1302
Simulation with Process Model
22 1191
24.7 Fitting Nonlinear Relationships 1312
22.1 Simulating an M/M/1 Queuing 24.8 Multiple Regression 1317
System 1191
22.2 Simulating an M/M/2 System 1195
@Risk Crib Sheet
22.3 Simulating aSeries System 1199 Appendix 1: 1336
22.4 Simulating Open Queuing Networks 1203
22.5 Simulating Erlang Service Times 1207
22.6 What Else Can Process Model Do? 1210 Cases
Appendix 2: 1350
Case 1 Help, I’m Not Getting Any
Simulation with the Excel Younger 1351
23
Add-in @Risk Case 2 Solar Energy for Your Home 1351
1212
Case 3 Golf-Sport: Managing Operations 1352
23.1 Introduction to @Risk: Case 4 Vision Corporation: Production Planning
The News Vendor Problem 1212 and Shipping 1355
23.2 Modeling Cash Flows from Case 5 Material Handling in a General
a New Product 1222 Mail-Handling Facility 1356
23.3 Product Scheduling Models 1232 Case 6 Selecting Corporate Training
23.4 Reliability and Warranty Modeling 1238 Programs 1359
x Contents