OPERATIONS RESEARCH：AN INTRODUCTIONPDF|Epub|txt|kindle电子书版本网盘下载

OPERATIONS RESEARCH：AN INTRODUCTIONPDF格式电子书版下载

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

Chapter 1 What Is Operations Research？1

1.1 Operations Research Models1

1.2 Solving the OR Model4

1.3 Queuing and Simulation Models5

1.4 Art of Modeling5

1.5 More Than Just Mathematics6

1.6 Phases of an OR Study8

1.7 About This Book9

Chapter 2 Introduction to Linear Programming11

2.1 Two-Variable LP Model11

2.2 Graphical LP Solution14

2.2.1 Solution of a Maximization Model15

2.2.2 Solution of a Minimization Model18

2.2.3 Graphical Solution with TORA20

2.3 Graphical Sensitivity Analysis23

2.3.1 Changes in the Objective Function Coefficients24

2.3.2 Change in Availability of Resources27

2.3.3 Unit Worth of a Resource28

2.4 Computer Solution of LP Problems33

2.4.1 LP Solution with TORA33

2.4.2 LP Solution with Excel Solver36

2.4.3 LP Solution with LINGO and AMPL38

2.5 Analysis of Selected LP Models47

Selected References66

Comprehensive Problems67

Chapter 3 The SimplexMethod71

3.1 LP Solution Space in Equation Form71

3.1.1 Converting Inequalities into Equations71

3.1.2 Dealing with Unrestricted Variables73

3.2 Transition from Graphical to Algebraic Solution75

3.3 The Simplex Method80

3.3.1 Iterative Nature of the Simplex Method80

3.3.2 Computational Details of the Simplex Algorithm83

3.3.3 Simplex iterations with TORA92

3.4 Artificial Starting Solution94

3.4.1 M-Method94

3.4.2 Two-Phase Method98

3.5 Special Cases in Simplex Method Application103

3.5.1 Degeneracy103

3.5.2 Alternative Optima106

3.5.3 Unbounded Solution109

3.5.4 Infeasible Solution110

Selected References112

Comprehensive Problems112

Chapter 4 Duality and Sensitivity Analysis115

4.1 Definition of the Dual Problem115

4.2 Primal-Dual Relationships120

4.2.1 Review of Simple Matrix Operations120

4.2.2 Simplex Tableau Layout122

4.2.3 Optimal Dual Solution122

4.2.4 Simplex Tableau Computations126

4.2.5 Primal and Dual Objective Value130

4.3 Economic Interpretation of Duality132

4.3.1 Economic Interpretation of Dual Variables132

4.3.2 Economic Interpretation of Dual Constraints135

4.4 Additional Simplex Algorithms for LP137

4.4.1 Dual Simplex Method137

4.4.2 Generalized Simplex Algorithm143

4.5 Postoptimal or Sensitivity Analysis144

4.5.1 Changes Affecting Feasibility145

4.5.2 Changes Affecting Optimality155

Selected References161

Comprehensive Problems162

Chapter 5 Transportation Model and Its Variants165

5.1 Definition of the Transportation Model165

5.2 Nontraditional Transportation Models172

5.3 The Transportation Algorithm177

5.3.1 Determination of the Starting Solution178

5.3.2 Iterative Computations of the Transportation Algorithm182

5.3.3 Solution of the Transportation Model with TORA187

5.3.4 Simplex Method Explanation of the Method of Multipliers195

5.4 The Assignment Model196

5.4.1 The Hungarian Method197

5.4.2 Simplex Explanation of the Hungarian Method202

5.5 The Transshipment Model203

Selected References208

Comprehensive Problems208

Chapter 6 Network Models213

6.1 Network Definitions214

6.2 Minimal Spanning Tree Algorithm215

6.3 Shortest-Route Problem220

6.3.1 Examples of the Shortest-Route Applications220

6.3.2 Shortest-Route Algorithms224

6.3.3 Linear Programming Formulation of the Shortest-Route Problem234

6.3.4 Excel Spreadsheet Solution of the Shortest-Route Problem237

6.4 Maximal Flow Model239

6.4.1 Enumeration of Cuts240

6.4.2 Maximal Flow Algorithm241

6.4.3 Linear Programming Formulation of the Maximum Flow Model250

6.4.4 Excel Spreadsheet Solution of the Maximum Flow Model250

6.5 Minimum-Cost Capacitated Flow Problem252

6.5.1 Network Representation252

6.5.2 Linear Programming Formulation254

6.5.3 Capacitated Network Simplex Algorithm259

6.5.4 Excel Spreadsheet Solution of the Minimum-Cost Capacitated Flow Model265

6.6 CPM and PERT266

6.6.1 Network Representation267

6.6.2 Critical Path （CPM） Computations272

6.6.3 Construction of the Time Schedule275

6.6.4 Linear Programming Formulation of CPM281

6.6.5 PERT Networks283

Selected References286

Comprehensive Problems286

Chapter 7 Advanced Linear Programming289

7.1 Simplex Method Fundamentals289

7.1.1 From Extreme Points to Basic Solutions290

7.1.2 Generalized Simplex Tableau in Matrix Form294

7.2 Revised Simplex Method297

7.2.1 Development of the Optimality and Feasibility Conditions298

7.2.2 Revised Simplex Algorithm300

7.3 Bounded Variables Algorithm305

7.4 Decomposition Algorithm312

7.5 Duality322

7.5.1 Matrix Definition of the Dual Problem322

7.5.2 Optimal Dual Solution322

7.6 Parametric Linear Programming326

7.6.1 Parametric Changes in C327

7.6.2 Parametric Changes in b329

7.7 Karmarkar Interior-Point Method332

7.7.1 Basic Idea of the Interior-Point Algorithm332

7.7.2 Interior-Point Algorithm334

Selected References344

Comprehensive Problems344

Chapter 8 Goal Programming347

8.1 A Goal Programming Formulation347

8.2 Goal Programming Algorithms352

8.2.1 The Weights Method352

8.2.2 The Preemptive Method354

Selected References359

Comprehensive Problems359

Chapter 9 Integer Linear Programming361

9.1 Illustrative Applications361

9.2 Integer Programming Algorithms372

9.2.1 Branch-and-Bound （B&B） Algorithm373

9.2.2 TORA-Generated B&B Tree379

9.2.3 Cutting Plane Algorithm384

9.2.4 Computational Considerations in ILP389

9.3 Solution of the Traveling Salesperson Problem390

9.3.1 B&B Solution Algorithm393

9.3.2 Cutting Plane Algorithm396

Selected References397

Comprehensive Problems397

Chapter 10 Deterministic Dynamic Programming401

10.1 Recursive Nature of Computations in DP401

10.2 Forward and Backward Recursion404

10.3 Selected DP Applications406

10.3.1 Knapsack/Flyaway Kit/Cargo-Loading Model407

10.3.2 Workforce Size Model415

10.3.3 Equipment Replacement Model418

10.3.4 Investment Model421

10.3.5 Inventory Models425

10.4 Problem of Dimensionality425

Selected References428

Comprehensive Problems428

Chapter 11 Deterministic InventoryModels429

11.1 General Inventory Model429

11.2 Static Economic Order Quantity （EOQ） Models430

11.2.1 Classic EOQ Model430

11.2.2 EOQ with Price Breaks435

11.2.3 Multi-Item EOQ with Storage Limitation439

11.3 Dynamic EOQ Models443

11.3.1 No-Setup Model444

11.3.2 Setup Model448

Selected References460

Comprehensive Problems460

Chapter 12 Review of Basic Probability463

12.1 Laws of Probability463

12.1.1 Addition Law of Probability464

12.1.2 Conditional Law of Probability465

12.2 Random Variables and Probability Distributions467

12.3 Expectation of a Random Variable469

12.3.1 Mean and Variance of a Random Variable470

12.3.2 Mean and Variance of Joint Random Variables471

12.4 Four Common Probability Distributions474

12.4.1 Binomial Distribution474

12.4.2 Poisson Distribution476

12.4.3 Negative Exponential Distribution477

12.4.4 Normal Distribution478

12.5 Empirical Distributions480

Selected References489

Chapter 13 Forecasting Models491

13.1 Moving Average Technique491

13.2 Exponential Smoothing495

13.3 Regression497

Selected References501

Comprehensive Problem502

Chapter 14 Decision Analysis and Games503

14.1 Decision Making under Certainty-Analytic Hierarchy Process（AHP）503

14.2 Decision Making under Risk513

14.2.1 Expected Value Criterion514

14.2.2 Variations of the Expected Value Criterion519

14.3 Decision under Uncertainty527

14.4 Game Theory532

14.4.1 Optimal Solution of Two-Person Zero-Sum Games532

14.4.2 Solution of Mixed Strategy Games536

Selected References543

Comprehensive Problems543

Chapter 15 Probabilistic Dynamic Programming547

15.1 A Game of Chance547

15.2 Investment Problem550

15.3 Maximization of the Event of Achieving a Goal554

Selected References558

Comprehensive Problem558

Chapter 16 Probabilistic Inventory Models559

16.1 Continuous Review Models559

16.1.1 “Probabilitized” EOQ Model559

16.1.2 Probabilistic EOQ Model562

16.2 Single-Period Models567

16.2.1 No Setup Model567

16.2.2 Setup Model （s-S Policy）571

16.3 Multiperiod Model573

Selected References576

Comprehensive Problems576

Chapter 17 Queuing Systems579

17.1 Why Study Queues？579

17.2 Elements of a Queuing Model581

17.3 Role of Exponential Distribution582

17.4 Pure Birth and Death Models （Relationship Between the Exponential and Poisson Distributions）585

17.4.1 Pure Birth Model586

17.4.2 Pure Death Model590

17.5 Generalized Poisson Queuing Model593

17.6 Specialized Poisson Queues597

17.6.1 Steady-State Measures of Performance599

17.6.2 Single-Server Models602

17.6.3 Multiple-Server Models611

17.6.4 Machine Servicing Model—（M/M/R）：（GDIK/K），R<K621

17.7 （M/G/1）：（GD/∞/∞）—Pollaczek-Khintchine （P-K） Formula624

17.8 Other Queuing Models627

17.9 Queuing Decision Models627

17.9.1 Cost Models627

17.9.2 Aspiration Level Model632

Selected References634

Comprehensive Problems634

Chapter 18 Simulation Modeling639

18.1 Monte Carlo Simulation639

18.2 Types of Simulation644

18.3 Elements of Discrete Event Simulation645

18.3.1 Generic Definition of Events645

18.3.2 Sampling from Probability Distributions647

18.4 Generation of Random Numbers656

18.5 Mechanics of Discrete Simulation657

18.5.1 Manual Simulation of a Single-Server Model657

18.5.2 Spreadsheet-Based Simulation of the Single-Server Model663

18.6 Methods for Gathering Statistical Observations666

18.6.1 Subinterval Method667

18.6.2 Replication Method669

18.6.3 Regenerative （Cycle） Method669

18.7 Simulation Languages672

Selected References674

Chapter 19 Markovian Decision Process675

19.1 Scope of the Markovian Decision Problem：The Gardener Problem675

19.2 Finite-Stage Dynamic Programming Model677

19.3 Infinite-Stage Model681

19.3.1 Exhaustive Enumeration Method681

19.3.2 Policy Iteration Method Without Discounting684

19.3.3 Policy Iteration Method with Discounting687

19.4 Linear Programming Solution690

19.5 Appendix： Review of Markov Chains693

19.5.1 Markov Processes694

19.5.2 Markov Chains694

Selected References700

Chapter 20 Classical Optimization Theory701

20.1 Unconstrained Problems701

20.1.1 Necessary and Sufficient Conditions702

20.1.2 The Newton-Raphson Method706

20.2 Constrained Problems708

20.2.1 Equality Constraints708

20.2.2 Inequality Constraints723

Selected References730

Chapter 21 Nonlinear Programming Algorithms731

21.1 Unconstrained Algorithms731

21.1.1 Direct Search Method731

21.1.2 Gradient Method735

21.2 Constrained Algorithms738

21.2.1 Separable Programming739

21.2.2 Quadratic Programming747

21.2.3 Geometric Programming752

21.2.4 Stochastic Programming757

21.2.5 Linear Combinations Method761

21.2.6 SUMT Algorithm763

Selected References764

Appendix A Review of Vectors and Matrices765

A.1 Vectors765

A.1.1 Definition of a Vector765

A.1.2 Addition （Subtraction） of Vectors765

A.1.3 Multiplication of Vectors by Scalars766

A.1.4 Linearly Independent Vectors766

A.2 Matrices766

A.2.1 Definition of a Matrix766

A.2.2 Types of Matrices766

A.2.3 Matrix Arithmetic Operations767

A.2.4 Determinant of a Square Matrix768

A.2.5 Nonsingular Matrix770

A.2.6 Inverse of a Nonsingular Matrix770

A.2.7 Methods of Computing the Inverse of Matrix771

A.3 Quadratic Forms775

A.4 Convex and Concave Functions777

Selected References777

Problems777

Appendix B TORA Primer779

B.1 Main Menu779

B.2 Input Mode and Format780

B.3 Input Data Screen780

B.4 Solve/Modify Menu781

B.5 Output Format782

B.6 Output Results782

Appendix C Statistical Tables785

Appendix D Partial Answers to Selected Problems789

Index825