OPERATIONS RESEARCH： Mathematical Programming【2025|PDF下载-Epub版本|mobi电子书|kindle百度云盘下载】

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1Introduction to Operations Research1

1.1 The Methodology of Operations Research1

1.2 Successful Applications of Operations Research5

1.3 Where to Read More about Operations Research6

1.4 About This Book7

2Introduction to Linear Programming8

2.1 What Is a Linear Programming Problem？8

2.2 The Graphical Solution of Two-Variable Linear Programming Problems15

2.3 Special Cases23

2.4 A Diet Problem29

2.5 A Work-Scheduling Problem32

2.6 A Capital Budgeting Problem36

2.7 Short- Term Financial Planning40

2.8 Blending Problems43

2.9 Production Process Models53

2.10 Using Linear Programming to Solve Multiperiod Decision Problems： An Inventory Model58

2.11 Multiperiod Financial Models63

2.12 Multiperiod Work Scheduling67

3The Simplex Algorithm83

3.1 How to Convert an LP to Standard Form83

3.2 Preview of the Simplex Algorithm86

3.3 The Simplex Algorithm92

3.4 Using the Simplex Algorithm to Solve Minimization Problems102

3.5 Alternative Optimal Solutions105

3.6 Unbounded LPs107

3.7 The LINDO Computer Package110

3.8 Matrix Generators， LINGO， and Scaling of LPs114

3.9 Degeneracy and the Convergence of the Simplex Algorithm119

3.10 The Big M Method123

3.11 The Two-Phase Simplex Method129

3.12 Variables That Are Unrestricted in Sign134

3.13 Karmarkar’s Method for Solving LPs140

3.14 Solving LPs with Spreadsheets141

4Sensitivity Analysis and Duality155

4.1 A Graphical Introduction to Sensitivity Analysis155

4.2 Some Important Formulas161

4.3 Sensitivity Analysis169

4.4 Sensitivity Analysis When More Than One Parameter Is Changed： The 100% Rule184

4.5 Finding the Dual of an LP194

4.6 Economic Interpretation of the Dual Problem197

4.7 The Dual Theorem and Its Consequences200

4.8 Shadow Prices210

4.9 Duality and Sensitivity Analysis220

4.10 Complementary Slackness223

4.11 The Dual Simplex Method227

4.12 An Application of Dual Prices： Data Envelopment Analysis （DEA）233

5Integer Programming260

5.1 Introduction to Integer Programming260

5.2 Formulating Integer Programming Problems263

5.3 The Branch-and-Bound Method for Solving Pure Integer Programming Problems298

5.4 The Brand-and-Bound Method for Solving Mixed Programming Problems311

5.5 Solving Knapsack Problems by the Branch-and-Bound Method312

5.6 Solving Combinatorial Optimization Problems by the Branch-and-Bound Method315

5.7 Implicit Enumeration329

5.8 The Cutting Plane Algorithm335

6Advanced Topics in Linear Programming350

6.1 The Revised Simplex Algorithm350

6.2 The Product Form of the Inverse355

6.3 Using Column Generation to Solve Large-Scale LPs358

6.4 The Dantzig-Wolfe Decomposition Algorithm365

6.5 The Simplex Method for Upper-Bounded Variables383

6.6 Karmarkar’s Method for Solving LPs387

7Nonlinear Programming402

7.1 Introductory Concepts402

7.2 Convex and Concave Functions415

7.3 Solving NLPs with One Variable423

7.4 Golden Section Search431

7.5 Unconstrained Maximization and Minimization with Several Variables437

7.6 The Method of Steepest Ascent443

7.7 Lagrange Multipliers447

7.8 The Kuhn-Tucker Conditions454

7.9 Quadratic Programming464

7.10 Separable Programming473

7.11 The Method of Feasible Directions479

8Deterministic Dynamic Programming490

8.1 Two Puzzles490

8.2 A Network Problem492

8.3 An Inventory Problem499

8.4 Resource Allocation Problems505

8.5 Equipment Replacement Problems517

8.6 Formulating Dynamic Programming Recursions520

8.7 The Wagner-Whitin Algorithm and the Silver-Meal Heuristic533

8.8 Forward Recursions539

8.9 Using Spreadsheets to Solve Dynamic Programming Problems542