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CONTENTS vii

6 Simplex-Based Sensitivity Case Problem 1 Distribution System Design 336
Appendix 7.1 Excel Solution of Transportation,
Analysis and Duality 254
Assignment and Transshipment Problems 338
6.1 Sensitivity Analysis with the Simplex
Tableau 255
Objective Function Coefficients 255 8 Network Models 344
Right-Hand Side Values 258
8.1 Shortest-Route Problem 345
Simultaneous Changes 265
A Shortest-Route Algorithm 346
6.2 Duality 266
8.2 Minimal Spanning Tree Problem 354
Interpretation of the Dual Variables 268
A Minimal Spanning Tree Algorithm 355
Using the Dual to Identify the Primal Solution 270
8.3 Maximal Flow Problem 357
Finding the Dual of Any Primal Problem 270
Summary 362
Summary 272
Worked Example 362
Worked Example 273
Problems 363
Problems 274
Case Problem Ambulance Routing 368
7 Transportation, Assignment 9 Project Scheduling:
and Transshipment Problems 279 PERT/CPM 370

7.1 Transportation Problem: A Network Model and 9.1 Project Scheduling With Known Activity
a Linear Programming Formulation 280 Times 372
Problem Variations 283 The Concept of a Critical Path 373
A General Linear Programming Model of the Determining the Critical Path 374
Transportation Problem 285 Contributions of PERT/CPM 378
7.2 Transportation Simplex Method: A Special- Summary of the PERT/CPM Critical Path
Purpose Solution Procedure 286 Procedure 379
Phase I: Finding an Initial Feasible Solution 288 Gantt Charts 380
Phase II: Iterating to the Optimal Solution 291 9.2 Project Scheduling With Uncertain Activity
Summary of the Transportation Simplex Times 381
Method 300 The Daugherty Porta-Vac Project 382
Problem Variations 302 Uncertain Activity Times 382
7.3 Assignment Problem: The Network Model and The Critical Path 385
a Linear Programming Formulation 303 Variability in Project Completion Time 386
Problem Variations 305
9.3 Considering Time–Cost Trade-Offs 388
A General Linear Programming Model of the
Crashing Activity Times 389
Assignment Problem 306
Summary 392
Multiple Assignments 307
Worked Example 392
7.4 Assignment Problem: A Special-Purpose Problems 394
Solution Procedure 307 Case Problem R.C. Coleman 401
Finding the Minimum Number of Lines 311 Appendix 9.1 Activity on Arrow Networks 402
Problem Variations 311
7.5 Transshipment Problem: The Network Model
and a Linear Programming Formulation 314 10 Inventory Models 405
Problem Variations 319 10.1 Principles of Inventory Management 406
A General Linear Programming Model of the The Role of Inventory 406
Transshipment Problem 320 Inventory Costs 407
7.6 A Production and Inventory Application 320 10.2 Economic Order Quantity
Summary 324 (EOQ) Model 408
Worked Example 325 The How-Much-to-Order Decision 411
Problems 327 The When-to-Order Decision 413

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