PRINCIPLES OF SEQUENCING AND SCHEDULING

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1 PRINCIPLES OF SEQUENCING AND SCHEDULING Kenneth R. Baker Tuck School of Business Dartmouth College Hanover, New Hampshire Dan Trietsch College of Engineering American University of Armenia Yerevan, Armenia WILEY A JOHN WILEY & SONS, INC. PUBLICATION

2 CONTENTS Preface xiii 1 Introduction Introduction to Sequencing and Scheduling, Scheduling Theory, Philosophy and Coverage of the Book, 6 References, 8 2 Single-Machine Sequencing Introduction, Preliminaries, Problems Without Due Dates: Elementary Results, Flowtime and Inventory, Minimizing Total Flowtime, Minimizing Total Weighted Flowtime, Problems with Due Dates: Elementary Results, 2"l Lateness Criteria, Minimizing the Number of Tardy Jobs, Minimizing Total Tardiness, Due Dates as Decisions, Summary, 31 References, 31 Exercises, 32

3 vi CONTENTS 3 Optimization Methods for the Single-Machine Problem Introduction, Adjacent Pairwise Interchange Methods, A Dynamic Programming Approach, Dominance Properties, A Branch and Bound Approach, Summary, 53 References, 55 Exercises, 55 4 Heuristic Methods for the Single-Machine Problem Introduction, Dispatching and Construction Procedures, Random Sampling, Neighborhood Search Techniques, Tabu Search, Simulated Annealing, Genetic Algorithms, The Evolutionary Solver, Summary, 79 References, 81 Exercises, 81 5 Earliness and Tardiness Costs Introduction, Minimizing Deviations from a Common Due Date, Four Basic Results, 88 j Due Dates as Decisions, The Restricted Version, Asymmetric Earliness and Tardiness Costs, Quadratic Costs, Job-Dependent Costs, Distinct Due Dates, Summary, 104 References, 105 Exercises, Sequencing for Stochastic Scheduling Introduction, Basic Stochastic Counterpart Models, The Deterministic Counterpart, Minimizing the Maximum Cost, The Jensen Gap, Stochastic Dominance and Association, 123

4 CONTENTS vii 6.7 Using Risk Solver, Summary, 132 References, 134 Exercises, Safe Scheduling Introduction, Meeting Service-Level Targets, Trading Off Tightness and Tardiness, The Stochastic E/T Problem, Setting Release Dates, The Stochastic 17-Problem: A Service-Level Approach, The Stochastic [/-Problem: An Economic Approach, Summary, 160 References, 161 Exercises, Extensions of the Basic Model Introduction, Nonsimultaneous Arrivals, Minimizing the Makespan, Minimizing Maximum Tardiness, Other Measures of Performance, Related Jobs, Minimizing Maximum Tardiness, Minimizing Total Flowtime with Strings, Minimizing Total Flowtime with Parallel Chains, Sequence-Dependent Setup Times', Dynamic Programming Solutions, Branch and Bound Solutions, Heuristic Solutions, Stochastic Models with Sequence-Dependent Setup Times, Setting Tight Due Dates, Revisiting the Tightness/Tardiness Trade-off, Summary, 195 References, 196 Exercises, Parallel-Machine Models Introduction, Minimizing the Makespan, Nonpreemptable Jobs, Nonpreemptable Related Jobs, Preemptable Jobs, 211

5 viii CONTENTS, 9.3 Minimizing Total Flowtime, Stochastic Models, The Makespan Problem with Exponential Processing Times, Safe Scheduling with Parallel Machines, Summary, 221 References, 222 Exercises, Flow Shop Scheduling Introduction, Permutation Schedules, The Two-Machine Problem, Johnson's Rule, A Proof of Johnson's Rule, The Model with Time Lags, The Model with Setups, Special Cases of The Three-Machine Problem, Minimizing the Makespan, Branch and Bound Solutions, Heuristic Solutions, Variations of the m-machine Model, Ordered Flow Shops, Flow Shops with Blocking, No-Wait Flow Shops, Summary, 247 References, 248 Exercises, Stochastic Flow Shop Scheduling Introduction, Stochastic Counterpart Models, Safe Scheduling Models with Stochastic Independence, Flow Shops with Linear Association, Empirical Observations, Summary, 267 References, 268 Exercises, Lot Streaming Procedures for the Flow Shop Introduction, The Basic Two-Machine Model, Preliminaries, The Continuous Version, 274

6 CONTENTS ix The Discrete Version, Models with Setups, The Three-Machine Model with Consistent Sublots, The Continuous Version, The-Discrete Version, The Three-Machine Model with Variable Sublots, Item and Batch Availability, The Continuous Version, The Discrete Version, Computational Experiments, The Fundamental Partition, Denning the Fundamental Partition, A Heuristic Procedure for s Sublots, Summary, 295 References, 297 Exercises, Scheduling Groups of Jobs Introduction, Scheduling Job Families, Minimizing Total Weighted Flowtime, Minimizing Maximum Lateness, Minimizing Makespan in the Two-Machine Flow Shop, Scheduling with Batch Availability, Scheduling with a Batch Processor, Minimizing the Makespan with Dynamic Arrivals, Minimizing Makespan in the Two-Machine Flow Shop, Minimizing Total Flowtime with Dynamic Arrivals, Batch-Dependent Processing Times, Summary, 320 References, 321 Exercises, The Job Shop Problem Introduction, Types of Schedules, Schedule Generation, The Shifting Bottleneck Procedure, Bottleneck Machines, Heuristic and Optimal Solutions, 339

7 x CONTENTS 14.5 Neighborhood Search Heuristics, Summary, 345 References, 346 Exercises, Simulation Models for the Dynamic Job Shop Introduction, Model Elements, Types of Dispatching Rules, Reducing Mean Flowtime, Meeting-Due Dates, Background, Some Clarifying Experiments, Experimental Results, Summary, 369 References, Network Methods for Project Scheduling Introduction, Logical Constraints and Network Construction, Temporal Analysis of Networks, The Time/Cost Trade-off, Traditional Probabilistic Network Analysis, The PERT Method, Theoretical Limitations of PERT, Summary, 393 References, 394 Exercises, 395 < 17 Resource-Constrained Project Scheduling Introduction, Extending the Job Shop Model, Extending the Project Model, Heuristic Construction and Search Algorithms, Construction Heuristics, Neighborhood Search Improvement Schemes, Selecting Priority Lists, Summary, 414 References, 415 Exercises, Safe Scheduling for Projects Introduction, Stochastic Balance Principles For Activity Networks, The Assembly Coordination Model, Balancing a General Project Network, 426

8 CONTENTS xi Additional Examples, Hierarchical Balancing, Crashing Stochastic Activities, Summary, 439 References, 441 Exercises, 441 Appendix A Practical Processing Time Distributions 445 A.I Important Processing Time Distributions, 445 A. 1.1 The Uniform Distribution, 445 A. 1.2 The Exponential Distribution, 446 A. 1.3 The Normal Distribution, 447 A. 1.4 The Lognormal Distribution, 447 A. 1.5 The Parkinson Distribution, 449 A.2 Increasing and Decreasing Completion Rates, 450 A.3 Stochastic Dominance, 451 A.4 Linearly Associated Processing Times, 452 References, 458 Appendix B The Critical Ratio Rule 459 B.I A Basic Trade-off Problem, 459 B.2 Optimal Policy for Discrete Probability Models, 461 B.3 A Special Discrete Case: Equally Likely Outcomes, 463 B.4 Optimal Policy for Continuous Probability Models, 463 B.5 A Special Continuous Case: The Normal Distribution, 467 B.6 Calculating d + ye(r) for the Normal Distribution, 469 References, 470 Appendix C Integer Programming Models for Sequencing 471 C.I Introduction, 471 C.2 The Single-Machine Model, 472 C.2.1 Sequence-Position Decisions, 472 C.2.2 Precedence Decisions, 473 C.2.3 Time-Indexed Decisions, 473 C.3 The Flow Shop Model, 475 References, 477 Name Index 479 Subject Index 483

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