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Elements of Scheduling Collected and Edited by Jan Karel Lenstra and David B Elements of Scheduling collected and edited by Jan Karel Lenstra and David B. Shmoys This website presents the fragments of a book on machine scheduling. Work on the book started in 1977 but was never completed. The existing material is now made available for teaching purposes. PRELIMINARIES Chapter 1 Deterministic machine scheduling problems Chapter 2 Tools from algorithms and complexity theory THE SINGLE MACHINE Chapter 3 Minmax criteria Chapter 4 Weighted sum of completion times Chapter 5 Weighted number of late jobs PARALLEL MACHINES Chapter 8 Minsum criteria Chapter 9 Minmax criteria, no preemption Chapter 10 Minmax criteria with preemption MULTI-OPERATION MODELS Chapter 12 Open shops Chapter 13 Flow shops Chapter 14 Job shops MORE SCHEDULING Chapter 15 Stochastic scheduling models Chapter 16 Scheduling in practice BIBLIOGRAPHY Bibliography 1 elements_of_scheduling.pdf January 15, 2020 1 SURVEY PAPERS Graham, Lawler, Lenstra, and Rinnooy Kan [1979] Lawler, Lenstra, Rinnooy Kan, and Shmoys [1993] Lenstra [1998] © Centrum Wiskunde & Informatica — Jan Karel Lenstra Back to top 2 elements_of_scheduling.pdf January 15, 2020 2 About Elements of Scheduling collected and edited by Jan Karel Lenstra and David B. Shmoys This website presents the fragments of a book on machine scheduling. Work on the book started in 1977 but was never completed. The existing material is now made available for teaching purposes. In the winter of 1976, Alexander Rinnooy Kan and Jan Karel Lenstra defended their PhD theses at the University of Amsterdam. Gene Lawler was on their committees. It was a natural idea to turn the theses into a textbook on schedul- ing. They set out to compile a survey with Ron Graham (1979), but progress on the book was hampered by the many research opportunities offered by the field. After David Shmoys joined the team in the mid 1980’s, several chapters were drafted, and the survey was rewritten (1993). Gene passed away in 1994. Colleagues were asked to contribute chapters or to complete existing drafts. However, by the turn of the century the project was losing its momentum, and finite convergence to completion fell beyond our reach. Over the years, several chapters have been used in the classroom. We continue to receive requests from colleagues who look for a text on the elements of scheduling at an advanced undergraduate or early graduate level. What exists is now available on this website. We have made a marginal effort in patching it upat some places but essentially put it up as it was written long ago. We did make an attempt to include most of the citations in the bibliography. We owe many thanks and apologies to our colleagues who contributed chapters that waited years to be published. We hope that the material, in spite of all the gaps and omissions that the reader will encounter, will serve a useful purpose. The help of Michael Guravage (Centrum Wiskunde & Informatica) and Shijiin Rajakrishnan (Cornell University) in formatting the chapters and realizing the website is gratefully acknowledged. Below we review the status of each of the chapters and provide pointers to the pdf files. PRELIMINARIES 1. Deterministic machine scheduling problems Eugene L. Lawler, Jan Karel Lenstra, Alexander H.G. Rinnooy Kan, David B. Shmoys Chapter 1 defines the class of scheduling problems under consideration and introduces the three-field classification. Notes and references are up todate until about 1990. 1 about.pdf January 15, 2020 3 2. Tools from algorithms and complexity theory David P. Williamson Chapter 2 reviews the tools and concepts from combinatorial optimization that are useful in designing scheduling algorithms: linear programming, network flows, dynamic programming, polynomial-time solvability, NP-hardness, and techniques for coping with NP-hardness. Notes and references are up to date until about 1997. THE SINGLE MACHINE 3. Minmax criteria Eugene L. Lawler, Jan Karel Lenstra, David B. Shmoys Chapter 3 considers two optimality criteria in a number of settings. For mini- mizing maximum cost, the focus is on polynomial-time optimization. For min- imizing maximum lateness, the full spectrum of polynomial-time optimization, approximation and branch-and-bound is covered. Notes and references are up to date until 1992. 4. Weighted sum of completion times Eugene L. Lawler, Maurice Queyranne, Andreas S. Schulz, David B. Shmoys Chapter 4 centers around Smith’s ratio rule. It follows two threads of work: the extension of the rule to other objective functions and various kinds of precedence constraints, and the design of approximation algorithms for NP-hard variants with general precedence constraints or release dates. Notes and references cover work up to 2006. 5. Weighted number of late jobs Eugene L. Lawler Chapter 5 deals with various problems with the objective of minimizing the unweighted or weighted number of late jobs, with dynamic programming as a leitmotiv. Notes and references are up to date until about 1990. 6. Total tardiness and beyond A draft describing the branch-and-bound methods of the 1970’s was made ob- solete by later developments and never rewritten. 7. Nonmonotonic and multiple criteria This is another blank spot. PARALLEL MACHINES 8. Minsum criteria Eugene L. Lawler Chapter 8 is a fragmented text, focusing on polynomial-time and pseudopolynomial- time optimization and providing pointers to results on NP-hardness, approxi- mation and branch-and bound. Notes and references are up to date until about 1990. 2 about.pdf January 15, 2020 4 9. Minmax criteria, no preemption David B. Shmoys, Jan Karel Lenstra Chapter 9 is about the design and performance analysis of approximation algo- rithms, including impossibility results and a brief excursion into probabilistic analysis. Notes and references are up to date until 1992. 10. Minmax criteria with preemption Eugene L. Lawler, Charles U. Martel Chapter 10 again focuses on polynomial-time optimization, using techniques ranging from the wrap-around rule to linear programming. Notes and references are up to date until 1990. 11. Precedence constraints This is the most glaring omission. MULTI-OPERATION MODELS 12. Open shops Gerhard J. Woeginger Chapter 12 is based on a paper that was written for the 35th Symposium on Theoretical Aspects of Computer Science (2018). It deals with the minimization of makespan in nonpreemptive open shops. A pivotal role is played by a vector sum theorem of Steinitz (1913). Many open problems are listed. References are up to date until 2018. 13. Flow shops Jan Karel Lenstra, David B. Shmoys Chapter 13 discusses the design of approximation algorithms using Johnson’s 2-machine flow shop algorithm and the vector sum theorem, and briefly reviews the empirical performance of heuristics. The literature on branch-and-bound and on flow shops with no wait in process or limited buffers is not covered. Notes and references cover work up to 1990. 14. Job shops Johann L. Hurink, Jan Karel Lenstra, David B. Shmoys Chapter 14 consists of three sections, presenting the disjunctive graph model, heuristics based on schedule construction and local search, and an approxima- tion result based on the vector sum theorem. The many detailed complexity results for special cases and the advances in branch-and-bound are not covered. References are up to date until 2001. MORE SCHEDULING 15. Stochastic scheduling models Michael L. Pinedo Chapter 15 gives an overview of stochastic counterparts of the models considered in Chapters 3–14. Notes and references are missing. 3 about.pdf January 15, 2020 5 16. Scheduling in practice Michael L. Pinedo Chapter 16 describes a diversity of practical applications of machine schedul- ing and discusses various aspects of scheduling systems. Figures, notes and references are missing. BIBLIOGRAPHY The bibliography consists of the literature cited in the 1993 survey, supple- mented with the references in Chapters 1–5, 810, 1214. Citations are collected in bibliographic notes at the end of each chapter, with the exception of Chapters 12 and 14, where they occur in the main text. The reader can download the surveys by Graham, Lawler, Lenstra, and Rinnooy Kan [1979] and Lawler, Lenstra, Rinnooy Kan, and Shmoys[1993], and a paper in memory of Gene Lawler by Lenstra [1998]. © Centrum Wiskunde & Informatica — Jan Karel Lenstra Back to top 4 about.pdf January 15, 2020 6 Contents 1. Deterministic Machine Scheduling Problems 1 Eugene L. Lawler, Jan Karel Lenstra, Alexander H.G. Rinnooy Kan, David B. Shmoys 1.1. Machines, jobs, and schedules 2 1.2. Single machines and parallel machines 3 1.3. Release dates, deadlines, and precedence constraints 5 1.4. Preemption 9 1.5. Optimality criteria 10 1.6. Multi-operation models 13 1.7. Problem classification 14 i Ch01.pdf January 15, 2020 7 1 Deterministic Machine Scheduling Problems Eugene L. Lawler University of California, Berkeley Jan Karel Lenstra Centrum Wiskunde & Informatica Alexander H.G. Rinnooy Kan University of Amsterdam David B. Shmoys Cornell University Scheduling theory is something of a jungle, encompassing a bewildering variety of problem types. In this book we shall be concerned with only a limited variety of the animals in this jungle, namely those which are deterministic machine scheduling problems. With the right techniques, some of these animals are easily domesticated. But others are quite intractable and submit to the taming techniques of combinatorial optimization with great difficulty. Before learning how to train these animals, we must be able to identify them and describe them. That is the purpose of this chapter. 1 Ch01.pdf January 15, 2020 8 2 1. Deterministic Machine Scheduling Problems 1.1. Machines, jobs, and schedules The number of pans to be heated in the preparation of a gourmet dinner exceeds the number of burners available. More ships are in a harbor than there are quays for unloading them. Tasks assigned to a multiprogrammed computer system compete for processing on a timesharing basis.
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