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Author: University of California, Berkeley. Computer Science Division Publisher: ISBN: Category : Languages : en Pages : 14
Book Description
Suppose n jobs, each with a specified release date, due date and processing time, are to be scheduled for processing by a single machine, with the objective of minimizing the number of jobs that are not completed by their due dates. Three results, in the form of two algorithms and one NP-completeness proof, are presented. Our first result is to show that if release dates and due dates are "compatible," i. e. similarly ordered, an optimal schedule can be found in O(n log n) time by a procedure that is a natural generalization of that of Moore for the case in which all release dates are equal. This result improves on an O(n squared) solution to this problem by Kise, Ibaraki and Mine. For our Second result, no particular relationship is assumed between the release dates and the due dates and the schedule is allowed to be preemptive. We show that a schedule minimizing the weighted number of late jobs can be found in O(n cubed W cubed) time where W is the sum of the integer weights assigned to the jobs. If the jobs are unweighted, then in effect W=n and the time bound reduces to O(n to the 6), thereby yielding a polynomial-bounded algorithm for a problem for which no such solution procedure was previously known. For our third result, we suppose that all release dates are equal and that each job has a deadline in addition to its due date. We show that it is an NP-hard problem to minimize the number of late jobs (with respect to due dates) while observing all deadlines. This result resolves an open question suggested by a result of J. Sidney.
Author: University of California, Berkeley. Computer Science Division Publisher: ISBN: Category : Languages : en Pages : 14
Book Description
Suppose n jobs, each with a specified release date, due date and processing time, are to be scheduled for processing by a single machine, with the objective of minimizing the number of jobs that are not completed by their due dates. Three results, in the form of two algorithms and one NP-completeness proof, are presented. Our first result is to show that if release dates and due dates are "compatible," i. e. similarly ordered, an optimal schedule can be found in O(n log n) time by a procedure that is a natural generalization of that of Moore for the case in which all release dates are equal. This result improves on an O(n squared) solution to this problem by Kise, Ibaraki and Mine. For our Second result, no particular relationship is assumed between the release dates and the due dates and the schedule is allowed to be preemptive. We show that a schedule minimizing the weighted number of late jobs can be found in O(n cubed W cubed) time where W is the sum of the integer weights assigned to the jobs. If the jobs are unweighted, then in effect W=n and the time bound reduces to O(n to the 6), thereby yielding a polynomial-bounded algorithm for a problem for which no such solution procedure was previously known. For our third result, we suppose that all release dates are equal and that each job has a deadline in addition to its due date. We show that it is an NP-hard problem to minimize the number of late jobs (with respect to due dates) while observing all deadlines. This result resolves an open question suggested by a result of J. Sidney.
Author: Gilbert Thoreau Howard Publisher: ISBN: Category : Production scheduling Languages : en Pages : 19
Book Description
Two algorithms have been formulated for scheduling n jobs through a single facility to minimize the number of late jobs when set-up times are sequence dependent. The first is a simple matrix algorithm which solves the problem when jobs must be processes in first-come, first-served (FCFS) order. The second is a branch and bound technique which arrives at an optimal solution with no restrictions on the sequence used. Both algorithms are demonstrated by examples. (Author).
Author: A.H.G. Rinnooy Kan Publisher: Springer Science & Business Media ISBN: 1461343836 Category : Business & Economics Languages : en Pages : 188
Book Description
1. Introduction.- 2. Problem Formulation.- 2.1. Notations and representations.- 2.2. Restrictive assumptions.- 2.3. Optimality criteria.- 2.3.1. Regular measures.- 2.3.1.1. Criteria based on completion times.- 2.3.1.2. Criteria based on due dates.- 2.3.1.3. Criteria based on inventory cost and utilization.- 2.3.2. Relations between criteria.- 2.3.3. Analysis of scheduling costs.- 2.4. Classification of problems.- 3. Methods of Solution.- 3.1. Complete enumeration.- 3.2. Combinatorial analysis.- 3.3. Mixed integer and non-linear programming.- 3.3.1. [Bowman 1959].- 3.3.2. [Pritsker et al. 1969].
Author: A. Bachem Publisher: Springer Science & Business Media ISBN: 3642688748 Category : Mathematics Languages : en Pages : 662
Book Description
In the late forties, Mathematical Programming became a scientific discipline in its own right. Since then it has experienced a tremendous growth. Beginning with economic and military applications, it is now among the most important fields of applied mathematics with extensive use in engineering, natural sciences, economics, and biological sciences. The lively activity in this area is demonstrated by the fact that as early as 1949 the first "Symposium on Mathe matical Programming" took place in Chicago. Since then mathematical programmers from all over the world have gath ered at the intfrnational symposia of the Mathematical Programming Society roughly every three years to present their recent research, to exchange ideas with their colleagues and to learn about the latest developments in their own and related fields. In 1982, the XI. International Symposium on Mathematical Programming was held at the University of Bonn, W. Germany, from August 23 to 27. It was organized by the Institut fUr Okonometrie und Operations Re search of the University of Bonn in collaboration with the Sonderforschungs bereich 21 of the Deutsche Forschungsgemeinschaft. This volume constitutes part of the outgrowth of this symposium and docu ments its scientific activities. Part I of the book contains information about the symposium, welcoming addresses, lists of committees and sponsors and a brief review about the Ful kerson Prize and the Dantzig Prize which were awarded during the opening ceremony.
Author: Michael L. Pinedo Publisher: Springer Science & Business Media ISBN: 1461423619 Category : Business & Economics Languages : en Pages : 673
Book Description
This new edition of the well established text Scheduling - Theory, Algorithms, and Systems provides an up-to-date coverage of important theoretical models in the scheduling literature as well as significant scheduling problems that occur in the real world. It again includes supplementary material in the form of slide-shows from industry and movies that show implementations of scheduling systems. The main structure of the book as per previous edition consists of three parts. The first part focuses on deterministic scheduling and the related combinatorial problems. The second part covers probabilistic scheduling models; in this part it is assumed that processing times and other problem data are random and not known in advance. The third part deals with scheduling in practice; it covers heuristics that are popular with practitioners and discusses system design and implementation issues. All three parts of this new edition have been revamped and streamlined. The references have been made completely up-to-date. Theoreticians and practitioners alike will find this book of interest. Graduate students in operations management, operations research, industrial engineering, and computer science will find the book an accessible and invaluable resource. Scheduling - Theory, Algorithms, and Systems will serve as an essential reference for professionals working on scheduling problems in manufacturing, services, and other environments. Reviews of third edition: This well-established text covers both the theory and practice of scheduling. The book begins with motivating examples and the penultimate chapter discusses some commercial scheduling systems and examples of their implementations." (Mathematical Reviews, 2009)
Author: Joseph Y-T. Leung Publisher: CRC Press ISBN: 0203489802 Category : Business & Economics Languages : en Pages : 1215
Book Description
This handbook provides full coverage of the most recent and advanced topics in scheduling, assembling researchers from all relevant disciplines to facilitate new insights. Presented in six parts, these experts provides introductory material, complete with tutorials and algorithms, then examine classical scheduling problems. Part 3 explores scheduling models that originate in areas such as computer science, operations research. The following section examines scheduling problems that arise in real-time systems. Part 5 discusses stochastic scheduling and queueing networks, and the final section discusses a range of applications in a variety of areas, from airlines to hospitals.
Author: Stanislaw Gawiejnowicz Publisher: Springer Science & Business Media ISBN: 3540694463 Category : Computers Languages : en Pages : 379
Book Description
Time-dependent scheduling involves problems in which the processing times of jobs depend on when those jobs are started. This book is a comprehensive study of complexity results and optimal and suboptimal algorithms concerning time-dependent scheduling in single-, parallel- and dedicated-machine environments. In addition to complexity issues and exact or heuristic algorithms which are typically presented in scheduling books, the author also includes more advanced topics such as matrix methods in time-dependent scheduling, and time-dependent scheduling with two criteria. The reader should be familiar with basic notions of calculus, discrete mathematics and combinatorial optimization theory, while the book offers introductory material on NP-complete problems, and the basics of scheduling theory. The author includes numerous examples, figures and tables, he presents different classes of algorithms using pseudocode, and he completes the book with an extensive bibliography, and author, symbol and subject indexes. The book is suitable for researchers working on scheduling, problem complexity, optimization, heuristics and local search algorithms.
Author: University of California, Berkeley. Computer Science Division
Author: University of California, Berkeley. Computer Science Division
Author: Gilbert Thoreau Howard
Author: A.H.G. Rinnooy Kan
Author: A. Bachem
Author: Michael L. Pinedo
Author: Joseph Y-T. Leung
Author: Suresh Chand
Author: S.C. Graves
Author: Candace A. Yano, Yeong-Dae Kim
Author: Stanislaw Gawiejnowicz