Chapter 9 Sequencing and scheduling: Algorithms and complexity

Lawler, Edward E.; Lenstra, Jan Karel; Kan, A. H. G. Rinnooy; Shmoys, David B.

doi:10.1016/s0927-0507(05)80189-6

Cited by 865 publications

(491 citation statements)

References 272 publications

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“…In the identical parallel machine environment , job Jj runs in time pj on every machine [8]. In the unrelated parallel machine scheduling environment, we are given speeds sij wEch characterize how fast job Jj runs on machine Mj, and pjj, the processing time of job Jj on machine Mi, is defined to be pjj = P j / S j j and thus depends on both the machine and the job [8]. Throughout this paper, unless specified otherwise, it is assumed that all jobs have release dates, We will give algorithms for both preemptive and nonpreemptive scheduling.…”

Section: Introductionmentioning

confidence: 99%

“…We will focus both on the one machine ( m = 1) environment and two fundamental variants of parallel machine scheduling. In the identical parallel machine environment , job Jj runs in time pj on every machine [8]. In the unrelated parallel machine scheduling environment, we are given speeds sij wEch characterize how fast job Jj runs on machine Mj, and pjj, the processing time of job Jj on machine Mi, is defined to be pjj = P j / S j j and thus depends on both the machine and the job [8].…”

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Scheduling jobs that arrive over time

Phillips

Stein

Wein³

1995

Lecture Notes in Computer Science

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A natural and basic problem in scheduling theory is to provide good average quality of service to a stream of jobs that arrive over time. In this paper we consider the problem of scheduling n jobs that are released over time in order t o minimize the average completion time of the set of jobs. In contrast to the problem of minimizing average completion time when ad jobs are available at time 0, ad the problems that we consider are NP-hard, and essentially nothing was known about constructing good approximations in polynonid time.We give the first constant-factor approximation algorithms for several variants of the single and parallel machine model. Many of the algorithms are based on interesting algorithmic and structural relationships between preemptive and nonpreemptive schedules and linear programming relaxations of both. Many of the algorithms generalize to the minimization of average weighted completion time as well. IntroductionTwo important characteristics of many real-world scheduling problems are that (1) the tasks to be scheduled arrive over time and (2) the goal is to optimize some function of average performance or satisfaction. In this pa& we study several scheduling models that include both of these characteristics; in particular we study the minimization of the average (weighted) completion time of a set of jobs with release dates. In most of these models polynomial-time algorithms were known to minimize average completion time when all the jobs were available at time 0; the introduction of release dates makes these problems NP-hard and little was known about approximation algorithms.Our major contribution is to give the first constant-factor approximation algorithms for the minimization of average completion time in these models. Our performance bounds come from the combination of two different types of results. First, we prove structural theorems about the relative quality of preemptive versus nonpreemptive schedules, and give algorithms t o convert from 1I the former to the latter with only a small degradation in schedule quality. Second, we give the first constant-approximation algorithms for preemptively scheduling parallel machines with release dates. When the machines are identical, we give a combinatorial algorithm which yields a two approximation. For unrelated machines, we give a new integer programming formulation. We then solve the linear programming relaxation and give methods to round the fractional solution to valid preemptive schedules; it is possible that these methods mill be of use in other settings.Models: We are given n jobs J 1 : . . . . J, where job J; has associated processing time p j , and a release date r j y before which it can not be processed on any machine. We will also be given m machines M I y . . . , M,. We will focus both on the one machine ( m = 1) environment and two fundamental variants of parallel machine scheduling. In the identical parallel machine environment , job Jj runs in time pj on every machine [8]. In the unrelated parallel machine scheduli...

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Scheduling jobs that arrive over time

Phillips

Stein

Wein³

1995

Lecture Notes in Computer Science

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“…In particular, much attention was given to interval scheduling [19], where jobs are given as intervals on the real line, each representing the time interval during which a job should be processed; each job has to be processed on some machine, and it is commonly assumed that a machine can process a single job at any given time.…”

Section: Introductionmentioning

confidence: 99%

Optimizing busy time on parallel machines

Mertzios

Shalom

Voloshin

et al. 2015

Theoretical Computer Science

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Abstract-We consider the following fundamental scheduling problem in which the input consists of n jobs to be scheduled on a set of identical machines of bounded capacity g (which is the maximal number of jobs that can be processed simultaneously by a single machine). Each job is associated with a start time and a completion time; it is supposed to be processed from the start time to the completion time (and in one of our extensions it has to be scheduled also in a continuous number of days; this corresponds to a two-dimensional version of the problem). We consider two versions of the problem. In the scheduling minimization version the goal is to minimize the total busy time of machines used to schedule all jobs. In the resource allocation maximization version the goal is to maximize the number of jobs that are scheduled for processing under a budget constraint given in terms of busy time. This is the first study of the maximization version of the problem. The minimization problem is known to be NP-Hard, thus the maximization problem is also NP-Hard. We consider various special cases, identify cases where an optimal solution can be computed in polynomial time, and mainly provide constant factor approximation algorithms for both minimization and maximization problems. Some of our results improve upon the best known results for this job scheduling problem. Our study has applications in power consumption, cloud computing and optimizing switching cost of optical networks.

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“…Estas heurísticas podem, de maneira genérica, ser classificadas em heurísticas construtivas e heurísticas de melhoramento. Grande parte destes algoritmos são do tipo construtivo, conforme pode ser observado nos estudos sobre heurísticas exatas e aproximadas apresentados por Horowitz & Sahni (1976) e Lawler et al (1989).…”

Section: Introductionunclassified

Uma heurística de trocas para o problema de sequenciamento de tarefas em processadores uniformes

Müller

Limberger

2000

Pesqui. Oper.

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ResumoO sequenciamento de tarefas independentes de forma não preemptiva em sistemas de processadores uniformes, com o objetivo de minimizar o tempo total de execução (makespan), é o assunto do presente artigo. Considera-se um conjunto de n tarefas, onde cada tarefa possui um tempo de processamento, e um conjunto m 2 de processadores com velocidades de processamento 1 = 1 2 ... m . Sendo o problema de encontrar o mínimo makespan considerado NP-difícil, desenvolveu-se uma heurística de trocas poderosa para resolvê-lo. A heurística proposta é composta de três fases: alocação inicial, balanceamento de carga e fase de dupla troca. A principal característica desta nova heurística é a de prescindir de uma pré-ordenação das tarefas. A heurística desenvolvida foi comparada com um limitante inferior da solução ótima e também com outras três heurísticas apresentando um desempenho superior, encontrando a solução ótima em um grande número de casos as custas de um baixo esforço computacional. Palavras-chave: Problemas de Seqüenciamento, Otimização Combinatória, Heurísticas. AbstractThis paper examines the nonpreemptive assignment of independent jobs to a system of uniform processors with the objective of reducing makespan, or the time required from the start of execution until all jobs are completed. We consider a set of n jobs, each having an execution time and a set of m 2 processors which are assumed to have different speeds (say 1 = 1 2 ... m ). Since the problem of finding a minimal makespan has been show to be NP-hard, we develop a powerful interchange heuristic. The heuristic proposed is composed by three phases: initial assignment, job reassignment and job interchange. The main feature of this method is not perform a pre-classification of the tasks. Some comparison are made with other heuristic schemes and a lower bound that validates the results obtained. The heuristic achieve optimal solutions for several instances in a short computational time.

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Chapter 9 Sequencing and scheduling: Algorithms and complexity

Cited by 865 publications

References 272 publications

Scheduling jobs that arrive over time

Scheduling jobs that arrive over time

Optimizing busy time on parallel machines

Uma heurística de trocas para o problema de sequenciamento de tarefas em processadores uniformes

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