Approximation schemes for job shop scheduling problems with controllable processing times

Jansen, Klaus; Mastrolilli, Monaldo; Solis-Oba, Roberto

doi:10.1016/j.ejor.2004.03.025

Cited by 45 publications

(18 citation statements)

References 28 publications

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“…Many different approaches, such as Simulated Annealing (SA) [14], Tabu Search (TS) [19], Genetic Algorithm (GA) [27], Neural Networks (NN) [6], Ant Colony Optimization (ACO) [26], Evolutionary Algorithm (EA) [22] and other heuristic approach [4,9,11,23], have been successfully applied to JSSP.…”

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confidence: 99%

Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems

2009

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confidence: 99%

Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems

2009

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“…As a matter of fact, scheduling problems with a nonrenewable resource, such as a total budget constraint, have received a lot of attention in the literature as time-cost-tradeoff problems, e.g., [2,11,12,20,21]. Surprisingly, the corresponding problems with a renewable resource, such as a personnel constraint, have received much less attention, although they are not less appealing from a practical viewpoint.…”

Section: Introduction and Related Workmentioning

confidence: 96%

Scheduling Parallel Jobs with Linear Speedup

Grigoriev

Uetz

2006

Approximation and Online Algorithms

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We consider a scheduling problem where a set of jobs is apriori distributed over parallel machines. The processing time of any job is dependent on the usage of a scarce renewable resource, e.g. personnel. An amount of k units of that resource can be allocated to the jobs at any time, and the more of that resource is allocated to a job, the smaller its processing time. The dependence of processing times on the amount of resources is linear for any job. The objective is to find a resource allocation and a schedule that minimizes the makespan. Utilizing an integer quadratic programming relaxation, we show how to obtain a (3 + ε)-approximation algorithm for that problem, for any ε > 0. This generalizes and improves previous results, respectively. Our approach relies on a fully polynomial time approximation scheme to solve the quadratic programming relaxation. This result is interesting in itself, because the underlying quadratic program is NP-hard to solve. We also derive lower bounds, and discuss further generalizations of the results.

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“…The polynomial time approximation schemes (PTAS) for job shop scheduling problems with makespan plus total resource consumption criterion, are presented in [48]. The authors, however, assume that the number of processors and the number of operations per job are the fixed given values.…”

Section: Job Shopmentioning

confidence: 99%

Resource Management in Machine Scheduling Problems: A Survey

Janiak

Lichtenstein

2007

dmms

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Abstract. The paper is a survey devoted to job scheduling problems with resource allocation. We present the results available in the scientific literature for commonly used models of job processing times and job release dates, i.e., the models in which the job processing time or the job release date is given as a linear or convex function dependent on the amount of the additional resource allotted to the job. The scheduling models with resource dependent processing times or resource dependent release dates extend the classical scheduling models to reflect more precisely scheduling problems that appear in real life. Thus, in this paper we present the computational complexity results and solution algorithms that have been developed for this kind of problems.

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Approximation schemes for job shop scheduling problems with controllable processing times

Cited by 45 publications

References 28 publications

Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems

Multi-population interactive coevolutionary algorithm for flexible job shop scheduling problems

Scheduling Parallel Jobs with Linear Speedup

Resource Management in Machine Scheduling Problems: A Survey

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