Scheduling deteriorating jobs to minimize makespan

Kubiak, Wiesław; Velde, S.L. van de

doi:10.1002/(sici)1520-6750(199808)45:5<511::aid-nav5>3.0.co;2-6

Cited by 69 publications

(25 citation statements)

References 8 publications

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“…As a special case of our problem without preemption, Kubiak and van de Velde (1998) show that the 1/p i = a i [1 + b i (s i − D) + ]/C max problem is NP-hard in the ordinary sense. On the other hand, the preemptive version of many scheduling problems may be solvable.…”

Section: Remark On Computational Complexitymentioning

confidence: 99%

Preemptive repayment policy for multiple loans

Ding

Cheng

et al. 2011

Ann Oper Res

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We study the multi-loan-repayment problem by formulating it as a singlemachine scheduling problem with preemptive and time-dependent processing times to minimize the makespan. We transform the scheduling problem into a continuous non-linear optimization problem and obtain an approximate solution by solving a series of the corresponding linear programming problems. We also identify agreeable conditions for the problem and discuss the computational complexity of the problem.

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Section: Remark On Computational Complexitymentioning

confidence: 99%

Preemptive repayment policy for multiple loans

Ding

Cheng

et al. 2011

Ann Oper Res

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“…Arrange the vectors x ∈ A in the order x (1) , x (2) , · · · , x (|A|) , where 0 H(x (1) ) H(x (2) ) · · · H(x (|A|) ). Assign the vectors x (1) , x (2) , · · · , x (i1) to set A H 1 until i 1 is found such that H(x (i1) ) (1 + ν)H(x (1) ) and H(x (i1+1) ) > (1 + ν)H(x (1) ).…”

Section: Procedures Partition (A H ν)mentioning

confidence: 99%

“…A number of real-world situations where deteriorating jobs occur were investigated, for the detailed application background of the case where the processing time of each job is increasing with its starting time (see, e.g., [1,2]). Usually, in such problems, the processing time of a deteriorating job is given by f i (t), where f i (t) is a nondecreasing function of the job start time t. In most of the related studies [3,4] , linear deterioration was assumed.…”

Section: Introductionmentioning

confidence: 99%

An approximation algorithm for parallel machine scheduling with simple linear deterioration

Ren

Kang

2007

J. of Shanghai Univ.

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In this paper, a parallel machine scheduling problem was considered , where the processing time of a job is a simple linear function of its starting time. The objective is to minimize makespan. A fully polynomial time approximation scheme for the problem of scheduling n deteriorating jobs on two identical machines was worked out. Furthermore, the result was generalized to the case of a fixed number of machines.

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“…After a while, deteriorating jobs were getting more attention. Some milestone studies are in the literature are respectively; Kubiak and Vende [3] investigated the computational complexity of makespan under deterioration. They developed a heuristic and branch-and-bound algorithm for the problem.…”

Section: Introductionmentioning

confidence: 99%

An efficient time algorithm for makespan objectives

Öztürkoğlu

2015

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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Abstract. This paper focuses on a single machine scheduling subject to machine deterioration with rate-modifying activities (RMA). The motivation for this study stems from the automatic-production line problem with one machine. The main question is to find the sequence in which jobs should be scheduled, how many maintenance activity (RMA) to use, if any, and where to insert them in the schedule during the time interval with optimal makespan objective. This problem is known to be NPhard and we give concise analyses of the problem and provide polynomial time algorithms to solve the makespan problem. We also propose an algorithm which can be applied to some scheduling problems with the actual processing time of job nonlinearly based on its position.

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Scheduling deteriorating jobs to minimize makespan

Cited by 69 publications

References 8 publications

Preemptive repayment policy for multiple loans

Preemptive repayment policy for multiple loans

An approximation algorithm for parallel machine scheduling with simple linear deterioration

An efficient time algorithm for makespan objectives

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