Scheduling with time dependent processing times: Review and extensions

Alidaee, Bahram; Womer, Norman Keith

doi:10.1057/palgrave.jors.2600740

Cited by 446 publications

(42 citation statements)

References 28 publications

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“…Surveys of this area of research can be found in Gawiejnowicz [6], Aidaee and Wormer [1] and Cheng et al [4]. In the classical model with start time dependent job processing times, no batching is allowed and the job or operation processing time is a nondecreasing function of its start time.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…, was studied by Alidaee and Womer [1] and Cheng and Ding [3] for the single-machine environment. Cheng and Ding [3] presented enumeration algorithms for C max and C i minimization.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Cheng and Ding [3] presented enumeration algorithms for C max and C i minimization. Alidaee and Womer [1] suggested an O(n log n) algorithm to minimize C max for the case where all a i = a. Our O(n log n) algorithm in Section 4 is similar to this algorithm.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Algorithm A is similar to the O(n log n) time algorithm of Alidaee and Womer [1] for scheduling deteriorating jobs with no batching.…”

Section: N and Runs In O(n Log N) Timementioning

confidence: 99%

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Batch scheduling of step deteriorating jobs

Barketau

Cheng

et al. 2007

J Sched

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In this paper we consider the problem of scheduling n jobs on a single machine, where the jobs are processed in batches and the processing time of each job is a step function depending on its waiting time, which is the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. For job i, if its waiting time is less than a given threshold value D, then it requires a basic processing time a i ; otherwise, it requires an extended processing time a i + b i . The objective is to minimize the completion time of the last job. We first show that the problem is NP-hard in the strong sense even if all b i are equal, it is NP-hard even if b i = a i for all i, and it is non-approximable in polynomial time with a constant performance guarantee ∆ < 3/2 unless P = N P. We then present O(n log n) and O(n 3F −1 log n/F F ) algorithms for the case where all a i are equal and for the case where there are F, F ≥ 2, distinct values of a i , respectively. We further propose an O(n 2 log n) approximation algorithm with a performance guarantee ∆ ≤ 1 + m * 2 /m * ≤ 3/2 for the general problem, where m * is the number of batches in an optimal schedule. All the above results apply or can be easily modified for the corresponding open-end bin packing problem.

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Section: Problem Descriptionmentioning

confidence: 99%

“…, was studied by Alidaee and Womer [1] and Cheng and Ding [3] for the single-machine environment. Cheng and Ding [3] presented enumeration algorithms for C max and C i minimization.…”

Section: Problem Descriptionmentioning

confidence: 99%

Section: Problem Descriptionmentioning

confidence: 99%

“…Algorithm A is similar to the O(n log n) time algorithm of Alidaee and Womer [1] for scheduling deteriorating jobs with no batching.…”

Section: N and Runs In O(n Log N) Timementioning

confidence: 99%

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Batch scheduling of step deteriorating jobs

Barketau

Cheng

et al. 2007

J Sched

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“…Ji et al (2007) address the same problem and develop a simple linear time algorithm with a worst case ratio of 5/4. For earlier results on scheduling with step-improving or step-deteriorating processing times, we refer the reader to two extensive survey papers by Alidaee and Womer (1999) and Cheng et al (2004).…”

Section: Introductionmentioning

confidence: 99%

Minimizing total completion time on a single machine with step improving jobs

Kim

Oron

2015

Journal of the Operational Research Society

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Production systems often experience a shock or a technological change, resulting in performance improvement. In such settings, job processing times become shorter if jobs start processing at, or after, a common critical date. This paper considers a single machine scheduling problem with step-improving processing times, where the effects are job-dependent. The objective is to minimize the total completion time. We show that the problem is NP-hard in general and discuss several special cases which can be solved in polynomial time. We formulate a Mixed Integer Programming model and develop an LP-based heuristic for the general problem. Finally, computational experiments show that the proposed heuristic yields very effective and efficient solutions.

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Introduction to Optimization

Ravindran

Ragsdell

Reklaitis³

2006

Engineering Optimization

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We consider the parallel-machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the total completion time. We give a fully polynomial-time approximation scheme (FPTAS) for the case with m identical machines, where m is fixed. This study solves an open problem that has been posed in the literature for ten years.

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Scheduling with time dependent processing times: Review and extensions

Cited by 446 publications

References 28 publications

Batch scheduling of step deteriorating jobs

Batch scheduling of step deteriorating jobs

Minimizing total completion time on a single machine with step improving jobs

Introduction to Optimization

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