A concise survey of scheduling with time-dependent processing times

Cheng, T.C.E.; Ding, Qingqing; Lin, Bertrand M.T.

doi:10.1016/s0377-2217(02)00909-8

Cited by 583 publications

(184 citation statements)

References 48 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%

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%

Batch scheduling of step deteriorating jobs

Barketau

Cheng

et al. 2007

J Sched

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“…Following changes in the production setting, job processing times begin to increase, or in some cases decrease, linearly at a predefined point in time. Cheng et al (2004) and the references within describe a variety of applications for this class of models, including fire fighting efforts, searching for items under worsening light or weather conditions and maintenance scheduling. Wu et al (2009) propose a branchand-bound algorithm as well as heuristic algorithms for solving a single machine scheduling problem with the objective of minimizing the makespan.…”

Section: Introductionmentioning

confidence: 99%

“…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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“…Under a time-dependent effect, the actual processing time of a job is a function of the start time of the job. Leaving aside less popular cumulative effects initiated by [5] and [6], the studies on the positional and the time-dependent effects have formed the bulk of publications in the area; see, e.g., a survey [7] and the book [8], the latter providing a comprehensive exposition on scheduling with time-dependent processing times. These two effects can be further classified as being either job-dependent or job-independent.…”

Section: Introductionmentioning

confidence: 99%

Combining time and position dependent effects on a single machine subject to rate-modifying activities

Rustogi

Strusevich

2014

Omega

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Citation for this version held on GALA:Rustogi, Kabir and Strusevich, Vitaly (2014) Combining time and position dependent effects on a single machine subject to rate-modifying activities. London: Greenwich Academic Literature Archive. We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and timedependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, e.g., maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects, on one hand, and between the positional effects and the start-time dependent effects, on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

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A concise survey of scheduling with time-dependent processing times

Cited by 583 publications

References 48 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

Combining time and position dependent effects on a single machine subject to rate-modifying activities

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