Parallel batch scheduling with inclusive processing set restrictions and non-identical capacities to minimize makespan

Shuguang Li

European Journal of Operational Research, 2017, vol. 260, issue 1, 12-20

Abstract: We consider the problem of scheduling n jobs on m parallel batching machines with inclusive processing set restrictions and non-identical capacities. The machines differ in their functionality but have the same processing speed. The inclusive processing set restriction has the following property: the machines can be linearly ordered such that a higher-indexed machine can process all those jobs that a lower-indexed machine can process. Each job is characterized by a processing time that specifies the minimum time needed to process the job, a release date before which it cannot be processed, and a machine index which is the smallest index among the machines that can process it. Each batching machine has a limited capacity and can process a batch of jobs simultaneously as long as its capacity is not violated. The capacities of the machines are non-identical. The processing time of a batch is the maximum of the processing times of the jobs belonging to it. Jobs in the same batch have a common start time and a common completion time. The goal is to find a non-preemptive schedule so as to minimize makespan (the maximum completion time). When all jobs are released at the same time, we present two fast algorithms with approximation ratios 3 and 9/4, respectively. For the general case with unequal release dates, we develop a polynomial time approximation scheme (PTAS), which is also the first PTAS even for the case with equal release dates and without processing set restrictions.

Keywords: Scheduling; Batching machines; Inclusive processing set restrictions; Non-identical capacities; Makespan (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:260:y:2017:i:1:p:12-20

DOI: 10.1016/j.ejor.2016.11.044

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