Approximation algorithms for the workload partition problem and applications to scheduling with variable processing times

Daniel Oron, Dvir Shabtay and George Steiner

European Journal of Operational Research, 2017, vol. 256, issue 2, 384-391

Abstract: In the Workload Partition Problem(WPP) we are given a set of n jobs to be scheduled on a set of m identical parallel machines. Each job has its own workload and the scheduling cost on each machine is a convex function of the total workload of the jobs assigned to it. The objective is to minimize the total cost on the set of m machines. Shabtay and Kaspi (2006) showed that the WPP is equivalent to a scheduling problem on m identical machines with controllable processing times and with the scheduling criterion of minimizing the makespan. They also proved that the WPP is NP-hard when m=2. However, they left as an open question whether the problem is ordinary or strongly NP-hard. Moreover, they provided no practical tools to solve the problem. We bridge those gaps in the literature by showing that the WWP problem is strongly NP-hard when m is part of the input. Furthermore, we present two different approximation algorithms for solving the WWP problem. The first one is a fully polynomial time approximation scheme (FPTAS) for a fixed number of machines, while the second is a modification of the well-known longest processing time (LPT) heuristic. We show that our modified LPT heuristic guarantees a solution with a constant approximation ratio, whose value depends on the instance parameters.

Keywords: Workload partition problem; Scheduling; Identical parallel machines; Controllable processing times; Approximation algorithms (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:256:y:2017:i:2:p:384-391

DOI: 10.1016/j.ejor.2016.06.062

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