An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

Billaut, Jean-Charles, Gribkovskaia, Irina and Strusevich, Vitaly A. (2008) An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times. IIE Transactions, 40 (4). pp. 478-493. ISSN 1545-8830 (electronic) 0740-817X (paper)

Abstract

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

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