Approximation schemes for scheduling on a single machine subject to cumulative deterioration and maintenance

Authors:
Hans Kellerer;Kabir Rustogi;Vitaly A. Strusevich
Affiliations:
Institut für Statistik und Operations Research, Universität Graz, Graz, Austria 8010;School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, London, UK SE10 9LS;School of Computing and Mathematical Sciences, University of Greenwich, Old Royal Naval College, London, UK SE10 9LS
Venue:
Journal of Scheduling
Year:
2013

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Abstract

We consider a scheduling problem on a single machine to minimize the makespan. The processing conditions are subject to cumulative deterioration, but can be restored by a single maintenance. We link the problem to the Subset-sum problem (if the duration of maintenance is constant) and to the Half-Product Problem (if the duration of maintenance depends on its start time). For both versions of the problem, we adapt the existing fully polynomial-time approximation schemes to our problems by handling the additive constants.