Single machine scheduling with time-dependent linear deterioration and rate-modifying maintenance

Kabir Rustogi and Vitaly A Strusevich
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Kabir Rustogi: University of Greenwich, London, UK
Vitaly A Strusevich: University of Greenwich, London, UK

Journal of the Operational Research Society, 2015, vol. 66, issue 3, 500-515

Abstract: We study single machine scheduling problems with linear time-dependent deterioration effects and maintenance activities. Maintenance periods (MPs) are included into the schedule, so that the machine, that gets worse during the processing, can be restored to a better state. We deal with a job-independent version of the deterioration effects, that is, all jobs share a common deterioration rate. However, we introduce a novel extension to such models and allow the deterioration rates to change after every MP. We study several versions of this generalized problem and design a range of polynomial-time solution algorithms that enable the decision-maker to determine possible sequences of jobs and MPs in the schedule, so that the makespan objective can be minimized. We show that all problems reduce to a linear assignment problem with a product matrix and can be solved by methods very similar to those used for solving problems with positional effects.

Date: 2015
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