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Single machine scheduling with a generalized job-dependent cumulative effect

Single machine scheduling with a generalized job-dependent cumulative effect

Rustogi, Kabir and Strusevich, Vitaly A. (2016) Single machine scheduling with a generalized job-dependent cumulative effect. Journal of Scheduling, 20 (6). pp. 583-592. ISSN 1094-6136 (Print), 1099-1425 (Online) (doi:https://doi.org/10.1007/s10951-016-0497-6)

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Abstract

We consider a single machine scheduling problem with changing processing times. The processing conditions are subject to a general cumulative effect, in which the processing time of a job depends on the sum of certain parameters associated with previously scheduled jobs. In previous papers, these parameters are assumed to be equal to the normal processing times of jobs, which seriously limits the practical application of this model. We further generalize this model by allowing every job to respond differently to these cumulative effects. For the introduced model, we solve the problem of minimizing the makespan, with and without precedence constraints. For the problem without precedence constraints, we also consider a situation in which a maintenance activity is included in the schedule, which can improve the processing conditions of the machine, not necessarily to its original state. The resulting problem is reformulated as a variant of a Boolean programming problem with a quadratic objective, known as a half-product, which allows us to develop a fully polynomial-time approximation scheme with the best possible running time.

Item Type: Article
Uncontrolled Keywords: Single machine; Deterioration; Precedence constraints; Maintenance; Approximation scheme; Half-product problem
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 26 Sep 2018 15:29
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: GREAT c
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/20040

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