Single machine scheduling with a generalized job-dependent cumulative effect

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 pa...

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Vydáno v:Journal of scheduling Ročník 20; číslo 6; s. 583 - 592
Hlavní autoři: Rustogi, Kabir, Strusevich, Vitaly A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.12.2017
Springer Nature B.V
Témata:
Artificial Intelligence
Boolean algebra
Business and Management
Calculus of Variations and Optimal Control; Optimization
Job shops
Mathematical models
Operations Research/Decision Theory
Optimization
Precedence constraints
Production scheduling
Scheduling
Supply Chain Management
Precedence constraints
Maintenance
Approximation scheme
Half-product problem
Deterioration
Single machine
ISSN:1094-6136, 1099-1425
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-016-0497-6