The single-processor scheduling problem with time restrictions: complexity and related problems

We consider the single-processor scheduling problem with time restrictions (STR) in order to minimize the makespan, where a set of independent jobs has to be processed on a single processor, subject only to the following constraint: During any time period of length α , the number of jobs being execu...

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Bibliographic Details
Published in:Journal of scheduling Vol. 22; no. 4; pp. 465 - 471
Main Authors: Benmansour, Rachid, Braun, Oliver, Hanafi, Saïd
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2019
Springer Nature B.V
Springer Verlag
Subjects:
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Computer Science
Formulations
Integer programming
Job shops
Mathematical models
Microprocessors
Mixed integer
Operations Research/Decision Theory
Optimization
Production scheduling
Scheduling
Supply Chain Management
Mixed integer programming
NP-hard
Scheduling
Single processor
Time restrictions
Parallel machine scheduling with a single server
ISSN:1094-6136, 1099-1425
Online Access:Get full text
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Summary:We consider the single-processor scheduling problem with time restrictions (STR) in order to minimize the makespan, where a set of independent jobs has to be processed on a single processor, subject only to the following constraint: During any time period of length α , the number of jobs being executed is less than or equal to a given integer value B . First, we prove that the STR problem is binary NP-hard even for B = 2 by pointing out an interesting analogy of this problem to the parallel machine scheduling problem with a single server with equal processing times. Next, we give a formal description of the STR problem by providing two mixed integer programming formulations to solve it optimally. The first is based on time-indexed variables and the second is based on assignment and positional date variables (APV). Both models were tested on randomly generated instances, and the experimental results show that the APV model performs very well and can solve problem instances of up to n = 500 jobs.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-018-0579-8