Scheduling to maximize the weighted number of on-time jobs on parallel machines with bounded job-rejection

We study a scheduling problem on parallel identical machines, where the objective function is maximizing the weighted number of jobs completed exactly at their due-dates. The scheduler may reject a subset of the jobs, and the total permitted rejection cost is assumed to be bounded. Thus, when a deci...

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Vydáno v:Journal of scheduling Ročník 26; číslo 2; s. 193 - 207
Hlavní autoři: Atsmony, Matan, Mosheiov, Gur
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.04.2023
Springer Nature B.V
Témata:
Algorithms
Artificial Intelligence
Business and Management
Calculus of Variations and Optimal Control; Optimization
Dynamic programming
Operations Research/Decision Theory
Optimization
Polynomials
Rejection
Run time (computers)
Scheduling
Supply Chain Management
Scheduling
Job-rejection
Dynamic programming
Just-in-time
Parallel identical machines
ISSN:1094-6136, 1099-1425
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Shrnutí:We study a scheduling problem on parallel identical machines, where the objective function is maximizing the weighted number of jobs completed exactly at their due-dates. The scheduler may reject a subset of the jobs, and the total permitted rejection cost is assumed to be bounded. Thus, when a decision has to be made regarding a certain job, the following options need to be considered: either ( i ) identify the set of machines on which the job can be scheduled on time, and assign the job to one of these machines, or ( ii ) reject the job (if possible), or ( iii ) delay the job. A pseudo-polynomial dynamic programming algorithm is introduced for this NP-hard problem. Medium size problems are solved in reasonable running times. We then study a different version of the problem, in which job-dependent due-windows are considered, and the job processing times are assumed to be identical. This version is proved to be NP-hard, and a pseudo-polynomial dynamic programming algorithm is introduced as well. Our numerical study indicates that medium size instances can be handled for this version. In addition, for both problems, an alternative solution procedure based on integer-linear-programming formulation is introduced.
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ISSN:1094-6136
1099-1425
DOI:10.1007/s10951-022-00745-7