Two-Agent Single Machine Scheduling with Deteriorating Jobs and Rejection
We consider two two-agent scheduling problems with deteriorating jobs and rejection. Two agents A and B compete for the usage of a single machine. The actual processing time of job JjX is pjX=bjXa+bt, X∈A,B, where bjX is the normal processing time of JjX, a≥0, b≥0 and t denotes the starting time of...
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| Vydáno v: | Mathematical problems in engineering Ročník 2022; s. 1 - 10 |
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| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Hindawi
28.11.2022
John Wiley & Sons, Inc |
| Témata: | |
| ISSN: | 1024-123X, 1563-5147 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | We consider two two-agent scheduling problems with deteriorating jobs and rejection. Two agents A and B compete for the usage of a single machine. The actual processing time of job JjX is pjX=bjXa+bt, X∈A,B, where bjX is the normal processing time of JjX, a≥0, b≥0 and t denotes the starting time of JjX. A job is either rejected by paying a rejection penalty, or accepted and processed on the machine. The objective is to minimize the sum of the completion time of the accepted A-jobs and total rejection penalty of the rejected A-jobs subject to an upper bound on the sum of the given objective function fB of the accepted B-jobs and total rejection penalty of the rejected B-jobs, where fB∈CmaxB,∑CjB. We give dynamic programming algorithms for them, respectively. When fB=CmaxB, we present a fully polynomial-time approximation scheme (FPTAS) for the case a=0 and b=1. When fB=∑CjB, a fully polynomial-time approximation scheme is also presented. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 1024-123X 1563-5147 |
| DOI: | 10.1155/2022/3565133 |