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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Bibliographic Details
Published in:Mathematical problems in engineering Vol. 2022; pp. 1 - 10
Main Authors: Li, Dawei, Li, Ganggang, Cheng, Fangzheng
Format: Journal Article
Language:English
Published: New York Hindawi 28.11.2022
John Wiley & Sons, Inc
Subjects:
Algorithms
Approximation
Completion time
Dynamic programming
Mathematical analysis
Polynomials
Rejection
Schedules
Scheduling
Upper bounds
ISSN:1024-123X, 1563-5147
Online Access:Get full text
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Summary: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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ISSN:1024-123X
1563-5147
DOI:10.1155/2022/3565133