Two-agent scheduling with rejection on a single machine

In this paper, we consider the two-agent scheduling problem with rejection on a single machine. In the problem we have two agents A and B with job families JA and JB, respectively. A job in JA or JB is either accepted and processed on the machine, or rejected with a certain rejection penalty having...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 39; no. 3-4; pp. 1183 - 1193
Main Authors: Feng, Qi, Fan, Baoqiang, Li, Shisheng, Shang, Weiping
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2015
Subjects:
Agent scheduling
Approximation algorithm
Pseudo-polynomial-time algorithm
Rejection
Single machine
Rejection
Approximation algorithm
Pseudo-polynomial-time algorithm
Single machine
Agent scheduling
ISSN:0307-904X
Online Access:Get full text
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Summary:In this paper, we consider the two-agent scheduling problem with rejection on a single machine. In the problem we have two agents A and B with job families JA and JB, respectively. A job in JA or JB is either accepted and processed on the machine, or rejected with a certain rejection penalty having to be paid. The objective is to minimize the sum of the given objective function fA of the accepted jobs and total rejection penalty of the rejected jobs of the first agent A, given that the second agent B only accepts schedules such that the sum of the given objective function fB of the accepted jobs and total rejection penalty of the rejected jobs of the agent B does not exceed a fixed value Q (Q is a positive integer), where fA and fB are non-decreasing functions on the completion times of their respective jobs. We show that, for all pairs (fA,fB)∈CmaxA,CmaxB,LmaxA,LmaxB,∑CjA,CmaxB,∑CjA,LmaxB,∑CjA,∑wjBUjB, the problems are NP-hard. When (fA,fB)=CmaxA,LmaxB, we provide a pseudo-polynomial-time algorithm. Moreover, when (fA,fB)=CmaxA,LmaxB and all B-jobs are accepted, we give a 2-approximation algorithm and an fully polynomial-time approximation scheme. Finally, for (fA,fB)∈∑CjA,LmaxB,∑CjA,∑wjBUjBK, we present pseudo-polynomial-time algorithms, respectively.
ISSN:0307-904X
DOI:10.1016/j.apm.2014.07.024