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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| Veröffentlicht in: | Applied mathematical modelling Jg. 39; H. 3-4; S. 1183 - 1193 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Feng, Qi Fan, Baoqiang Shang, Weiping Li, Shisheng |
| Author_xml | – sequence: 1 givenname: Qi surname: Feng fullname: Feng, Qi email: fengqishuxue@126.com organization: College of Science, Zhongyuan University of Technology, Zhengzhou 450007, PR China – sequence: 2 givenname: Baoqiang surname: Fan fullname: Fan, Baoqiang organization: Department of Mathematics and Information, Ludong University, Yantai 264025, PR China – sequence: 3 givenname: Shisheng surname: Li fullname: Li, Shisheng organization: College of Science, Zhongyuan University of Technology, Zhengzhou 450007, PR China – sequence: 4 givenname: Weiping surname: Shang fullname: Shang, Weiping organization: Department of Mathematics, Zhengzhou University, Zhengzhou 450052, PR China |
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| Cites_doi | 10.1016/j.cor.2008.12.003 10.1287/opre.1090.0744 10.1016/j.ejor.2007.04.040 10.1016/j.tcs.2006.07.011 10.1016/j.tcs.2010.02.006 10.1016/S0167-5060(08)70356-X 10.1007/s10878-006-9001-0 10.1016/S0304-3975(00)00288-7 10.1016/j.tcs.2010.06.008 10.1016/j.ejor.2008.10.006 10.1016/j.ejor.2007.11.047 10.1137/S0895480196300522 10.1016/S0196-6774(03)00078-6 10.1023/A:1022231419049 10.1007/s10107-002-0324-z 10.1016/0025-5610(94)00058-2 10.1287/opre.1030.0092 10.1016/j.tcs.2008.02.015 10.1016/0377-2217(89)90427-X 10.1007/s10479-006-0164-y |
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