Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time
•Bicriteria scheduling problems on identical parallel machines.•Simultaneous optimization of the two objectives: the makespan and the total completion time.•Developing approximation algorithms relative to each objective’s optimal value.•A tradeoff curve of the approximation ratio.•Lower bound of the...
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| Vydáno v: | European journal of operational research Ročník 305; číslo 2; s. 594 - 607 |
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| Jazyk: | angličtina |
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Elsevier B.V
01.03.2023
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| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •Bicriteria scheduling problems on identical parallel machines.•Simultaneous optimization of the two objectives: the makespan and the total completion time.•Developing approximation algorithms relative to each objective’s optimal value.•A tradeoff curve of the approximation ratio.•Lower bound of the approximation ratio which cannot be improved by any algorithm.
We consider bicriteria scheduling problems with identical machines in parallel and two popular but conflicting objectives, namely, the makespan and the total completion time. Assuming no prioritization of the two objectives, we are interested in the simultaneous optimization of the two objectives and approximation algorithms relative to an ideal schedule – which may not exist – that has both objectives at their minimum. For the problem with a given number of machines, we propose a fast (ρ1,ρ2)-approximation algorithm where ρ1 and ρ2 represent approximation ratios with regard to the makespan and the total completion time, respectively. We also analyze the problem’s inapproximability by proposing a lower bound of the approximation ratio, which cannot be improved by any algorithm. |
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| AbstractList | •Bicriteria scheduling problems on identical parallel machines.•Simultaneous optimization of the two objectives: the makespan and the total completion time.•Developing approximation algorithms relative to each objective’s optimal value.•A tradeoff curve of the approximation ratio.•Lower bound of the approximation ratio which cannot be improved by any algorithm.
We consider bicriteria scheduling problems with identical machines in parallel and two popular but conflicting objectives, namely, the makespan and the total completion time. Assuming no prioritization of the two objectives, we are interested in the simultaneous optimization of the two objectives and approximation algorithms relative to an ideal schedule – which may not exist – that has both objectives at their minimum. For the problem with a given number of machines, we propose a fast (ρ1,ρ2)-approximation algorithm where ρ1 and ρ2 represent approximation ratios with regard to the makespan and the total completion time, respectively. We also analyze the problem’s inapproximability by proposing a lower bound of the approximation ratio, which cannot be improved by any algorithm. |
| Author | Pinedo, Michael L. Jiang, Xiaojuan Lee, Kangbok |
| Author_xml | – sequence: 1 givenname: Xiaojuan surname: Jiang fullname: Jiang, Xiaojuan email: x.jiang@sjtu.edu.cn organization: Antai College of Economics and Management, Shanghai Jiao Tong University, 1954 Huashan Road, Shanghai, 200030, China – sequence: 2 givenname: Kangbok orcidid: 0000-0002-3526-9865 surname: Lee fullname: Lee, Kangbok email: kblee@postech.ac.kr organization: Department of Industrial and Management Engineering, Pohang University of Science and Technology, 77 Cheongam-Ro, Nam-Gu, Pohang, 37673, Korea – sequence: 3 givenname: Michael L. orcidid: 0000-0001-7814-0642 surname: Pinedo fullname: Pinedo, Michael L. email: mpinedo@stern.nyu.edu organization: Department of Technology, Operations, and Statistics, Stern School of Business, New York University, 44 West 4th Street, New York, NY 10012, USA |
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| Cites_doi | 10.1007/BF00288685 10.1137/S0097539797327180 10.1137/15M102695X 10.1016/j.ejor.2014.03.026 10.1007/BF01294129 10.1287/opre.41.4.797 10.1007/BF00263740 10.1016/0377-2217(93)E0212-G 10.1145/361011.361064 10.1016/S0305-0548(02)00021-7 10.1057/palgrave.jors.2601016 10.1287/opre.1090.0744 10.1007/s10951-005-1637-6 10.1016/0305-0548(90)90022-Y 10.1137/0117039 10.1016/j.ejor.2014.12.012 10.1016/j.ejor.2004.07.011 10.1016/S0304-3975(03)00288-3 10.1016/j.ipl.2009.02.007 10.1287/opre.1030.0092 10.1016/S0167-5060(08)70356-X 10.1016/S0167-6377(97)00025-4 10.1016/j.ijpe.2012.05.016 10.1016/0167-6377(95)00023-D 10.1016/S0925-5273(00)00039-6 10.1016/j.ejor.2020.08.010 10.1016/S0167-5060(08)70743-X |
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| Keywords | Scheduling Makespan Approximation algorithm Total completion time Inapproximability |
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| Title | Approximation algorithms for bicriteria scheduling problems on identical parallel machines for makespan and total completion time |
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