Distributionally robust single machine scheduling with the total tardiness criterion
•A distributionally robust optimization (DRO) model is adopted to minimize the total tardiness criterion for machine scheduling.•An explicit expression is derived as an upper bound approximation for the robust objective.•Branch-and-bound and beam search algorithms are proposed to solve the problem.•...
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| Veröffentlicht in: | Computers & operations research Jg. 101; S. 13 - 28 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier Ltd
01.01.2019
Pergamon Press Inc |
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| ISSN: | 0305-0548, 1873-765X, 0305-0548 |
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| Abstract | •A distributionally robust optimization (DRO) model is adopted to minimize the total tardiness criterion for machine scheduling.•An explicit expression is derived as an upper bound approximation for the robust objective.•Branch-and-bound and beam search algorithms are proposed to solve the problem.•Experimental results confirm the efficacy of the proposed algorithms.•Simulation experiments verify the effectiveness of the proposed DRO model.
This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of each job is assumed to be an unknown random variable within a given distributional set, which is described by mean and variance information. The proposed DRO model aims to find an optimal sequence that minimizes the expected worst-case total tardiness. To the best of our knowledge, it is the first time in the relevant literature that a DRO approach is adopted to minimize the total tardiness criterion for machine scheduling. An explicit expression is derived as an upper bound approximation for the robust objective, and then we transform the DRO problem into a mixed integer second-order cone programming problem. To solve this problem, a branch-and-bound algorithm with several novel bounding procedures and dominance rules is designed. Computational experiments confirm that the bounding procedures and dominance rules contribute significantly to the algorithm’s efficiency, and problem instances with up to 30 jobs can be optimally solved within 40 s. To tackle large-scale problem instances, we further design a beam search algorithm with filtering and recovering phases. Additional experiments with instances beyond 30 jobs confirm the efficacy of this beam search algorithm. To test the effectiveness of the proposed DRO model, we compare the robust sequences to nominal sequences under different processing time distributions. Experimental results show that the robust sequences perform better than nominal sequences, especially when the due dates are relatively loose. |
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| AbstractList | This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of each job is assumed to be an unknown random variable within a given distributional set, which is described by mean and variance information. The proposed DRO model aims to find an optimal sequence that minimizes the expected worst-case total tardiness. To the best of our knowledge, it is the first time in the relevant literature that a DRO approach is adopted to minimize the total tardiness criterion for machine scheduling. An explicit expression is derived as an upper bound approximation for the robust objective, and then we transform the DRO problem into a mixed integer second-order cone programming problem. To solve this problem, a branch-and-bound algorithm with several novel bounding procedures and dominance rules is designed. Computational experiments confirm that the bounding procedures and dominance rules contribute significantly to the algorithm’s efficiency, and problem instances with up to 30 jobs can be optimally solved within 40 s. To tackle large-scale problem instances, we further design a beam search algorithm with filtering and recovering phases. Additional experiments with instances beyond 30 jobs confirm the efficacy of this beam search algorithm. To test the effectiveness of the proposed DRO model, we compare the robust sequences to nominal sequences under different processing time distributions. Experimental results show that the robust sequences perform better than nominal sequences, especially when the due dates are relatively loose. •A distributionally robust optimization (DRO) model is adopted to minimize the total tardiness criterion for machine scheduling.•An explicit expression is derived as an upper bound approximation for the robust objective.•Branch-and-bound and beam search algorithms are proposed to solve the problem.•Experimental results confirm the efficacy of the proposed algorithms.•Simulation experiments verify the effectiveness of the proposed DRO model. This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of each job is assumed to be an unknown random variable within a given distributional set, which is described by mean and variance information. The proposed DRO model aims to find an optimal sequence that minimizes the expected worst-case total tardiness. To the best of our knowledge, it is the first time in the relevant literature that a DRO approach is adopted to minimize the total tardiness criterion for machine scheduling. An explicit expression is derived as an upper bound approximation for the robust objective, and then we transform the DRO problem into a mixed integer second-order cone programming problem. To solve this problem, a branch-and-bound algorithm with several novel bounding procedures and dominance rules is designed. Computational experiments confirm that the bounding procedures and dominance rules contribute significantly to the algorithm’s efficiency, and problem instances with up to 30 jobs can be optimally solved within 40 s. To tackle large-scale problem instances, we further design a beam search algorithm with filtering and recovering phases. Additional experiments with instances beyond 30 jobs confirm the efficacy of this beam search algorithm. To test the effectiveness of the proposed DRO model, we compare the robust sequences to nominal sequences under different processing time distributions. Experimental results show that the robust sequences perform better than nominal sequences, especially when the due dates are relatively loose. |
| Author | Zhang, Yuli Niu, Shengsheng Song, Shiji Chiong, Raymond Ding, Jian-Ya |
| Author_xml | – sequence: 1 givenname: Shengsheng surname: Niu fullname: Niu, Shengsheng email: nsc14@mails.tsinghua.edu.cn organization: Department of Automation, Tsinghua University, Beijing 100084, PR China – sequence: 2 givenname: Shiji orcidid: 0000-0002-4258-5217 surname: Song fullname: Song, Shiji email: shijis@mail.tsinghua.edu.cn organization: Department of Automation, Tsinghua University, Beijing 100084, PR China – sequence: 3 givenname: Jian-Ya surname: Ding fullname: Ding, Jian-Ya email: ding-jy@mails.tsinghua.edu.cn organization: Department of Automation, Tsinghua University, Beijing 100084, PR China – sequence: 4 givenname: Yuli surname: Zhang fullname: Zhang, Yuli email: zhangyuli@bit.edu.cn organization: School of Management and Economics, Beijing Institute of Technology; and Sustainable Development Research Institute for Economy and Society of Beijing, Beijing 100081, PR China – sequence: 5 givenname: Raymond surname: Chiong fullname: Chiong, Raymond email: raymond.chiong@newcastle.edu.au organization: School of Electrical Engineering and Computing, The University of Newcastle, Callaghan, NSW 2308, Australia |
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| Keywords | Branch-and-bound Beam search Single machine scheduling Total tardiness Distributionally robust optimization |
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| Snippet | •A distributionally robust optimization (DRO) model is adopted to minimize the total tardiness criterion for machine scheduling.•An explicit expression is... This paper proposes a distributionally robust optimization (DRO) model for single machine scheduling with uncertain processing times. The processing time of... |
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| SubjectTerms | Algorithms Beam search Branch-and-bound Computational mathematics Criteria Distributionally robust optimization Filtration Job shops Mixed integer Operations research Optimization Processing speed Random variables Robust control Robustness Scheduling Scheduling algorithms Search algorithms Single machine scheduling Stochastic models Total tardiness Upper bounds |
| Title | Distributionally robust single machine scheduling with the total tardiness criterion |
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