Mixed-integer linear programming and constraint programming formulations for solving distributed flexible job shop scheduling problem
•Four different MILP models based on four different modeling ideas are proposed.•A constraint programming (CP) model is designed.•MILP and CP models prove the optimality of 62 benchmark instances.•CP model obtains new best solutions for 11 benchmark instances. This paper intends to address the distr...
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| Veröffentlicht in: | Computers & industrial engineering Jg. 142; S. 106347 |
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| Hauptverfasser: | , , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
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Elsevier Ltd
01.04.2020
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| ISSN: | 0360-8352, 1879-0550 |
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| Abstract | •Four different MILP models based on four different modeling ideas are proposed.•A constraint programming (CP) model is designed.•MILP and CP models prove the optimality of 62 benchmark instances.•CP model obtains new best solutions for 11 benchmark instances.
This paper intends to address the distributed flexible job shop scheduling problem (DFJSP) with minimizing maximum completion time (makespan). In order to solve this problem, we propose four mixed integer linear programming (MILP) models as well as a constraint programming (CP) model, among which four MILP models are formulated based on four different modeling ideas. MILP models are effective in solving small-scaled problems to optimality. DFJSP is NP-hard, therefore, we propose an efficient constraint programming (CP) model based on interval decision variables and domain filtering algorithms. Numerical experiments are conducted to evaluate the performance of the proposed MILP models and CP model. The results show that the sequence-based MILP model is the most efficient one, and the proposed CP model is effective in finding good quality solutions for the both the small-sized and large-sized instances. The CP model incomparably outperforms the state-of-the-art algorithms and obtains new best solutions for 11 benchmark problems. Moreover, the best MILP model and CP model have proved the optimality of 62 best-known solutions. |
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| AbstractList | •Four different MILP models based on four different modeling ideas are proposed.•A constraint programming (CP) model is designed.•MILP and CP models prove the optimality of 62 benchmark instances.•CP model obtains new best solutions for 11 benchmark instances.
This paper intends to address the distributed flexible job shop scheduling problem (DFJSP) with minimizing maximum completion time (makespan). In order to solve this problem, we propose four mixed integer linear programming (MILP) models as well as a constraint programming (CP) model, among which four MILP models are formulated based on four different modeling ideas. MILP models are effective in solving small-scaled problems to optimality. DFJSP is NP-hard, therefore, we propose an efficient constraint programming (CP) model based on interval decision variables and domain filtering algorithms. Numerical experiments are conducted to evaluate the performance of the proposed MILP models and CP model. The results show that the sequence-based MILP model is the most efficient one, and the proposed CP model is effective in finding good quality solutions for the both the small-sized and large-sized instances. The CP model incomparably outperforms the state-of-the-art algorithms and obtains new best solutions for 11 benchmark problems. Moreover, the best MILP model and CP model have proved the optimality of 62 best-known solutions. |
| ArticleNumber | 106347 |
| Author | Zhang, Biao Zhang, Chaoyong Ren, Yaping Meng, Leilei Lv, Chang |
| Author_xml | – sequence: 1 givenname: Leilei orcidid: 0000-0003-1439-4832 surname: Meng fullname: Meng, Leilei organization: School of Computer Science, Liaocheng University, Liaocheng 252059, China – sequence: 2 givenname: Chaoyong surname: Zhang fullname: Zhang, Chaoyong email: zcyhust@hust.edu.cn organization: State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074,China – sequence: 3 givenname: Yaping surname: Ren fullname: Ren, Yaping organization: School of Intelligent Systems Science and Engineering, Jinan University (Zhuhai Campus), Zhuhai 519070, China – sequence: 4 givenname: Biao orcidid: 0000-0002-4898-2731 surname: Zhang fullname: Zhang, Biao organization: School of Computer Science, Liaocheng University, Liaocheng 252059, China – sequence: 5 givenname: Chang surname: Lv fullname: Lv, Chang organization: State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074,China |
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| Title | Mixed-integer linear programming and constraint programming formulations for solving distributed flexible job shop scheduling problem |
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