Machine-Oriented Decomposition of Flowshop Scheduling Problems Using Lagrangian Relaxation

In this paper, the Lagrangian decomposition and coordination technique is applied to flowshop scheduling problems in which the sum of the changeover cost and the tardiness penalty is minimized. The proposed method possesses a feature that the scheduling problem is decomposed not into single job-leve...

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Published inShisutemu Seigyo Jouhou Gakkai rombunshi Vol. 14; no. 5; pp. 244 - 251
Main Authors NISHI, Tatsushi, HASHIMOTO, Iori, HASEBE, Shinji
Format Journal Article
LanguageJapanese
Published THE INSTITUTE OF SYSTEMS, CONTROL AND INFORMATION ENGINEERS (ISCIE) 2001
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ISSN1342-5668
2185-811X
DOI10.5687/iscie.14.244

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Abstract In this paper, the Lagrangian decomposition and coordination technique is applied to flowshop scheduling problems in which the sum of the changeover cost and the tardiness penalty is minimized. The proposed method possesses a feature that the scheduling problem is decomposed not into single job-level subproblems but into single machine-level subproblems. By decomposing the problem into one-machine multi-operation subproblems, the changeover cost and/or changeover time can easily be embedded in the objective function. In the proposed method, each subproblem for a single machine is solved by combining the simulated annealing method and the neighborhood search algorithm. In order to avoid oscillations in multiplier values, a new Lagrangian function is used to solve each subproblem. The effectiveness of the proposed method is verified by comparing the results of the example problems solved by the proposed method with those solved by the simulated annealing method in which a schedule of the entire machine is successively improved.
AbstractList In this paper, the Lagrangian decomposition and coordination technique is applied to flowshop scheduling problems in which the sum of the changeover cost and the tardiness penalty is minimized. The proposed method possesses a feature that the scheduling problem is decomposed not into single job-level subproblems but into single machine-level subproblems. By decomposing the problem into one-machine multi-operation subproblems, the changeover cost and/or changeover time can easily be embedded in the objective function. In the proposed method, each subproblem for a single machine is solved by combining the simulated annealing method and the neighborhood search algorithm. In order to avoid oscillations in multiplier values, a new Lagrangian function is used to solve each subproblem. The effectiveness of the proposed method is verified by comparing the results of the example problems solved by the proposed method with those solved by the simulated annealing method in which a schedule of the entire machine is successively improved.
Author HASEBE, Shinji
HASHIMOTO, Iori
NISHI, Tatsushi
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References [3] H. Chen, C. Chu and J. M. Proth : A more efficient Lagrangian relaxation approach to job-shop scheduling problems; Proceedings of the IEEE International Conference on Robotics and Automation, pp. 496-501 (1995)
[6] 玉置, 杉本, 荒木 : 非正規目的関数のもとでの並列機械スケジューリング問題の定式化と解法;生産スケジューリング・シンポジウム'96講演論文集, PP.67-72 (1996)
[1] 米田 : ラグランジュ緩和法によるスケジューリング;システム/制御/情報, Vo1.41, No.4, pp.130-138 (1997)
[5] F. D. Croce, G. Menga, R. Tadei, M. Cavalotto and L. Petri : Cellular control of manufacturing systems; European Journal of Operational Research, Vol. 69, pp. 498-509 (1996)
[2] D. J. Hoitomt, P. B. Luh and K. R. Pattipati : A practical approach to job-shop scheduling problems; IEEE Transactions on Robotics and Automation, Vol. 9, No. 1, pp. 1-13 (1993)
[4] M. Jinyan, S. Y. Chai and W. Youyi : FMS jobshop scheduling using Lagrangian relaxation; Proceedings of the IEEE International Conference on Robotics and Automation, pp. 490-495 (1995)
[7] M. L. Fisher : The Lagrangian relaxation method for solving integer programming problems; Management Science, Vol. 27, No. 1, pp. 1-18 (1981)
References_xml – reference: [7] M. L. Fisher : The Lagrangian relaxation method for solving integer programming problems; Management Science, Vol. 27, No. 1, pp. 1-18 (1981)
– reference: [3] H. Chen, C. Chu and J. M. Proth : A more efficient Lagrangian relaxation approach to job-shop scheduling problems; Proceedings of the IEEE International Conference on Robotics and Automation, pp. 496-501 (1995)
– reference: [6] 玉置, 杉本, 荒木 : 非正規目的関数のもとでの並列機械スケジューリング問題の定式化と解法;生産スケジューリング・シンポジウム'96講演論文集, PP.67-72 (1996)
– reference: [1] 米田 : ラグランジュ緩和法によるスケジューリング;システム/制御/情報, Vo1.41, No.4, pp.130-138 (1997)
– reference: [2] D. J. Hoitomt, P. B. Luh and K. R. Pattipati : A practical approach to job-shop scheduling problems; IEEE Transactions on Robotics and Automation, Vol. 9, No. 1, pp. 1-13 (1993)
– reference: [5] F. D. Croce, G. Menga, R. Tadei, M. Cavalotto and L. Petri : Cellular control of manufacturing systems; European Journal of Operational Research, Vol. 69, pp. 498-509 (1996)
– reference: [4] M. Jinyan, S. Y. Chai and W. Youyi : FMS jobshop scheduling using Lagrangian relaxation; Proceedings of the IEEE International Conference on Robotics and Automation, pp. 490-495 (1995)
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Snippet In this paper, the Lagrangian decomposition and coordination technique is applied to flowshop scheduling problems in which the sum of the changeover cost and...
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StartPage 244
SubjectTerms changeover cost
decentralized scheduling
flowshop scheduling
Lagrangian relaxation
simulated annealing
Title Machine-Oriented Decomposition of Flowshop Scheduling Problems Using Lagrangian Relaxation
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