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An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem

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  • Pan, Quan-Ke
  • Ruiz, Rubén

Abstract

In the no-idle flowshop, machines cannot be idle after finishing one job and before starting the next one. Therefore, start times of jobs must be delayed to guarantee this constraint. In practice machines show this behavior as it might be technically unfeasible or uneconomical to stop a machine in between jobs. This has important ramifications in the modern industry including fiber glass processing, foundries, production of integrated circuits and the steel making industry, among others. However, to assume that all machines in the shop have this no-idle constraint is not realistic. To the best of our knowledge, this is the first paper to study the mixed no-idle extension where only some machines have the no-idle constraint. We present a mixed integer programming model for this new problem and the equations to calculate the makespan. We also propose a set of formulas to accelerate the calculation of insertions that is used both in heuristics as well as in the local search procedures. An effective iterated greedy (IG) algorithm is proposed. We use an NEH-based heuristic to construct a high quality initial solution. A local search using the proposed accelerations is employed to emphasize intensification and exploration in the IG. A new destruction and construction procedure is also shown. To evaluate the proposed algorithm, we present several adaptations of other well-known and recent metaheuristics for the problem and conduct a comprehensive set of computational and statistical experiments with a total of 1750 instances. The results show that the proposed IG algorithm outperforms existing methods in the no-idle and in the mixed no-idle scenarios by a significant margin.

Suggested Citation

  • Pan, Quan-Ke & Ruiz, Rubén, 2014. "An effective iterated greedy algorithm for the mixed no-idle permutation flowshop scheduling problem," Omega, Elsevier, vol. 44(C), pages 41-50.
    • Handle: RePEc:eee:jomega:v:44:y:2014:i:c:p:41-50
    DOI: 10.1016/j.omega.2013.10.002
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    Cited by:

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    2. Zewen Sun & Xingsheng Gu, 2017. "Hybrid Algorithm Based on an Estimation of Distribution Algorithm and Cuckoo Search for the No Idle Permutation Flow Shop Scheduling Problem with the Total Tardiness Criterion Minimization," Sustainability, MDPI, vol. 9(6), pages 1-16, June.
    3. Pagnozzi, Federico & Stützle, Thomas, 2021. "Automatic design of hybrid stochastic local search algorithms for permutation flowshop problems with additional constraints," Operations Research Perspectives, Elsevier, vol. 8(C).
    4. Chen-Yang Cheng & Shih-Wei Lin & Pourya Pourhejazy & Kuo-Ching Ying & Yu-Zhe Lin, 2021. "No-Idle Flowshop Scheduling for Energy-Efficient Production: An Improved Optimization Framework," Mathematics, MDPI, vol. 9(12), pages 1-18, June.
    5. Wei Jiang & Yilan Shen & Lingxuan Liu & Xiancong Zhao & Leyuan Shi, 2022. "A new method for a class of parallel batch machine scheduling problem," Flexible Services and Manufacturing Journal, Springer, vol. 34(2), pages 518-550, June.
    6. Kuo-Ching Ying & Yi-Ju Tsai, 2017. "Minimising total cost for training and assigning multiskilled workers in production systems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(10), pages 2978-2989, May.
    7. Yang, Lixing & Qi, Jianguo & Li, Shukai & Gao, Yuan, 2016. "Collaborative optimization for train scheduling and train stop planning on high-speed railways," Omega, Elsevier, vol. 64(C), pages 57-76.
    8. Fernandez-Viagas, Victor & Molina-Pariente, Jose M. & Framinan, Jose M., 2020. "Generalised accelerations for insertion-based heuristics in permutation flowshop scheduling," European Journal of Operational Research, Elsevier, vol. 282(3), pages 858-872.
    9. Chenyao Zhang & Yuyan Han & Yuting Wang & Junqing Li & Kaizhou Gao, 2023. "A Distributed Blocking Flowshop Scheduling with Setup Times Using Multi-Factory Collaboration Iterated Greedy Algorithm," Mathematics, MDPI, vol. 11(3), pages 1-25, January.
    10. Wang, Yuhang & Han, Yuyan & Wang, Yuting & Tasgetiren, M. Fatih & Li, Junqing & Gao, Kaizhou, 2023. "Intelligent optimization under the makespan constraint: Rapid evaluation mechanisms based on the critical machine for the distributed flowshop group scheduling problem," European Journal of Operational Research, Elsevier, vol. 311(3), pages 816-832.
    11. Said Aqil & Karam Allali, 2021. "On a bi-criteria flow shop scheduling problem under constraints of blocking and sequence dependent setup time," Annals of Operations Research, Springer, vol. 296(1), pages 615-637, January.
    12. Fernando Luis Rossi & Marcelo Seido Nagano, 2022. "Beam search-based heuristics for the mixed no-idle flowshop with total flowtime criterion," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1311-1346, December.
    13. Ruiz, Rubén & Pan, Quan-Ke & Naderi, Bahman, 2019. "Iterated Greedy methods for the distributed permutation flowshop scheduling problem," Omega, Elsevier, vol. 83(C), pages 213-222.
    14. Yong Wang & Yuting Wang & Yuyan Han, 2023. "A Variant Iterated Greedy Algorithm Integrating Multiple Decoding Rules for Hybrid Blocking Flow Shop Scheduling Problem," Mathematics, MDPI, vol. 11(11), pages 1-25, May.
    15. Fang Wang & Yunqing Rao & Chaoyong Zhang & Qiuhua Tang & Liping Zhang, 2016. "Estimation of Distribution Algorithm for Energy-Efficient Scheduling in Turning Processes," Sustainability, MDPI, vol. 8(8), pages 1-20, August.
    16. Victor Fernandez-Viagas & Luis Sanchez-Mediano & Alvaro Angulo-Cortes & David Gomez-Medina & Jose Manuel Molina-Pariente, 2022. "The Permutation Flow Shop Scheduling Problem with Human Resources: MILP Models, Decoding Procedures, NEH-Based Heuristics, and an Iterated Greedy Algorithm," Mathematics, MDPI, vol. 10(19), pages 1-32, September.
    17. Hatami, Sara & Ruiz, Rubén & Andrés-Romano, Carlos, 2015. "Heuristics and metaheuristics for the distributed assembly permutation flowshop scheduling problem with sequence dependent setup times," International Journal of Production Economics, Elsevier, vol. 169(C), pages 76-88.
    18. Libralesso, Luc & Focke, Pablo Andres & Secardin, Aurélien & Jost, Vincent, 2022. "Iterative beam search algorithms for the permutation flowshop," European Journal of Operational Research, Elsevier, vol. 301(1), pages 217-234.
    19. Lin, Shih-Wei & Ying, Kuo-Ching, 2016. "Optimization of makespan for no-wait flowshop scheduling problems using efficient matheuristics," Omega, Elsevier, vol. 64(C), pages 115-125.
    20. Pan, Quan-Ke & Gao, Liang & Li, Xin-Yu & Gao, Kai-Zhou, 2017. "Effective metaheuristics for scheduling a hybrid flowshop with sequence-dependent setup times," Applied Mathematics and Computation, Elsevier, vol. 303(C), pages 89-112.
    21. Perez-Gonzalez, Paz & Framinan, Jose M., 2024. "A review and classification on distributed permutation flowshop scheduling problems," European Journal of Operational Research, Elsevier, vol. 312(1), pages 1-21.

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