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A truncated column generation algorithm for the parallel batch scheduling problem to minimize total flow time

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  • Ozturk, Onur

Abstract

In this paper, we present a column generation based decomposition method for the parallel batch scheduling of jobs on identical parallel machines. Jobs have different release dates, processing times and sizes while machines have limited capacity. The objective is the minimization of total flow time, i.e., sum of completion times of all processed jobs. The straightforward mixed integer linear programming model of the problem is efficient for small size instances. To deal with larger instances, we develop a time indexed column generation model in which each column represents the set of jobs processed together in the same batch and the time instant for the beginning of batch processing. We obtain approximate solutions with a rounding technique followed by another mathematical model to schedule batches on machines. Numerical test results show that the proposed model is able to return high quality solutions within short computation times.

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  • Ozturk, Onur, 2020. "A truncated column generation algorithm for the parallel batch scheduling problem to minimize total flow time," European Journal of Operational Research, Elsevier, vol. 286(2), pages 432-443.
    • Handle: RePEc:eee:ejores:v:286:y:2020:i:2:p:432-443
    DOI: 10.1016/j.ejor.2020.03.044
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    8. Li, Shuguang, 2017. "Approximation algorithms for scheduling jobs with release times and arbitrary sizes on batch machines with non-identical capacities," European Journal of Operational Research, Elsevier, vol. 263(3), pages 815-826.
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    Cited by:

    1. Yang, Fan & Davari, Morteza & Wei, Wenchao & Hermans, Ben & Leus, Roel, 2022. "Scheduling a single parallel-batching machine with non-identical job sizes and incompatible job families," European Journal of Operational Research, Elsevier, vol. 303(2), pages 602-615.
    2. Xu, Jun & Wang, Jun-Qiang & Liu, Zhixin, 2022. "Parallel batch scheduling: Impact of increasing machine capacity," Omega, Elsevier, vol. 108(C).
    3. Liu, Baoli & Li, Zhi-Chun & Wang, Yadong, 2023. "A branch-and-price heuristic algorithm for the bunkering operation problem of a liquefied natural gas bunkering station in the inland waterways," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 145-170.
    4. Omid Shahvari & Rasaratnam Logendran & Madjid Tavana, 2022. "An efficient model-based branch-and-price algorithm for unrelated-parallel machine batching and scheduling problems," Journal of Scheduling, Springer, vol. 25(5), pages 589-621, October.
    5. A. Alfieri & A. Druetto & A. Grosso & F. Salassa, 2021. "Column generation for minimizing total completion time in a parallel-batching environment," Journal of Scheduling, Springer, vol. 24(6), pages 569-588, December.
    6. Tian, Zheng & Zheng, Li, 2024. "Single machine parallel-batch scheduling under time-of-use electricity prices: New formulations and optimisation approaches," European Journal of Operational Research, Elsevier, vol. 312(2), pages 512-524.
    7. Zhang, Han & Li, Kai & Jia, Zhao-hong & Chu, Chengbin, 2023. "Minimizing total completion time on non-identical parallel batch machines with arbitrary release times using ant colony optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1024-1046.
    8. Alessandro Druetto & Erica Pastore & Elena Rener, 2023. "Parallel batching with multi-size jobs and incompatible job families," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 440-458, July.
    9. Husseinzadeh Kashan, Ali & Ozturk, Onur, 2022. "Improved MILP formulation equipped with valid inequalities for scheduling a batch processing machine with non-identical job sizes," Omega, Elsevier, vol. 112(C).

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