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A constraint programming approach for a batch processing problem with non-identical job sizes

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  • Malapert, Arnaud
  • Guéret, Christelle
  • Rousseau, Louis-Martin

Abstract

This paper presents a constraint programming approach for a batch processing machine on which a finite number of jobs of non-identical sizes must be scheduled. A parallel batch processing machine can process several jobs simultaneously and the objective is to minimize the maximal lateness. The constraint programming formulation proposed relies on the decomposition of the problem into finding an assignment of the jobs to the batches, and then minimizing the lateness of the batches on a single machine. This formulation is enhanced by a new optimization constraint which is based on a relaxed problem and applies cost-based domain filtering techniques. Experimental results demonstrate the efficiency of cost-based domain filtering techniques. Comparisons to other exact approaches clearly show the benefits of the proposed approach: it can optimally solve problems that are one order of magnitude greater than those solved by a mathematical formulation or by a branch-and-price.

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  • Malapert, Arnaud & Guéret, Christelle & Rousseau, Louis-Martin, 2012. "A constraint programming approach for a batch processing problem with non-identical job sizes," European Journal of Operational Research, Elsevier, vol. 221(3), pages 533-545.
    • Handle: RePEc:eee:ejores:v:221:y:2012:i:3:p:533-545
    DOI: 10.1016/j.ejor.2012.04.008
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    References listed on IDEAS

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    Cited by:

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    3. Li, Xueping & Zhang, Kaike, 2018. "Single batch processing machine scheduling with two-dimensional bin packing constraints," International Journal of Production Economics, Elsevier, vol. 196(C), pages 113-121.
    4. Nascimento, Paulo Jorge & Silva, Cristóvão & Antunes, Carlos Henggeler & Moniz, Samuel, 2024. "Optimal decomposition approach for solving large nesting and scheduling problems of additive manufacturing systems," European Journal of Operational Research, Elsevier, vol. 317(1), pages 92-110.
    5. Min Kong & Xinbao Liu & Jun Pei & Panos M. Pardalos & Nenad Mladenovic, 2020. "Parallel-batching scheduling with nonlinear processing times on a single and unrelated parallel machines," Journal of Global Optimization, Springer, vol. 78(4), pages 693-715, December.
    6. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    7. 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.
    8. 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.
    9. Ozturk, Onur & Begen, Mehmet A. & Zaric, Gregory S., 2014. "A branch and bound based heuristic for makespan minimization of washing operations in hospital sterilization services," European Journal of Operational Research, Elsevier, vol. 239(1), pages 214-226.
    10. 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.
    11. Zhang, Hongbin & Yang, Yu & Wu, Feng, 2024. "Scheduling a set of jobs with convex piecewise linear cost functions on a single-batch-processing machine," Omega, Elsevier, vol. 122(C).
    12. M. Vimala Rani & M. Mathirajan, 2020. "Performance evaluation of due-date based dispatching rules in dynamic scheduling of diffusion furnace," OPSEARCH, Springer;Operational Research Society of India, vol. 57(2), pages 462-512, June.
    13. Wang, Kai & Pesch, Erwin & Kress, Dominik & Fridman, Ilia & Boysen, Nils, 2022. "The Piggyback Transportation Problem: Transporting drones launched from a flying warehouse," European Journal of Operational Research, Elsevier, vol. 296(2), pages 504-519.
    14. Aurélien Froger & Michel Gendreau & Jorge E. Mendoza & Eric Pinson & Louis-Martin Rousseau, 2018. "Solving a wind turbine maintenance scheduling problem," Journal of Scheduling, Springer, vol. 21(1), pages 53-76, February.
    15. 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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