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An effective discrete differential evolution algorithm for scheduling uniform parallel batch processing machines with non-identical capacities and arbitrary job sizes

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  • Zhou, Shengchao
  • Liu, Ming
  • Chen, Huaping
  • Li, Xueping

Abstract

Batch processing machines (BPMs) simultaneously process multiple jobs in a batch, which are commonly used in many industrial systems. This paper studies the scheduling problem of uniform parallel batch processing machines with arbitrary job sizes. These batch processing machines have non-identical capacities and different speeds. The objective is to minimize the makespan (or maximize the machine utilization). We formulate this problem as a mixed integer programming model. Since the problem is strongly NP-hard, an effective differential evolution-based hybrid algorithm is proposed for solving large-scale problems. Firstly, in this algorithm, individuals in the population are represented as discrete job sequences, and novel mutation and crossover operators are designed based on this representation. Next, a heuristic is developed to form batches and schedule the resulting batches on the uniform parallel machines. Then, the performance of the proposed algorithm is evaluated by comparing its results to a commercial solver (CPLEX), a random keys genetic algorithm (RKGA) and a particle swarm optimization (PSO) algorithm. Experimental results demonstrate the superiority of the proposed algorithm in terms of solution quality and robustness, especially for large-scale instances.

Suggested Citation

  • Zhou, Shengchao & Liu, Ming & Chen, Huaping & Li, Xueping, 2016. "An effective discrete differential evolution algorithm for scheduling uniform parallel batch processing machines with non-identical capacities and arbitrary job sizes," International Journal of Production Economics, Elsevier, vol. 179(C), pages 1-11.
    • Handle: RePEc:eee:proeco:v:179:y:2016:i:c:p:1-11
    DOI: 10.1016/j.ijpe.2016.05.014
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    References listed on IDEAS

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    1. Damodaran, Purushothaman & Kumar Manjeshwar, Praveen & Srihari, Krishnaswami, 2006. "Minimizing makespan on a batch-processing machine with non-identical job sizes using genetic algorithms," International Journal of Production Economics, Elsevier, vol. 103(2), pages 882-891, October.
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    5. Melouk, Sharif & Damodaran, Purushothaman & Chang, Ping-Yu, 2004. "Minimizing makespan for single machine batch processing with non-identical job sizes using simulated annealing," International Journal of Production Economics, Elsevier, vol. 87(2), pages 141-147, January.
    6. Purushothaman Damodaran & Neal S. Hirani & Mario C. Velez-Gallego, 2009. "Scheduling identical parallel batch processing machines to minimise makespan using genetic algorithms," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 3(2), pages 187-206.
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    Citations

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    Cited by:

    1. 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.
    2. Rujapa Nanthapodej & Cheng-Hsiang Liu & Krisanarach Nitisiri & Sirorat Pattanapairoj, 2021. "Hybrid Differential Evolution Algorithm and Adaptive Large Neighborhood Search to Solve Parallel Machine Scheduling to Minimize Energy Consumption in Consideration of Machine-Load Balance Problems," Sustainability, MDPI, vol. 13(10), pages 1-25, May.
    3. Jun-Ho Lee & Hoon Jang, 2019. "Uniform Parallel Machine Scheduling with Dedicated Machines, Job Splitting and Setup Resources," Sustainability, MDPI, vol. 11(24), pages 1-23, December.
    4. 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.
    5. 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.
    6. 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).
    7. Zhou, Shengchao & Xie, Jianhui & Du, Ni & Pang, Yan, 2018. "A random-keys genetic algorithm for scheduling unrelated parallel batch processing machines with different capacities and arbitrary job sizes," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 254-268.

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