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The multi-stage multi-product batch-sizing problem in the steel industry

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  • Liu, Guoli
  • Li, Feng
  • Yang, Xianyan
  • Qiu, Shuang

Abstract

In this paper, we consider a batch-sizing problem with multiple periods and multiple types of products that arises in the steel industry. In this problem, products of a product type are produced in series of stages to fulfill the demand. Each stage consists of a work-in-process storage with inventory capacity and a production machine with a production rate. It incurs an inventory cost in the work-in-process storage of a stage, and also incurs a setup cost whenever a production batch is formed in the first stage. The problem is to determine the formation of each production batch in each period such that the total cost of setup and inventory is minimized. For the problem, we first provide a mixed-integer quadratic programming model and then propose some optimality properties. Based on the proposed properties, we design an optimal algorithm to solve the problem in polynomial time. Finally, we report the performances of the mixed-integer quadratic programming model and the optimal algorithm based on actual production data. The computational results confirm the reliability and validity of the optimal algorithm.

Suggested Citation

  • Liu, Guoli & Li, Feng & Yang, Xianyan & Qiu, Shuang, 2020. "The multi-stage multi-product batch-sizing problem in the steel industry," Applied Mathematics and Computation, Elsevier, vol. 369(C).
  • Handle: RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308227
    DOI: 10.1016/j.amc.2019.124830
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    References listed on IDEAS

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    1. Michael Florian & Morton Klein, 1971. "Deterministic Production Planning with Concave Costs and Capacity Constraints," Management Science, INFORMS, vol. 18(1), pages 12-20, September.
    2. Hwang, Juhwen & Wan, Yat-wah, 2013. "A supplier–retailer supply chain with intermediate storage for batch ordering," International Journal of Production Economics, Elsevier, vol. 142(2), pages 343-352.
    3. Bicheno, John & Holweg, Matthias & Niessmann, Jens, 2001. "Constraint batch sizing in a lean environment," International Journal of Production Economics, Elsevier, vol. 73(1), pages 41-49, August.
    4. Peter McKenzie & Shekhar Jayanthi, 2007. "Ball Aerospace Explores Operational and Financial Trade-Offs in Batch Sizing in Implementing JIT," Interfaces, INFORMS, vol. 37(2), pages 108-119, April.
    5. Sarker, Bhaba R. & Jamal, A.M.M. & Mondal, Sanjay, 2008. "Optimal batch sizing in a multi-stage production system with rework consideration," European Journal of Operational Research, Elsevier, vol. 184(3), pages 915-929, February.
    6. Öncü Hazır & Safia Kedad-Sidhoum, 2014. "Batch sizing and just-in-time scheduling with common due date," Annals of Operations Research, Springer, vol. 213(1), pages 187-202, February.
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