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A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages

Author

Listed:
  • Yajaira Cardona-Valdés

    (Centro de Investigación en Matemáticas Aplicadas, Universidad Autónoma de Coahuila, Blvd. V. Carranza s/n. Col. República Oriente, Saltillo C.P. 25280, Coahuila, Mexico
    These authors contributed equally to this work.)

  • Samuel Nucamendi-Guillén

    (Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
    These authors contributed equally to this work.)

  • Rodrigo E. Peimbert-García

    (School of Engineering and Sciences, Tecnológico de Monterrey, Eugenio Garza Sada 2501 Sur, Monterrey, Nuevo León 64849, Mexico
    These authors contributed equally to this work.
    Current address: School of Engineering, Macquarie University. Balaclava Road, North Ryde, Sydney 2109, Australia.)

  • Gustavo Macedo-Barragán

    (Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
    These authors contributed equally to this work.)

  • Eduardo Díaz-Medina

    (Facultad de Ingeniería, Universidad Panamericana, Álvaro del Portillo 49, Zapopan, Jalisco 45010, Mexico
    These authors contributed equally to this work.)

Abstract

This paper addresses the multi-product, multi-period capacitated lot sizing problem. In particular, this work determines the optimal lot size allowing for shortages (imposed by budget restrictions), but with a penalty cost. The developed models are well suited to the usually rather inflexible production resources found in retail industries. Two models are proposed based on mixed-integer formulations: (i) one that allows shortage and (ii) one that forces fulfilling the demand. Both models are implemented over test instances and a case study of a real industry. By investigating the properties of the obtained solutions, we can determine whether the shortage allowance will benefit the company. The experimental results indicate that, for the test instances, the fact of allowing shortages produces savings up to 17% in comparison with the model without shortages, whereas concerning the current situation of the company, these savings represent 33% of the total costs while preserving the revenue.

Suggested Citation

  • Yajaira Cardona-Valdés & Samuel Nucamendi-Guillén & Rodrigo E. Peimbert-García & Gustavo Macedo-Barragán & Eduardo Díaz-Medina, 2020. "A New Formulation for the Capacitated Lot Sizing Problem with Batch Ordering Allowing Shortages," Mathematics, MDPI, vol. 8(6), pages 1-16, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:878-:d:365725
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    References listed on IDEAS

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    1. Liao, Jui-Jung & Huang, Kuo-Nan & Chung, Kun-Jen, 2012. "Lot-sizing decisions for deteriorating items with two warehouses under an order-size-dependent trade credit," International Journal of Production Economics, Elsevier, vol. 137(1), pages 102-115.
    2. Guan, Yongpei & Liu, Tieming, 2010. "Stochastic lot-sizing problem with inventory-bounds and constant order-capacities," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1398-1409, December.
    3. Minner, Stefan, 2003. "Multiple-supplier inventory models in supply chain management: A review," International Journal of Production Economics, Elsevier, vol. 81(1), pages 265-279, January.
    4. Fan, Jie & Wang, Guoqing, 2018. "Joint optimization of dynamic lot and warehouse sizing problems," European Journal of Operational Research, Elsevier, vol. 267(3), pages 849-854.
    5. Yang, Yi & Yuan, Quan & Xue, Weili & Zhou, Yun, 2014. "Analysis of batch ordering inventory models with setup cost and capacity constraint," International Journal of Production Economics, Elsevier, vol. 155(C), pages 340-350.
    6. Bruno, Giuseppe & Genovese, Andrea & Piccolo, Carmela, 2014. "The capacitated Lot Sizing model: A powerful tool for logistics decision making," International Journal of Production Economics, Elsevier, vol. 155(C), pages 380-390.
    7. Na Liu & Shuyun Ren & Tsan-Ming Choi & Chi-Leung Hui & Sau-Fun Ng, 2013. "Sales Forecasting for Fashion Retailing Service Industry: A Review," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-9, November.
    8. Drexl, A. & Kimms, A., 1997. "Lot sizing and scheduling -- Survey and extensions," European Journal of Operational Research, Elsevier, vol. 99(2), pages 221-235, June.
    9. Nicole DeHoratius & Adam J. Mersereau & Linus Schrage, 2008. "Retail Inventory Management When Records Are Inaccurate," Manufacturing & Service Operations Management, INFORMS, vol. 10(2), pages 257-277, November.
    10. Ferreira, Deisemara & Clark, Alistair R. & Almada-Lobo, Bernardo & Morabito, Reinaldo, 2012. "Single-stage formulations for synchronised two-stage lot sizing and scheduling in soft drink production," International Journal of Production Economics, Elsevier, vol. 136(2), pages 255-265.
    11. Akbalik, Ayse & Hadj-Alouane, Atidel B. & Sauer, Nathalie & Ghribi, Houcem, 2017. "NP-hard and polynomial cases for the single-item lot sizing problem with batch ordering under capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 257(2), pages 483-493.
    12. Helber, Stefan & Sahling, Florian, 2010. "A fix-and-optimize approach for the multi-level capacitated lot sizing problem," International Journal of Production Economics, Elsevier, vol. 123(2), pages 247-256, February.
    13. Wen-Lian Hsu, 1983. "On the General Feasibility Test of Scheduling Lot Sizes for Several Products on One Machine," Management Science, INFORMS, vol. 29(1), pages 93-105, January.
    14. HSU, Wen-Lian, 1983. "On the general feasibility test of scheduling lot sizes for several products on one machine," LIDAM Reprints CORE 515, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    15. Uday S. Karmarkar, 1987. "Lot Sizes, Lead Times and In-Process Inventories," Management Science, INFORMS, vol. 33(3), pages 409-418, March.
    16. Kuik, Roelof & Salomon, Marc & van Wassenhove, Luk N., 1994. "Batching decisions: structure and models," European Journal of Operational Research, Elsevier, vol. 75(2), pages 243-263, June.
    17. Hariga, Moncer & Ben-Daya, Mohamed, 1999. "Some stochastic inventory models with deterministic variable lead time," European Journal of Operational Research, Elsevier, vol. 113(1), pages 42-51, February.
    18. Rezaei, Jafar & Davoodi, Mansoor, 2011. "Multi-objective models for lot-sizing with supplier selection," International Journal of Production Economics, Elsevier, vol. 130(1), pages 77-86, March.
    19. Karimi, B. & Fatemi Ghomi, S. M. T. & Wilson, J. M., 2003. "The capacitated lot sizing problem: a review of models and algorithms," Omega, Elsevier, vol. 31(5), pages 365-378, October.
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