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Solving lot-sizing problem with quantity discount and transportation cost

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  • Amy Lee
  • He-Yau Kang
  • Chun-Mei Lai

Abstract

Owing to today's increasingly competitive market and ever-changing manufacturing environment, the inventory problem is becoming more complicated to solve. The incorporation of heuristics methods has become a new trend to tackle the complex problem in the past decade. This article considers a lot-sizing problem, and the objective is to minimise total costs, where the costs include ordering, holding, purchase and transportation costs, under the requirement that no inventory shortage is allowed in the system. We first formulate the lot-sizing problem as a mixed integer programming (MIP) model. Next, an efficient genetic algorithm (GA) model is constructed for solving large-scale lot-sizing problems. An illustrative example with two cases in a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that both the MIP model and the GA model are effective and relatively accurate tools for determining the replenishment for touch panel manufacturing for multi-periods with quantity discount and batch transportation. The contributions of this article are to construct an MIP model to obtain an optimal solution when the problem is not too complicated itself and to present a GA model to find a near-optimal solution efficiently when the problem is complicated.

Suggested Citation

  • Amy Lee & He-Yau Kang & Chun-Mei Lai, 2013. "Solving lot-sizing problem with quantity discount and transportation cost," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(4), pages 760-774.
  • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:4:p:760-774
    DOI: 10.1080/00207721.2011.618644
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    Cited by:

    1. Zamani Dadaneh, Dariush & Moradi, Sajad & Alizadeh, Behrooz, 2023. "Simultaneous planning of purchase orders, production, and inventory management under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 265(C).
    2. R. Sundararajan & M. Palanivel & S. Vaithyasubramanian, 2023. "On the EOQ Models with Advertisement-Price-Dependent Demand and Quantity Discount with Expiration Date Under Shortage," SN Operations Research Forum, Springer, vol. 4(4), pages 1-31, December.
    3. He-Yau Kang & Amy H.I. Lee & Chien-Wei Wu & Cheng-Han Lee, 2017. "An efficient method for dynamic-demand joint replenishment problem with multiple suppliers and multiple vehicles," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 1065-1084, February.
    4. Zhang, Guoqing & Shi, Jianmai & Chaudhry, Sohail S. & Li, Xindan, 2019. "Multi-period multi-product acquisition planning with uncertain demands and supplier quantity discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 132(C), pages 117-140.

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