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The deterministic multi-item dynamic lot size problem with joint business volume discount

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  • Jiefeng Xu
  • Leonard Lu
  • Fred Glover

Abstract

This paper considers the multi-item dynamic lot size model where joint business volume discount is applied for all items purchased whenever the total dollar value of an order reaches a certain level. Multi-item discounts are prevalent in practical applications, yet the literature has only considered limited instances of single-item models. We establish the mathematical formulation and design an effective dynamic programming based heuristic. Computational results disclose our approach obtains high quality solutions that dominate the best known heuristic for the simplified one-item case, and that proves vastly superior to the state-of-the-art CPLEX MIP code for the multi-item case (for which no alternative heuristics have been devised). We obtained significantly better solutions than CPLEX for the more complex problems, while running from 4800 to over 100,000 times faster. Enhanced variants of our method improve these outcomes further. Copyright Kluwer Academic Publishers 2000

Suggested Citation

  • Jiefeng Xu & Leonard Lu & Fred Glover, 2000. "The deterministic multi-item dynamic lot size problem with joint business volume discount," Annals of Operations Research, Springer, vol. 96(1), pages 317-337, November.
    • Handle: RePEc:spr:annopr:v:96:y:2000:i:1:p:317-337:10.1023/a:1018999418377
    DOI: 10.1023/A:1018999418377
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    Citations

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    Cited by:

    1. Li, Zhaolin & Ou, Jinwen & Liang, Guitian, 2021. "Optimizing hospital drug procurement with rebate contracts," Omega, Elsevier, vol. 105(C).
    2. Goossens, D.R. & Maas, A.J.T. & Spieksma, F.C.R. & van de Klundert, J.J., 2007. "Exact algorithms for procurement problems under a total quantity discount structure," European Journal of Operational Research, Elsevier, vol. 178(2), pages 603-626, April.
    3. Joris van de Klundert & Jeroen Kuipers & Frits C. R. Spieksma & Maarten Winkels, 2005. "Selecting Telecommunication Carriers to Obtain Volume Discounts," Interfaces, INFORMS, vol. 35(2), pages 124-132, April.
    4. Hsu, Chaug-Ing & Li, Hui-Chieh, 2011. "Reliability evaluation and adjustment of supply chain network design with demand fluctuations," International Journal of Production Economics, Elsevier, vol. 132(1), pages 131-145, July.
    5. Jose L. Andrade-Pineda & David Canca & Pedro L. Gonzalez-R, 2017. "On modelling non-linear quantity discounts in a supplier selection problem by mixed linear integer optimization," Annals of Operations Research, Springer, vol. 258(2), pages 301-346, November.
    6. Cunha, Artur Lovato & Santos, Maristela Oliveira & Morabito, Reinaldo & Barbosa-Póvoa, Ana, 2018. "An integrated approach for production lot sizing and raw material purchasing," European Journal of Operational Research, Elsevier, vol. 269(3), pages 923-938.
    7. Ke, Ginger Y. & Bookbinder, James H., 2012. "Discount pricing for a family of items: The supplier's optimal decisions," International Journal of Production Economics, Elsevier, vol. 135(1), pages 255-264.
    8. Qin, Hu & Luo, Meifeng & Gao, Xiang & Lim, Andrew, 2012. "The freight allocation problem with all-units quantity-based discount: A heuristic algorithm," Omega, Elsevier, vol. 40(4), pages 415-423.
    9. Kuo, R.J. & Pai, C.M. & Lin, R.H. & Chu, H.C., 2015. "The integration of association rule mining and artificial immune network for supplier selection and order quantity allocation," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 958-972.
    10. Crama, Y. & Pascual J., R. & Torres, A., 2004. "Optimal procurement decisions in the presence of total quantity discounts and alternative product recipes," European Journal of Operational Research, Elsevier, vol. 159(2), pages 364-378, December.
    11. Milind Dawande & Srinagesh Gavirneni & Yinping Mu & Suresh Sethi & Chelliah Sriskandarajah, 2010. "On the Interaction Between Demand Substitution and Production Changeovers," Manufacturing & Service Operations Management, INFORMS, vol. 12(4), pages 682-691, September.

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