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Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives

Author

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  • Jinn-Tsair Teng
  • Leopoldo Cárdenas-Barrón
  • Kuo-Ren Lou
  • Hui Wee

Abstract

In this article, we first complement an inappropriate mathematical error on the total cost in the previously published paper by Chung and Wee [2007, ‘Optimal the Economic Lot Size of a Three-stage Supply Chain With Backlogging Derived Without Derivatives’, European Journal of Operational Research, 183, 933–943] related to buyer–distributor–vendor three-stage supply chain with backlogging derived without derivatives. Then, an arithmetic–geometric inequality method is proposed not only to simplify the algebraic method of completing prefect squares, but also to complement their shortcomings. In addition, we provide a closed-form solution to integral number of deliveries for the distributor and the vendor without using complex derivatives. Furthermore, our method can solve many cases in which their method cannot, because they did not consider that a squared root of a negative number does not exist. Finally, we use some numerical examples to show that our proposed optimal solution is cheaper to operate than theirs.

Suggested Citation

  • Jinn-Tsair Teng & Leopoldo Cárdenas-Barrón & Kuo-Ren Lou & Hui Wee, 2013. "Optimal economic order quantity for buyer–distributor–vendor supply chain with backlogging derived without derivatives," International Journal of Systems Science, Taylor & Francis Journals, vol. 44(5), pages 986-994.
    • Handle: RePEc:taf:tsysxx:v:44:y:2013:i:5:p:986-994
    DOI: 10.1080/00207721.2011.652226
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    Cited by:

    1. Amir Hossein Nobil & Amir Hosein Afshar Sedigh & Leopoldo Eduardo Cárdenas-Barrón, 2020. "A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints," Annals of Operations Research, Springer, vol. 286(1), pages 265-301, March.
    2. Li, Ruihai & Skouri, Konstantina & Teng, Jinn-Tsair & Yang, Wen-Goang, 2018. "Seller's optimal replenishment policy and payment term among advance, cash, and credit payments," International Journal of Production Economics, Elsevier, vol. 197(C), pages 35-42.
    3. Monami Das Roy & Shib Sankar Sana, 2021. "Inter-dependent lead-time and ordering cost reduction strategy: a supply chain model with quality control, lead-time dependent backorder and price-sensitive stochastic demand," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 690-710, September.
    4. Gerardo Treviño-Garza & Krystel K. Castillo-Villar & Leopoldo Eduardo Cárdenas-Barrón, 2015. "Joint determination of the lot size and number of shipments for a family of integrated vendor–buyer systems considering defective products," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(9), pages 1705-1716, July.
    5. Arpita Roy & Shib Sankar Sana & Kripasindhu Chaudhuri, 2018. "Optimal Pricing of competing retailers under uncertain demand-a two layer supply chain model," Annals of Operations Research, Springer, vol. 260(1), pages 481-500, January.

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