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An optimal ordering and replenishment policy for a vendor-buyer system under varying replenishment intervals and delayed payment

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  • Ata Allah Taleizadeh
  • Hamid Reza Zarei
  • Bhaba R. Sarker

Abstract

The replenishment intervals can be probabilistic when the system or the supplier has problem with manufacturing or shipping the goods. In this paper, an economic order quantity (EOQ) model with probabilistic replenishment intervals and permissible delay in payments with partial backordering is developed. This paper considers three different possible situations and suggests optimal inventory policy for each situation separately regarding the amount of expected order quantity and replenishment-up-to level that maximises the expected cyclic profit for the buyers. The model is analysed for the uniform and exponential probability distribution functions (PDF) for time of replenishment and a closed-form solution is achieved in all cases. Finally, a sensitivity analysis is performed to know the general functional behaviour and to clarify the applicability of the proposed model when the system behaviour is unstable. The results indicate that a customer can obtain the optimum replenishment-up-to level and order quantity when the replenishment intervals is probabilistic in three different possible situations. [Received: 17 August 2017; Revised: 10 January 2018; Revised: 23 August 2018; Accepted: 11 November 2018]

Suggested Citation

  • Ata Allah Taleizadeh & Hamid Reza Zarei & Bhaba R. Sarker, 2019. "An optimal ordering and replenishment policy for a vendor-buyer system under varying replenishment intervals and delayed payment," European Journal of Industrial Engineering, Inderscience Enterprises Ltd, vol. 13(2), pages 264-298.
  • Handle: RePEc:ids:eujine:v:13:y:2019:i:2:p:264-298
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    Citations

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    Cited by:

    1. Lin Feng & Konstantina Skouri & Wan-Chih Wang & Jinn-Tsair Teng, 2022. "Optimal selling price, replenishment cycle and payment time among advance, cash, and credit payments from the seller’s perspective," Annals of Operations Research, Springer, vol. 315(2), pages 791-812, August.
    2. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.
    3. Barron, Yonit, 2023. "A stochastic card balance management problem with continuous and batch-type bilateral transactions," Operations Research Perspectives, Elsevier, vol. 10(C).

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