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

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]