Economic order quantity with partial backorders under supplier credit

This paper deals with the problem of economic order quantity with partial backorders under supplier credit. In practice, the supplier allows a certain fixed credit period to settle the account for stimulating retailer's demand. In addition, in some situations, the supplier also may offer a cash discount to encourage retailer to pay for his purchases quickly. This study develops an inventory model with credit period and cash discount simultaneously. We also consider both backorders and lost sales during the shortage period. The objective of this model is to determine the optimal replenishment policies so that the total cost per unit time is minimized. Numerical examples are presented to illustrate the proposed model and the sensitivity analysis of the optimal solution with respect to parameters of the system is also included.