Economic order quantity with allowable shortage and quantity discounts under permissible delay in payments

This paper deals with the inventory problem of economic order quantity with shortage and quantity discounts under permissible delay in payments. 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 quantity discount to encourage retailer to increase order quantity. The objective of this model is to determine the optimal order quantity and optimal positive stock period so that the total relevant cost per year is minimized. Also, numerical examples are presented to illustrate the proposed model.