An EOQ model with partial delayed payment and partial backordering

In many transactions concerning selling and buying, a specified delay of payment is offered or accepted by the seller. This can be regarded as a kind of discount and has potential consequences for the order size. These kinds of effects are not explicitly incorporated in the classical formulas for economic order quantities (EOQ). In this research we consider an EOQ problem under partial delayed payment. A fraction of the purchasing cost must be paid at the beginning of the period and the remaining amount can be paid later. Shortages are permitted and occur as a combination of backorders and lost sales. The aim of this paper is to determine the order and shortage quantities.