The further generalization of a kind of optimal economic order quantity model

This paper generalizes a kind of economic order quantity model as follows: first, shortages are allowed to occur and are backlogged partially, the loss rate during the shortage period is proportional to the quantities of actual backorder. Second, the order cost is flexible and depends linearly on the order lot-size. Under such assumptions, we discuss the inventory problems with multiple periods and partial backlogging over a finite planning period for a deteriorating item that decays at a constant rate. A proposed solution procedure is presented for finding the optimal replenishment policy. We prove the existence and uniqueness of this optimal ordering policy and also point out that the cost function achieves the minimum under such policy. Two examples are shown to illustrate the model and solution procedure.