An economic order quantity model with backorders and all-units discounts

In this paper we study an inventory model with backorders where the purchase unit price depends on the ordered quantity. This situation appears in practice when a salesperson offers a fixed compensation to a client for not losing the sale and there are quantity discounts. The optimal policy is obtained through a sequential optimization procedure in two stages that relies on a quadratic function (first stage) and on the objective function of the classical EOQ model (second stage). An algorithm is developed for the model and some extensions are commented.