Optimal ordering policies for a single deteriorating item with ramp-type demand rate under permissible delay in payments

In this paper, we assume that the supplier offers the retailer a credit period (i.e., M) and the retailer purchases a single deteriorating item from the supplier to satisfy the market demand, and shortages are not allowed. With the consideration of trade credit, we develop an inventory model for a single deteriorating item with ramp-type demand rate. Unlike the previous research, on the one hand, we consider both cases of and thoroughly (where is the changing point from linear demand to the constant demand and T is the replenishment cycle time). On the other hand, our objective is to optimal the replenishment cycle time T to minimise the average total cost, while the previous study is to determine the optimal shortage time point. Then, we obtain some theoretical results and employ an alternative approach to find the optimal replenishment policy efficiently. In order to verify whether the credit period offered by the supplier is significant to affect retailer's ordering behaviour, we make a comparison between models without and with the strategy of delay in payments. Through numerical examples, we show that when the delay period is longer than the changing point , the advantage of the delay in payments is more obvious, and thus it can entice more potential retailers to order more quantities. Therefore, our study can offer a reference for suppliers to set trade credit period reasonably and retailers to order rationally when they deal with a deteriorating item facing ramp-type demand rate.