Inventory Control Model with Stochastic Replenishment Period Length and Delayed Payment for Deteriorating Item

In classic inventory control system، purchasing cost must be paid when purchased items are received. Furthermore، in the mentioned models، items may have infinite lifetime، while in the real world، we have some items deteriorate over the time. Also، in order to increase the sales، the suppliers may allow the retailers to pay the purchasing cost some times after receiving the ordered products. Moreover، in the real life cases، the supplier may visit the retailer and send the ordered quantity at random time and the retailer faces to stochastic lead time; then، in this case، the retailer may face to shortage. In this paper، we will extend the periodic inventory control model under delay in payment، stochastic visit interval and partial backordering for a deteriorating item. Under general probability distribution function between replenishment epochs، we show the concavity of the expected profit function and give the condition that must hold for the optimal replenish-up-to-level in order to maximize the profit. In order to show the applicability of the proposed model، the numerical examples and sensitivity analysis are provided.