Optimal decision of retailer for replenishment cycle under a deteriorating product supply chain

In order to minimize the total cost of the retailer, an optimal replenishment cycle is studied by considering the deteriorating product, two-level trade credits, the limited storage capacity of their own warehouse and credit-linked order quantity simultaneously. A two-echelon supply chain model, which consists of a supplier and a retailer, is established. Then, the retailer＇s optimal replenishment cycle under all the cases are derived by using the optimization theory and method. On the basis of these, the effects of system parameters on the optimal replenishment cycle are examined by using the numerical studies. The results show that, when the retailer＇s trade credit period is longer （shorter） than the customer＇s trade credit period, the optimal replenishment cycle should he increased （decreased） as the retailer＇s trade credit period increases; if the minimum order quantity is high （low）, the optimal replenishment cycle should be increased （not changed） as the minimum order quantity increases.

Optimal production lot size with process deterioration under an extended inspection policy

A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.