Joint inspection and inventory control for deteriorating items with time-dependent demand and deteriorating rate

In this paper, we consider inventory control problems for deteriorating items with maximum serviceable lifetime under mixed sales situation, both of the demand and the deterioration rate are depending on time. A model is presented to formulate the process of mixed sales that deteriorated items are sold to consumers together with serviceable items, where penalty cost for the sales of deteriorated products is included. From the literature search, this study is one of the first researches on the joint inspection and inventory control policies under the mixed sales situation with time-dependent demand and deterioration rate. An additional ordering contract is designed to improve the inventory holder’s profit. The optimal ordering time and ordering quantities are characterized for the additional ordering contract. We show that it would be more beneficial for the inventory holder to employ an additional order. Furthermore, two different inspection policies are considered in this study: (i) one inspection during the cycle; (ii) continuous monitoring in the cycle. The numerical results show that the net profit would increase if one inspection or continuous monitoring is conducted. These results provide useful insights to guide decision-making in inventory control problems of deteriorating products.