Optimal ordering policy in an economic order quantity (EOQ) model for non-instantaneous deteriorating items with defective quality and permissible delay in payments

Economic order quantity (EOQ) model has been used extensively over a century. Many studies have altered and modified the model in order to imitate the actual inventory problem. This article is concerned with the finding of the optimal replenishment cycle time for the inventory issues where items received are partly with imperfect quality and involve deterioration after the inspection time. Also, for financial safety, for the supplier, when the permissible delay in payments can promote their sales and reduce their on-hand stock level. For the retailer, he/she can sell the items and accumulate revenue and earn interest within the trade-credit period. At the end of the period, it is usually assumed that the retailer pays off all units bought, and starts to pay the capital opportunity cost for the items in stock. Different scenarios based on the combination of the inspection time, the certain period of time in which the item has no deterioration and the trade-credit period have been considered here. In order to minimize the total relevant inventory cost, mathematical theorems have been developed to determine the existence and the uniqueness of the optimal solution. Numerical calculations and illustrations demonstrate the application and the performance of the proposed theories.