The article deals with a production inventory system for deteriorating items where the production rate of the system is a random variable within a finite range and the unit production cost depends on production lotsize as well as the rate of production. In the model, the maximum life-cycle of the products is finite and all the products are totally expired at the end of the life-time of the product. Shortages are allowed and partially backlogged. The backlogging rate is depended on length of the waiting time for the next replenishment. The main objective is to find out the optimal production lot-size such that the average expected cost per unit time of the inventory system is minimum. The different cases according to the value of the product’s life-time, production run-time and cycle length of the system are discussed analytically and numerically. A numerical example and its sensitivity analysis along with its managerial insights are presented to illustrate the behavior of the proposed production-inventory model.
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