An inventory model for controllable probabilistic deterioration rate under shortages

This article presents a production inventory model for three level production rates with characterizing the preservation technology for deteriorating items to reduce the deterioration rate. The deterioration of the product is considered as probabilistic to make the research a more realistic one. In this paper, a production inventory model with deteriorative items in which three different rates of productions are considered. Two models are considered; the production inventory model without shortages is studied first and with shortages is investigated next. In this paper, shortages are allowed to occur and demand during the stock out period is completely backlogged. Few propositions have been developed and the necessary and sufficient conditions of the existence and uniqueness of the global optimal solutions are suggested. A suitable mathematical model is developed, and the optimal production lot size, which minimizes the total average cost, is derived. The global optimal solution is derived, and an illustrative example is provided and numerically verified. Sensitivity analysis of the optimal solution with respect to the key parameters of the model has been carried out and the implications are discussed. The analysis of the model shows that the solution of the model is quite stable and can be applied for optimizing the total inventory cost of deteriorating items inventory for the business enterprises.