Production inventory models for deteriorating items with production quantity dependent demand and Weibull decay

Production scheduling is an important part of manufacturing. For production scheduling, inventory models play a dominant role. Most of the inventory models of deteriorating items assume that the rate of deterioration is known and constant. In this paper, we concern ourselves with a production inventory system with the assumption that the life time of the product is random and follows a Weibull distribution. The Weibull rate of decay includes increasing, decreasing and constant rates of decay. Assuming that the demand rate is a function of production quantity in a cycle and using the differential equations, the optimal production scheduling policies are derived. The sensitivity of the model with respect to the parameters and cost is also studied. This model is much useful for analysing the production schedules of the seasonal products. It is observed that the decay distribution has an influence on the production schedule.