Inventory model for deteriorating items with Weibull rate of replenishment and selling price dependent demand

In this paper, we develop and analyse an inventory model with the assumption that the rate of production is random and follows a Weibull distribution and the demand is a function of selling price. Using the differential equations, the instantaneous state of inventory is obtained. With suitable cost considerations, the total cost function and profit rate function are derived. By maximising the profit rate function, the optimal ordering and pricing policies are obtained. The sensitivity of the model with respect to the parameters and costs is also analysed. It is observed that this model is much useful in analysing the inventory situations arising at food processing industries, pulse and edible oil processing industries, petrochemical industries, etc., where the rate of production is influenced by random factors such as raw material availability, maintenance of the machines, packaging, environmental conditions, etc.