Optimal Pricing and Production Scheduling Policies for an Inventory Model with Stock Dependent Production and Weibull Decay

The classical Economic Order Quantity (EPQ) models consider that the production rate is fixed and constant. But in many manufacturing and production processes the production rate is a function of stock on hand. For this sort of situations we develop and analyze an EPQ model with the assumption that the production rate is a function of the on-hand inventory and demand is a function of selling price. It is further assumed that lifetime of the item is random and follows three parameter Weibull distribution. With suitable cost considerations the total cost and profit rate functions are derived. By maximizing the profit rate function the optimal pricing and production scheduling policies are derived. The sensitivity analysis of the model reveals that the stock dependent nature of production rate is having significant influence on the optimal production quantity and production up-time and that the selling price dependent demand parameters tremendously influence the optimal values of the unit selling price and profit rate.