A production inventory model which considers the dependence of production rate on demand and inventory level

This study presents a production inventory model for deteriorating products in which the production rate at any instant depends on the demand and the inventory level. While the demand rate is assumed to decrease exponentially, shortages are allowed and excess demand is backlogged as well. Optimal expressions are obtained for the production scheduling period, maximum inventory level, unfilled order backlog and the total average cost. Some cases of the model are briefly discussed. A numerical example illustrates the practicality of the model. The sensitivity of these solutions to changes in underlying parameter values is also discussed.