A deterministic production inventory model for deteriorating items with an exponential declining demand

This study presents a production inventory model for deteriorating products with an exponentially declining demand over a fixed time horizon. The production rate at any instant depends on the demand. The proposed model allows for shortages, and excess demand is back-logged as well. Approximate expressions are obtained for the production scheduling period, maximum inventory level, unfilled order backlog and total average cost. In addition, special cases of the model are briefly discussed. A numerical example demonstrates the proposed method's effectiveness.