Criterion for the Optimal Solution of an Inventory Model with a Linear Trend in Demand

This paper studies an economic order quantity model without shortage. It assumes that the production rate is greater than the increasing linear demand rate. The purpose of this paper is threefold. First, we find the criterion for the existence of interior critical points. Second, the necessary and sufficient conditions to locate optimal solutions are derived. Third, we point out some questionable results of the sensitive analysis in previous paper. Some numerical examples are given to demonstrate how the procedure works. In addition, we relax the assumption to construct a new inventory model that will reduce the total cost.