On the optimality of inventory models with deteriorating items for demand and on-hand inventory dependent production rate

In this paper we present two flexible production lot size inventory models for deteriorating items in which the production rate at any instant depends on the demand and the on-hand inventory level at that instant. Each of demand and deterioration rate are general continuous functions of time. For one model, shortages are allowed but are partially backordered. Also, all cost components are affected by inflation and the time value of money. For each model, a closed form of the per unit time total relevant cost is derived and sufficient conditions that minimize this total cost are built. Then, mathematical methods are used to show that, under certain conditions, each of the underlying inventory systems can attain a unique global optimal solution.