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 inventorymodels for deteriorating items in which the production rateat any instant depends on the demand and the on-hand inventorylevel at that instant. Each of demand and deterioration rateare general continuous functions of time. For one model, shortagesare allowed but are partially backordered. Also, all cost componentsare affected by inflation and the time value of money. For eachmodel, a closed form of the per unit time total relevant costis derived and sufficient conditions that minimize this totalcost are built. Then, mathematical methods are used to showthat, under certain conditions, each of the underlying inventorysystem can attain a unique global optimal solution.