I3 : Incomplete Information Inventory Models

Inventory control is among the most important topics in operations research because of large investments in inventory and their effect on the profitability of the firms. A systematic analysis of inventory problems began with the development of the classical EOQ formula of Ford W. Harris in 1913, and a substantial amount of research was reported in 1958 by Kenneth J. Arrow, Samuel Karlin, and Herbert Scarf. A critical assumption in this vast literature has been that the level of inventory at any given time is fully observed. Some of the most celebrated results such as the optimality of basestock or (s,S) policies have been obtained under the assumption of full observation. Yet the inventory level is often not fully observed in practice, as elaborated below. In such an environment of incomplete information, inventories are known to be partially observed and most of the well-known inventory policies are not even admissible, let alone optimal.Reasons for partial observation of inventory levels may include replenishment errors, employee theft, customer shoplifting, improper handling of damaged merchandise, misplaced inventories, uncertain yield, imperfect inventory audits, and incorrect recording of sales. Details on some of these causes and their consequences are provided below and further discussion is available