Effects of Centralization on Expected Costs in a Multi-location Newsboy Problem

This is a single-period, single-product inventory model with several individual sources of demand. It is a multi-location problem with an opportunity for centralization. The holding and penalty cost functions at each location are assumed to be identical. Two types of inventory system are considered in this paper: the decentralized system and the centralized system. The decentralized system is a system in which a separate inventory is kept to satisfy the demand at each source of demand. The centralized system is a system in which all demands are satisfied from one central warehouse. This paper demonstrates that, for any probability distribution of a location's demands, the following properties are always true: given that the holding and penalty cost functions are identical at all locations, (1) if the holding and penalty cost functions are concave functions, then the expected holding and penalty costs in a decentralized system exceed those in a centralized system, except that (2) if the holding and penalty cost functions are linear functions, and for any i≠j, P_ij, the coefficient of correlation between the ith location's demand and the jth location's demand is equal to 1, then the expected holding and penalty costs in a decentralized system are equal to those in a centralized system.