10 The Impact of the Number of Warehouses on Inventories in a Distribution System

In the strategic design of a distribution system, the right number of stock points for the various products is an important question. In the last decade, a strong trend in the consumer goods industry led to centralizing the inventory in a single echelon consisting of a few parallel warehouses or even a single distribution center for a Europe-wide distribution system. Centralizing inventory is justified by the reduction in total stock which mostly overcompensates the increasing transportation cost. The effect of centralization is usually described by the “Square-Root Law”, stating that the total stock increases with the square root of the number of stock points. However, the usual case where the warehouses are replenished in full truck loads and where a given fill rate has to be satisfied, the Square-Root Law is not valid. This paper presents a new analysis of this case and a relationship between the demand to be served by a warehouse and the necessary safety and cycle stock. As a consequence, the impact of the number of parallel warehouses in a distribution system on the total stock can be derived. This paper concerns a core subject of the International Workshop on Distribution Logistics (IWDL), founded by Jo van Nunen and the author in 1994 and continued in a series of more than 10 meetings, the last of which has been organized by Jo in s’Hertogenbosch in May 2009. The IWDL united international experts in location theory, network design, inventory theory, routing and warehousing. Thanks to Jo’s strong orientation towards the practice of distribution logistics, the IWDL stimulated application oriented research also on interrelations between these fields, like network-routing, routing-inventory and network-inventory. This paper falls into the latter area. 10.