Stock allocation among a central warehouse and identical regional warehouses in a particular push inventory control system

Abstract

A multi-echeleon inventory system with one central warehouse and n regional warehouses is considered. Customer demand is satisfied from the regional warehouses. A push type control system is used, implying that the allocation of stock is coordinated by the central unit. Given an initial system stock, a fixed planning horizon and two shipping possibilities from the central warehouse until the next system replenishment, the problem of deciding how much to ship initially to each warehouse is addressed. The stock retained at the central warehouse will be allocated to the branches at the second shipping opportunity so as to, if possible, balance the inventory levels, thus maximizing the customer service until the time of the next replenishment. An approximation of the multi-variate probability distribution of the inventory levels at the regional warehouses, after the second shipping opportunity, is presented. Given a desired customer service level, the optimal initial system stock and the associated allocation are derived on the basis of this approximation. Characteristics of the optimal solution are discussed. The performance is compared with a simple ship-all policy, and with an extreme policy allowing a complete redistribution of the inventory among the regional warehouses at the second shipping opportunity. The results show that significant benefits can be achieved by the retention of some stock at the central warehouse.