Centralized Safety Stocks in an Arborescent Inventory System

Abstract

We deal with an arborescent inventory system consisting of one central warehouse and m branch warehouse in this paper. The central warehouse places orders once every cycle with fixed cycle length CL, and the branch warehouse has two oppertunities to receive inventory replenishment from the central warehouse in each cycle. The central warehouse ships out most of its inventory at the begining of each cycle, while retaining total safety stocks at the central warehouse. Demands in each period in each branch warehouse are independent, and follow normal distribution. Due to the fact that deviation of demand in a longer period is larger than that in a shorter period, inventory imbalance in the longer period is more serious than that in the shorter period. To correct imbalance of inventories in branch warehouses, the central warehouse allocates the centralized safety stocks to proper branch warehouses at a proper instance in each cycle. Giving the allocation instance of the centralized safety stocks, we derive a calculation function of system ship-up-to-level and the centralized safety stocks. On the other hand, given the system ship-up-to-level and the centralized safety stocks, the optimal allocation instance of the centralized safety stocks is calculated. The proposed model is evaluated by comparing average inventory level with a traditional two-phase push control inventory system.