Impact of Aggregation on Safety Inventory

In practice, supply chains have varying degrees of inventory aggregation. For example, Barnes Noble sells books from retail stores with inventory geographically distributed across the country. Amazon, in contrast, ships all its books from a few facilities. Seven-Eleven Japan has many small convenience stores densely distributed across Japan. In contrast, supermarkets tend to be much larger, with fewer outlets that are not as densely distributed. Redbox rents its movies from tens of thousands of kiosks distributed across the United States. In contrast, Netflix centralizes its DVD inventory at fewer than fifty distribution centers. 

Our goal is to understand how aggregation in each of these cases affects forecast accuracy and safety inventories. Consider k regions, with demand in each region normally distributed with the following characteristics  

There are two ways to serve demand in the A regions. One is to have local inventories in each region and the other is to aggregate all inventories into one centralized facility. Our goal is to compare safety inventories in the two cases. With a replenishment lead time of L and a desired cycle service level CSL, the total safety inventory in the decentralized case is (using Equation 12.5)  

If all inventories are aggregated in a central location, we need to evaluate the distribution of aggregated demand. The aggregate demand is normally distributed, with a mean of D, standard deviation of and a variance of var( ) ), as follows  

Observe that Equation 12.13 is like Eqnation 12.1 except that we are aggregating across k regions rather than L periods. If all k regions have demand that is identically distribnted, with mean D and standard deviation oo, and have the same correlation p, Equation 12.13 can be simplified as 

---