EXAMPLE 4.39 Aggregating demand in a Supply Chain

In Example 4.33, we learned that the lead time demands for SurgeArresters in two markets are Normally distributed with

Based on the given means, we found that the mean aggregated demand is 3104. The variance and standard deviation of the aggregated cannot be computed from the information given so far. Not surprisingly, demands in the two markets are not independent because of the proximity of the regions. Therefore, Rule 2 for variances does not apply. We need to know , the correlation between and , to apply Rule 3. Historically, the correlation between Milwaukee demand and Chicago demand is about . To find the variance of the overall demand, we use Rule 3:

233

The variance of the sum is greater than the sum of the variances because of the positive correlation between the two markets. We find the standard deviation from the variance,

Notice that even though the variance of the sum is greater than the sum of the variances, the standard deviation of the sum is less than the sum of the standard deviations. Here lies the potential benefit of a centralized warehouse. To protect against stockouts, ElectroWorks maintains safety stock for a given product at each warehouse. Safety stock is extra stock in hand over and above the mean demand. For example, if ElectroWorks has a policy of holding two standard deviations of safety stock, then the amount of safety stock (rounded to the nearest integer) at warehouses would be

The combined safety stock for the Milwaukee and Chicago warehouses is 640 units, which is 40 more units required than if distribution was operated out of a centralized warehouse. Now imagine the implication for safety stock when you take into consideration not just one part but thousands of parts that need to be stored.