1. Retailer A faces a normally distributed demand with mean 100 and standard deviation 50. Retailer B faces a normally distributed demand with mean 150 and standard deviation 80. You consider two configurations: (i) a single warehouse supplies both retailers, or (ii) each retailer is supplied by its own dedicated warehouse. In either case, you set the amount of inventory in stock such that the stockout probability is 5% (i.e. 95% of the time you want to be able to meet the demand). This means that for configuration (ii) both retailers must stockout 5% of the time (no matter which retailer you visit the stockout probability is 5%).

(a) Suppose that the demand at A and B are uncorrelated. How much inventory will be held in total under the two configurations, i.e. calculate for configuration (i) how much inventory is held in stock at the warehouse, and for configuration (ii) calculate the total amount of inventory held across both warehouses. Which configuration do you prefer?

(b) Repeat (a) assuming that the correlation in demand is 1. Give intuition as to why there is no benefit in demand pooling

2. The effect of demand pooling is the difference in the amount of inventory held between configuration (i) and configuration (ii). Discuss the impact of correlation on demand pooling.

3. Give examples of the following situations: (a) positively correlated demand for a single product at two different stores, (b) positively correlated demand for two different products at a single store, (c) negatively correlated demand for a single product at two different stores, (d) negatively correlated demand for two different products at a single store.