Consider the following supply chain where demand for a single product occurs in N = 10 retail locations. Each store is replenished directly from a supplier with LD weeks of lead time. To provide good customer service, the retailer uses a base-stock policy and targets an in-stock probability of . Alternatively, suppose the retailer builds a distribution center to provide consolidated distribution as illustrated in the following figure. The distribution center receives all shipments from the supplier and then replenishes each of the retail stores. The lead time for the distribution center is L2 weeks from the supplier. The lead time to replenish each of the retail stores is L1 weeks. To ensure a reliable delivery to the retail stores, the distribution center operates at a high in-stock probability and uses a base-stock policy to order from the supplier. The distribution center provides the retailer with a centralized location for inventory while still allowing the retailer to position inventory close to the customer.

a) Suppose that each retail store observes a random demand that is normally distributed with mean 200 units per week with a standard deviation of 60 units. The in-stock probability for the retail stores and the distribution center is 99.5% (Use this in-stock probability in all questions). Assume that retail store demands are independent. Set L1 = 1 week. Vary LD = L2 = 2,...,10. Consider the direct from supplier setting. Calculate the optimal basestock level, safety stock and expected inventory for each retail store. Consider the consolidated distribution setting. Calculate the optimal basestock level, safety stock and expected inventory levels for each retail store and the distribution center. Calculate the total expected inventory in direct from supplier and the consolidated distribution settings. Report all your results organized in a table. Compare the direct from supplier setting with the consolidated distribution setting, and explain all your findings clearly.

b) Vary standard deviation of demand at a retail store from 10 to 70 in 10 unit increments. Plot the total inventory in direct from supplier and consolidated shipments settings as a function of the standard deviation. Assume LD = 8, L1 = 1, L2 = 7 weeks. Summarize your observations.

c) Suppose that the demands at the retail stores are correlated. Observe that when i = for i = 1,...,N, N 2 r = N1 i=1 N j=i+1 ij (N 1)N 2 . where ij is the correlation coefficient for store i and j demands. Vary r from 5 to 30 in one unit increments, and plot the total inventory of direct from supplier and consolidated shipments settings as a function of r. Summarize your observations.

d) Consider N = 10,50,100 and r = 5,0,5. Calculate the total inventory of direct from supplier and consolidated shipments settings for the 9 cases. Report your results in a table and summarize your observations. e) Consider the demand data for the 10 retail stores over 125 weeks in the attached Excel file. Note that demand at retail stores might be correlated. Assume LD = 8, L1 = 1, L2 = 7 weeks. Calculate the total inventory of direct from supplier and consolidated shipments settings using the data set. Discuss your results.