Question 2. [Logistics Improvement]Consider the following excerpt from a NYTIMES article about Restoration Hardware:

Despite its early promise.Restoration has had trouble becoming a mass market player. What went wrong? High on its own buzz, the company expanded at breakneck speed, more than doubling the number of stores, to 94. Company managers agree, for example, that Restorations original inventory system, which called for all furniture to be kept at stores instead of at a central warehouse, was a disaster.

Let's look at one Restoration Hardware product, a leather chair. Average weekly sales of this chair in each store has a mean of 1.25 and standard deviation of 1.12.

(a) If each store holds its own inventory (all stock is kept at stores), then what is the company's total safety stock in 94 stores? The company policy is to target a 99.25 percent in-stock probability. The replenishment lead time is 12 weeks. (3 points)

Safety stock at one store:

99.25% service = Z of 2.43

Std dev. During lead time = (sqrt(12)*1.12) = 3.88

Safety stock = 2.43*3.88 = 9.43 (1 store)

Total safety stock at all stores:

Std dev. During lead time = sqrt(12)* (1.12*94) = 364.7

Safety stock = 2.43*364.7 = 886.221 (94 locations)

(b) Suppose Restoration Hardware builds a central warehouse to serve the 94 stores. The lead time from the supplier to the central warehouse is 12 weeks. The lead time foam the central warehouse to each store is one week. Suppose the warehouse operates with a 99 percent in-stock probability, but the stores maintain a 99.25 percent in-stock probability. What would be the new total safety stock at 94 stores? What would be the warehouse safety stock? (Consider warehouse demand as the sum of 94 store demands). (3 points)

Safety stock at one store:

Warehouse demand mean and standard deviation:

Safety stock at warehouse:

Total safety stock at warehouse and all stores:

(c) Please qualitatively explain each the following three issues (no more than a few sentences for each issue): (3 points) 1. Which of the two previous parts ((a) and (b)) have lower total system safety stock and explain why is it so?

2. Why may the theoretical savings in total safety stock (difference between (a) and (b)) computed above many not be fully realized in practice?

3. Why may the warehouse demand standard deviation calculation above may underestimate the actual variability?