The target company imports brass lamps from chine. Weekly demand at target's distribution center for lamps is normally distributed with an average of 40000 and a standard deviation of 1200. Each lamp costs $100. Target incurs a holding cost rate of 10$ per year to carry inventory. Each order shipped from china incurs a fixed cost of $40,000 for transportation and distribution costs. To keep calculations easy, assume that a year has 50 weeks.

1. What is the economic order quantity of lamps for the distribution center?

2. If the delivery lead time from China is 4 weeks and Target wants to provide its customers a cycle service level of 95%, how much safety stock should it carry? What major assumption is needed to answer this question? ("z-value" for 95 % service level is 1.65)

3. Fastship is a new shipping company that promises to reduce the delivery lead time for lamps from 4 weeks to 1 week using faster shipping and expedited customs clearance Using Fastship will add $1 to the transportation cost of each lamp compared to the current approach (The fixed transportation and distribution cost of $40,000 per order will not change.) Should Target use Fastship? Why or why not? Quantify the impact of the change

4. Suppose Target decided not to use Fastship. It has 8 distribution centers each of which has the characteristics in part (a). What would be the impact of target centralizing the 9 DCs into one.