3- Tom and Stacy work together to order items for a large clothing retailer. They disagree about ordering a popular jeans brand from Italy. The demand for the jeans is variable and follows Normal distribution. They use (Q, R) policy to manage their inventory. Stacy suggests that they should order 200 pairs when their inventory reaches or falls below 50. While Tom agrees that the order size should be 200, he thinks that they should place an order when their inventory reaches or falls below 80. Explain why each of the following statements is true or false.

a. Stacys policy results in higher service levels than those under Toms policy.

b. Stacys policy is expected to result in more number of orders placed in a year than that under Toms policy.

c. Toms policy results in lower average shortage cost in a year than that under Stacys policy.

d. Toms policy results in lower total expected annual cost than that under Stacys policy.

4. Tom in Problem 3 argues with Stacy that, if they place an order when the inventory reaches or falls below 50 (as Stacy suggests), then they need to increase their order size to 230. Explain why each of the following statements is true or false.

a. Under Toms new policy (i.e., ordering 230 when inventory reaches 50) the likelihood of shortage is less than that under Stacys policy.

b. The fraction of customers who face shortage under Toms new policy is the same as that under Stacys policy.

c. Stacys policy is expected to result in more number of orders placed in a year.

d. Toms new policy results in lower average shortage cost in a year.

e. Toms policy results in lower expected annual inventory holding cost in a year.

5. Finally, Tom and Stacy in Problem 3 come to an agreement and decide to place an order for 200 pairs of jeans when their inventory reaches or falls below 60. This results in cycle-service level of 90 percent. However, they get a call from the supplier of jeans in Italy, informing them that the demand for the jeans has increased throughout Europe. Because the supplier does not have enough capacity to satisfy the new demand, future orders will take twice the time to deliver. Specifically, the suppliers order lead time is doubled from 1 week to 2 weeks. Tom and Stacy decide not to change the new ordering policy they agreed upon, since their demand has not changed. If the new policy is implemented, explain why each of the following statements is true or false.

a. The cycle-service level is reduced, but fill rate remains the same.

b. Total average annual inventory holding cost is decreased.

c. Total average annual order setup cost is decreased.

d. Total average annual shortage cost is increased.

6. Tom and Stacy in Problem 5 come to the conclusion that since the supplier lead time is doubled, they should double their reorder point from 60 to 120 to maintain cycle-service level of 90 percent. The order size remains at 200 pairs. Explain why each of the following statements is true or false.

a. Doubling reorder point results in higher cycle-service level than 90 percent.

b. Doubling reorder point increases expected annual inventory holding cost compared to current annual holding cost.

c. Doubling reorder point results in a safety inventory smaller than what is needed to achieve cycle-service level of 90 percent.

d. Doubling reorder point makes the total average annual shortage cost remain the same.