1: Zara plan to sell some skirts for this year's summer season. Since the skirt is a fashion product, Zara will produce them once only near the season and there is no replenishment opportunity (like newspaper). The production cost for each skirt is HK$50. Zara can sell it for HK$100. If Zara cannot sell them all, it is paid HK$20 for each unsold skirt. The demand estimation for this year's summer season is listed below.

Possible

Demand    probability
1000        5%
1500        15%
1800        19%
2000       23.5%
2300       37.5%

What is the optimal ordering quantity? What is the tradeoff in your mind between a larger order quantity and a small one?

2: A multi-national firm has four regional warehouses. Demand at each warehouse is normally distributed with a mean of 10,000 per week and a standard deviation of 2,000. Holding cost is 25%, and each unit of product costs the company $10. Each order incurs an ordering cost of $1,000 (primarily from fixed transportation costs), and lead time is 1 week. The company wants the probability of stocking out in a flow to be no more than 5 %. Assume 50 working weeks in a year.

a. Assuming that each warehouse operates independently, what should be the optimal ordering quantity at each warehouse? How much safety stock does each warehouse hold? How much average inventory is held (at all four warehouses combined), and at what annual cost (holding + purchasing+ ordering)?

b. Assume that the firm has centralized all inventories in a single warehouse and that the probability of stocking out in a cycle can still be no more than 5%. Ideally, how much shall the company order? how much safety stock shall the company target at?

And how much average inventory can the company now expect to hold, and at what annual cost?