SafetyStock(9points)

a. (4 points) Using the fixed-time period inventory model, and given an normally distributed daily demand of mean 120 units and standard deviation 10 units, 1 week between inventory reviews, 3 days for lead time, 113 units of inventory on hand, a target service level of 98%, what is the optimal order quantity?

b. (5 points) A company wants to determine its reorder point (ROP) for maintaining a 96% product availability rate. The market demand during lead time shows a discrete distribution pattern as follows:

Demand Quantity 80

90

100

110

120

130

Probability 0.15 0.15 0.35 0.17 0.15 0.03

What is the safety stock

ROP) If the company reduces the target to an 80% availability rate, what will be the safety stock?

4. Risk Pooling (20 points)

A mail-order firm has four regional warehouses. Weekly demand at each warehouse is normally distributed with a mean of 10,000 units and a standard deviation of 2,000 units. The company purchases each unit of product at $10. Annual holding cost of one unit of product is 25% of its value. 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 during the lead time at each warehouse to be no more than 5%. Assume 50 working weeks in a year.

a. (2 points) What is the optimal order quantity for one single warehouse?

b. (2 points) Assuming that each warehouse operates independently, how much

safety stock does each warehouse hold?

c. (2 points) How much average inventory is held at each warehouse?

that the company

should hold? (Hint: different from

2

d. (2 points) What are the combined annual holding costs and ordering costs for all four warehouses? 10

e. (2 points) On average, how long - in weeks - does a unit of product spend in the warehouse before being sold (Hint: Little's Law)?

f. (2 points) Assume that the firm has centralized all inventories in a single warehouse and that the probability of stocking out during the lead time is still no more than 5%. What is this optimal order quantity for the central warehouse?

g. (2 points) How much safety stock does the central warehouse hold?

h. (2 points) Ideally, how much average inventory can the company now expect

to hold?

i. (2 points) What are the annual holding cost and ordering cost for this central

warehouse? 10

j. (2 points) On average, how long - in weeks - does a unit of product spend in

the central warehouse before being sold (Hint: Little's Law)?

5. Time-series Analysis (9 points)

a. (3 points) A company wants to forecast demand using the simple mov