Problem Set on Inventory Management

M7 Problem Set – Inventory Management (100 pts)

Question-1 (40 pts)

InstaCam sells 1200 cameras per year, and the demand pattern throughout the year is very steady. The

store orders its cameras from a regional supplier at a cost of $250 each. Each time an order is placed, an

ordering cost of $125 is incurred. Holding costs are about 8.33% of the cost of the item annually.

Currently, InstaCam orders cameras every quarter – i.e, in quantities of 300 units.

a. For the current ordering policy (10 pts)

1. What is the average inventory held? (2 pts)

2. What is the number of orders placed annually? (4 pts)

3. What is the total annual cost of holding and ordering? (4 pts)

b. What is the economic ordering quantity – that minimizes the sum of holding and ordering costs?

(5 pts)

c. For the EOQ (12 pts)

1. What is the average inventory held? (2 pts)

2. What is the number of orders placed annually? (4 pts)

3. What is the number of days between orders? Assume InstaCam works 300 days a year.

(2 pts)

4. What is the total annual cost of holding and ordering? (2 pts)

5. How much does InstaCam save by switching from the current order quantity to the

EOQ? (2 pts)

d. Suppose the supplier has a lead time of 5 days. What reorder level should InstaCam use? (3 pts)

e. If InstaCam places an order of at least 150 cameras each time it orders, the supplier will reduce

the price of each camera by $5. Should InstaCam use an order quantity of 150 units in order to

get this discount? Calculate all costs and savings and make a recommendation. (10 pts)

Question-2 (30 pts)

HappyNY is an Internet order business that sells one popular New Year greeting card once a year. The

cost of the paper on which the card is printed is $0.05 per card, and the cost of printing is $0.15 per

card. The company receives $2.15 per card sold. Since the cards have the current year printed on them,

unsold cards have no salvage value. Its customers are from all over the country; demand is normally

distributed with mean 8,000 and standard deviation 1500.

(Each question below is worth 5 points.)

a.

b.

c.

d.

e.

f.

What is the cost of an unsold greeting card?

What is the cost of a “shortage”, i.e., not having a card when there is demand for it?

What is the critical fractile for HappyNY? What does this mean?

What is the optimal order quantity for the New Year greeting card?

If HappyNY uses the quantity in (d), what is the risk it is taking of a shortage?

A market research survey is able to reduce the standard deviation of demand to 1000 cards.

What is the effect of this on the optimal order quantity?

Question-3 (30 pts)

The number of laptops sold each week by large electronics discount store is normally

distributed with a mean of 50 units and a standard deviation of 10 units. The holding cost of a

laptop is about $85 per year. Ordering costs are $100 per order. The Taiwanese supplier of the

laptops provides a lead time of 2 weeks. Assume that the store is open all year round.

(Each question below is worth 5 points)

a. What is the economic order quantity (EOQ) for this laptop?

b. What is the total annual holding plus ordering cost for this laptop?

c. The VP of Marketing has specified a 99% service level for these laptops. What should the

reorder point (ROP) be to achieve this service level?

d. What is the safety stock needed to attain the 99% service level?

e. If management decides that a 95% service level is acceptable, what are the new ROP

and the new safety stock?

f. Because of a strike supplier lead time increases to 4 weeks for the foreseeable future.

What are the new ROP and the new safety stock for a 99% service level?

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