Question

CheapBuy is an electronics retail chain selling Gateway netbooks. The demand for the Gateway netbook LT20 at their local store is normally distributed with a mean of 38 netbooks/week and standard deviation of 6 netbooks/week. CheapBuy orders netbooks from Gateway at unit cost of $220. The annual cost of carrying inventory at the store is 5% of the purchase cost per unit per year. It takes 2 weeks to receive a delivery. Each time CheapBuy places an order it incurs a fixed cost of $100. The store continuously reviews its inventory and orders when inventory falls below its reorder point. (Do NOT round numbers, especially inventory, to integer. Round numbers to 2nd decimal place.)

a. Compute the safety stock (number of netbooks) needed to maintain a service level of 95%.

b. What is the average demand during lead time?

c. What is the reorder point?

d. What is the optimal order quantity (Assuming 52 weeks a year)? How much additional safety stock would be needed if CheapBuy wishes to increase the service level at their local store from 95% to 98%?

Answer 1

a. Compute the safety stock (number of netbooks) needed to maintain a service level of 95%.

The safety stock at 95% service level

Safety stock = z * st. dev. Of demand * sqrt (L)

Where,

z value for the desired Service Level at 95%= 1.65

Standard deviation of weekly demand =6 units

L is the lead time = 2 weeks

Therefore,

Safety stock = 1.65 * 6 * √2 = 14 units

b. What is the average demand during lead time?

Average demand during lead time = D (L)

Where,

Average weekly demand D = 38 units

Lead time L = 2 weeks

Therefore,

Average demand during lead time = 38 * 2 = 76 units

c. What is the reorder point?

Formula to calculate reorder point -

Reorder Point = Average demand during lead time + safety stock

Now putting the values from (a) and (b) into formula, we get

Reorder Point = 76 + 14 = 90 units

d. What is the optimal order quantity (Assuming 52 weeks a year)?

Annual demand D = 38 unit per week * 52 weeks a year = 1,976 unit per year

Ordering cost S = $100 per order

Holding or carrying cost H =5% of the unit purchase cost= $220 * 5% = $11 per unit per annum

The optimal order quantity is the economic order quantity (EOQ). Formula of economic order quantity (EOQ)

EOQ = sqrt (2* D*S/H) = sqrt(2 * 1,976 * 20 /2) = 189.55 units

How much additional safety stock would be needed if CheapBuy wishes to increase the service level at their local store from 95% to 98%?

The safety stock at 98% service level

Safety stock = z * st. dev. Of demand * sqrt (L)

Where,

z value for the desired Service Level at 98%= 2.054

Standard deviation of weekly demand =6 units

L is the lead time = 2 weeks

Therefore,

Safety stock = 2.054 * 6 * √2 = 17.43 units

Therefore,

Additional safety stock = the safety stock at 98% service level - The safety stock at 95% service level

= 17.43 -14 = 3.43 units