Question

The CQ EMBA Bagel and Coffee Shop carries Gimme!’s freshly roasted coffee. The Kingston branch has the coffee shipped over from Ithaca. There is a fixed fee of $30 for each shipment of coffee. Gimme! charges the Bagel and Coffee Shop $12/pound for the coffee and the Bagel and Coffee Shop uses a 20% interest rate for holding cost. The Kingston branch uses 20 pounds of coffee per day with a standard deviation of 4 pounds per day. The lead time for new coffee to arrive to the Kingston branch once it is ordered is 4 days. Since the CQ EMBA students cannot live without coffee, the coffee shop would like to maintain a service level of 99.9%. a) Currently, the coffee shop orders 200 pounds of coffee when the amount of coffee in inventory goes down to 100 pounds. What is the annual fixed ordering cost and holding cost if they continue to use this policy? b) One of the EMBA students suggested that the coffee shop can improve its inventory policy by using an optimal reorder point and order quantity. Compute the optimal order quantity and reorder point the coffee shop should use.

Answer 1

Average daily demand, d = 20 lbs.
Std.Dev of daily demand, σ = 4 lbs.
Fixed ordering cost, K = $30
Cost per pound, C = $12
Carrying cost per pound, h = 20% of C = $2.4
Lead time, L = 4 days
Cycle service level = 99.9% which leads to z = 3.09

(a)

Order size, Q = 200 lbs.
Reorder point, R = 100 lbs.

Annual demand, D = 365*d = 365*20 = 7300 lbs.

Annual fixed ordering cost = (D/Q) * K = (7300/200)*30 = $1,095

Annual holding cost for cycle stock = (Q/2) * h = (200/2) * 2.4 = $240

Safety stock = R - d.L = 100 - 20*4 = 20

Annual holding cost for safety stock = Safety stock * h = 20*2.4 = $48

So, annual holding cost for both cycle stock and safety stock = 240+48 = $288

(b)

EOQ = (2.D.K / h)^1/2 = SQRT(2*7300*30 / 2.4) = 427.2 lbs.

Required safety stock = z.σ.√L = 3.09*4*√4 = 24.72 lbs.

R = d.L + Safety stock = 20*4 + 24.72 = 104.72 lbs.

So, the optimal order quantity and reorder point are Q = 427.2 lbs. and R = 104.72 lbs respectively.