Question

You are working for an outdoor apparel company and have been tasked with choosing order quantities for next season's line of ski jackets. For each jacket style, you have cost information as well as a forecast from the marketing department specifying the mean and standard deviation of expected demand, which you can assume will follow a normal distribution.

One of the jackets, the Algonquin Parka, has total landed cost of $90 per unit and will retail for $195. Any leftover jackets will be sold at a 60% discount off the retail price. According to marketing, the most likely value of demand (i.e. the mean of the demand distribution) is 2000 units, with a standard deviation of 300 units.

a. What is the underage cost, c_u, i.e. the cost of not stocking an incremental unit that a customer would have wanted to buy? Round your answer to the nearest integer.

b. What is the overage cost, c_o, i.e. the cost of stocking an incremental unit that does not sell? Round your answer to the nearest integer.

c. What is the optimal order quantity for the Algonquin parka? Round your answer to the nearest integer.

Answer 1

Cost price(CP) = $90

Selling price(SP) = $195

Salvage value(V) = $195 - (60% of $195) = $195-$117 = $78

Average daily demand (d) = 2000 units

Standard deviation of daily demand (d) = 300 units

a) Underage cost(Cu) = SP-CP = $195-$90 = $105

b) Overage cost(Co) = CP-V = $90-$78 = $12

C) Service level = Cu/(Cu + Co) = 105/(105+12) = 105/117 = 0.90 = 90%

At 90% service level value of Z = 1.28

Optimal order quantity = d + Z × d

= 2000 + (1.28 × 300)

= 2000+384

= 2384 units