Question

The UnLimited offers the sweaters to Fashionables at the wholesale price of $40 per sweater, and Fashionables plans to sell each sweater at the retail price of $70 per unit. The UnLimited does not accept any returns of unsold inventory. However, Fashionables can sell all of the unsold sweaters at the end of the season at the fire-sale price of $20 each. As a forecast for demand, Fashionables will use a normal distribution with a mean of 600 and a standard deviation of 100. How many units of sweaters should Fashionables order to maximize its expected profit?

Answer 1

Selling price(SP) = $70

Cost price (CP) = $40

Salvage value(V) = $20

Average daily demand (d) = 600 units

Standard deviation of daily demand (d) = 100 units

Overage cost(Co) = CP - V = $40-$20 = $20

Underage cost(Cu) = SP-CP = $70-$40 = $30

Service level = Cu/(Co + Cu) = 30/(20+30) = 30/50 = 0.60 = 60%

So the optimal service level is 60%

At 60% service level value of Z = 0.25

Optimal order quantity = d + Z x d

= 600 + 0.25 x 100

= 600 + 25

= 625 units

So fashionable should order 625 units of sweaters to maximize expected profit