Question

The manager at Sportmart, sporting goods store, has to decide on the number of skis to purchase for the winter season. Based on past demand data and weather forecast for the year, management has forecasted demand to be normally distributed, with a mean of 350 and a standard deviation of 150. Each pair of skis costs $100 and retails for $250. Any unsold skis at the end of the season are disposed of for $85. Assume that it costs $10 to hold a pair of skis in inventory for the season.

(a) How many skis should the manager order to maximize expected profits?

(b) Evaluate the maximum expected profit.

(c) The manager has decided to order 450 pairs of skis for the upcoming season. Evaluate the expected lost sales.

(d) The manager has decided to order 450 pairs of skis for the upcoming season. Evaluate the expected leftovers.

Answer 1

Average demand (mean)= 350

Standard deviation of demand (stdev)=100

Material costc = $100

Pricep =$250

Salvage values =85 – 5 = $80

Cost of understockingCu=p– c = 250 – 100 = $150

Cost of overstockingCo=c– s= 100 – 80 = $20

Optimal cycle service levelCSL* =Cu/(Cu+ Co) = 150/170 = 0.88

Optimal order sizeO* = NORMINV(CSL*, , ) = 468

When Demand is Normally Distributed,

Expected profits =(p– s)Fs((O– )/) – (p– s)fs((O– )/) – O(c– s)F(O, , ) + O(p– c)[1 – F(O, , )]

Expected overstock = (O– )Fs((O–)/) + fs((O– )/

Expected understock = (– O)[1 – Fs((O–)/)] + fs((O– )/)