3. IceLogos supplies local youth ice-hockey teams organizations with game-ready

Question

3. IceLogos supplies local youth ice-hockey teams organizations with game-ready hockey sweaters. IceLogos has four major youth organizations that it supplies, shown in the table below. Demand for game sweaters for the upcoming ice-hockey season is expected to be normally distributed for each youth organization with the means and standard deviations shown below. IceLogo currently produces each sweater at a cost of S15 and it is sold for S50. Any leftover inventory at the end of the selling season is donated to charity. IceLogo receives a tax benefit of S6 per sweater for the donation, but must pay $3 per sweater in holding costs for unsold inventory Mean De mand Standard Deviation 2,000 2,500 2,000 2,200 Youth Organization 5,000 7,000 4,500 4,000 Cincinnati Swords Johnstown Jets Mason Mighty Ducks TriState Spartans a) b) c) How many sweaters should IceLogo produce for each youth organization? What is the expected profit from this policy? On average, how many sweaters does IceLogo expect to donate to charity at the end of the season?

Explanation / Answer

Cu = Cost of underage = Selling price - Production Cost = $50 - $15 = $35
Co = Cost of overage = Production Cost - Salvage value = $15 - ($6 - $3) = $12

Critical factor = Cu / (Cu+Co) = 35/(35+12) = 0.7447

(a)

Under optimality, the Critical factor must equate the in-stock probability

So, Z = NORMSINV(0.7447) = 0.658 where Z ~ Normal(0,1)

The otimal order quantities are shown in the following table:

(b)

(c)

Organization Mean demand
Std. deviation
Z Order Qty
= + Z* CW 5000 2000 0.658 6315.7 JJ 7000 2500 0.658 8644.6 MMD 4500 2000 0.658 5815.7 TS 4000 2200 0.658 5447.3

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