If a supplier manufactures compact discs at $2 per unit and sells them to music

Question

If a supplier manufactures compact discs at $2 per unit and sells them to music store at $7 per unit. The retailer sells each to the end consumer at $16. The supplier agrees to buy back discs that have not sold at $3 after the season. Assume demand is uncertain and follows N(1000,300).

a) What is the optimal order size for Music store under the buyback policy?

b) How many discs are expected to be unsold at the end of the season with the optimal size?

c) What is the expected profit for the retailer if ordering the optimal size?

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O*· (c-v)- (b - Sm) ·Expected overstock at retailer

Where: Sm is salvage value for manufacturer

b is buyback price (Salvage for retailer)

c is wholesale price to retailer

v is manufacturing cost per unit

Expected retailer profit =

(p-c) ·(O* - Expected overstock) -(c-b) ·Expected overstock

where p is sale price

Explanation / Answer

a) For music store, Underage cost, Cu = 16 - 7 = 9

Overage cost, Co = 7 - 3 = 4

Optimal service leve = Cu/(Cu+Co) = 9/(9+4) = 0.6923

Z value = NORMSINV(0.6923) = 0.5024

Optimal order size for Music store = 1000 + 0.5024*300 = 1151

(b) For z = 0.5024, L(z) = 0.1971 (L(z) is loss function value taken from standard normal table)

Expected overstock = *L(z) = 300*0.1971 = 210

(c) Expected Profit for the retailer = (16-7)*(1151-210) - (7-3)*210 = $ 7629

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