If a supplier manufactures compact discs at $1 per unit and sells them to music

Question

If a supplier manufactures compact discs at $1 per unit and sells them to music store at $5 per unit. The retailer sells each to the end consumer at $10. The supplier agrees to buy back discs that have not sold at $2. Assume demand is uncertain. We know optimal order size for Music store under the policy is 1,096, and demand follows N(1000,300). (the expected return to supplier is 174). Evaluate the expected profits of the supplier and retailer.

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

Answer a:  Optimal Order size is 922 Pices where they can made a profit of $ 4610

Answer b: 0

Answer c:

Expected Profit of Manufacturer Expected Profit of Retailer Manufacturing cost (MO) $1 Cost Price (CP) $5 Selling price (SP) $5 Selling price (SP) $10 Buy Back $2 Buy Back $2 No. of optimal unit sold 1096 No. of optimal unit sold 1096 Return from retailer Units 174 Return from supplier Units 174 Total MO $1*1096 1096 Total Unit sold Unit 922 Total SP $5*1096 5480 Total CP $5*1096 5480 Salvage Value $2*174 384 Total SP $10*922 9220 Profit =(SP-MO)-return 4000 Return Value $2*174 384   Profit =(SP-CP)-return 3356

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