A fashion retailer sells a short life fashion product. Suppose that the retailer gets the product from the manufacturer at the wholesale price of $155, and sells the product at the retail selling price of $500. This retailer will sell the product in the store for 3 weeks only. And unsold quantity of this product will be salvaged at a price of $40. Suppose that the demand of this product for this three weeks selling season is estimated to be normally distributed with a mean of 100 and a variance of 900.
a) What is retailer's optimal stocking quantity? "What is the service level (also called fill rate) with this optimal stocking quantity?
b) Suppose that the manufacturer produces the product at a cost of $63. And the manufacturer and the retailer are managed by the same firm and behave like a whole supply chain, than what is the optimal product quantity for this supply chain?
c) Is the retailer's optimal stocking quantity equal to the supply chain's? If No 'what does it mean?
d) Explain why a return contract such as buy-back can successfully coordinate this supply chain. Find the buy-back price that can achieve coordination when the wholesale price is $155.