Inputs
Mean Demand 4,000
Standard Deviation of Demand 1,600
Benetton’s Sale Price, c = 36.00$
Benetton’s Cost, v = 20.00$
Salvage value for Benetton, sm = 10.00$
Retailer’s Sale Price, p = 55.00$
Salvage value, sr = 25.00$
Order size, O = 3,931
Contract
alpha = 0.35
beta = –
Q = 5,307
q = 3,931
Output
Retailer’s Expected purchase = 4,418
Retailer’s Expected sales = 3,813
Manufacturer’s profits = 61,791$
Retailer’s profits = 65,804$
Supply chain profit = 127,595$
Benetton has entered into a quantity flexibility contract with a retailer for a seasonal product. If the retailer orders O
units, Benetton is willing to provide up to another 35 percent if needed. Benetton’s production cost is $20, and it
charges the retailer a wholesale price of $36. The retailer prices to customers at $55 per unit. Any unsold units can
be sold by the retailer at a salvage value of $25. Benetton can salvage only $10 per unit for its leftover inventory. The
retailer forecasts demand to be normally distributed, with a mean of 4,000 and a standard deviation of 1,600.
a. How many units Oshould the retailer order?
b. What is the expected quantity purchased by the retailer (recall that the retailer can increase the order by up to 35
percent after observing demand)?
c. What is the expected quantity sold by the retailer?
d. What is the expected overstock at the retailer?
e. What is the expected profit for the retailer?
f. What is the expected profit for Benetton?