Buyback Contracts
Inputs
Mean Demand, μ10,000
Standard Deviation of demand 5,000
VideosRUs’s Cost, c = 10$
VideosRUs’s Sale price, p = 19.99$
VideosRUs’s Salvage value, s = b = 4.99$
Studio’s Cost, v1$
Studio’s Sale price, c10$
Studio’s buyback price, b–$
Intermediate Calculations
Cost of Understocking, Cu 9.99$
Cost of Overstocking, Co 5.01$
Outputs
Order size, O* 12,144
Expected overstock 3,248
Expected understock 1,103
VideosRUs Expected Profit 72,609$
Publisher’s E(Profit) 109,300$
Total Supply Chain Profit = 181,909$
A movie studio sells the latest movie on DVD to VideosRUs at $10 per DVD. The
marginal production cost for the movie studio is $1 per DVD. VideosRUs prices
each DVD at $19.99 to its customers. DVDs are kept on the regular rack for a one–
month period, after which they are discounted down to $4.99 (a price at which they
sell out). VideosRUs places a single order for DVDs. Its current forecast is that
sales will be normally distributed, with a mean of 10,000 and a standard deviation of
5,000.
a. How many DVDs should VideosRUs order? What is its expected profit? How
many DVDs does it expect to sell at a discount?
b. What is the profit that the studio makes given VideosRUs’ actions?
Buyback Contracts
Inputs
Mean Demand, μ10,000
Standard Deviation of demand 5,000
VideosRUs’s Cost, c = 10$
VideosRUs’s Sale price, p = 19.99$
VideosRUs’s Salvage value, s = b = 8.99$
Studio’s Cost, v1$
Studio’s Sale price, c10$
Studio’s buyback price, b4$
Intermediate Calculations
Cost of Understocking, Cu 9.99$
Cost of Overstocking, Co 1.01$
Outputs
VideosRUs’s order size, O* 16,648
Expected overstock 6,862
Expected understock 214
VideosRUs’s Expected Profit 90,835$
Studio’s E(Profit) 122,386$
Total Supply Chain Profit = 213,221$
A movie studio sells the latest movie on DVD to VideosRUs at $10 per DVD. The marginal
production cost for the movie studio is $1 per DVD. VideosRUs prices each DVD at $19.99
to its customers. DVDs are kept on the regular rack for a one-month period, after which they are
discounted down to $4.99 (a price at which they sell out). VideosRUs places a single order for
DVDs. Its current forecast is that sales will be normally distributed, with a mean of 10,000 and a
standard deviation of 5,000.
(c) A plan under discussion is for the studio to refund VideosRUs $4 per DVD that does not sell
during the one-month period. As before, VideosRUs will discount them to $4.99 and sell any that
remain. Under this plan, how many DVDs should VideosRUs order? What is the expected profit for
VideosRUs? How many DVDs are expected to be unsold at the end of the month? What is the
expected profit for the studio? What should the studio do?