A publisher sells books to Barnes & Noble at $12 each.
The marginal production
cost for the publisher is $1 per book. Barnes & Noble prices the book to its
customers at $24 and expects demand over the next two months to be normally
distributed, with a mean of 20,000 and a standard deviation of 5,000. Barnes &
Noble places a single order with the publisher for delivery at the beginning of the
two-month period. Currently, Barnes & Noble discounts any unsold books at the end
of two months down to $3, and any books that did not sell at full price sell at this
price.
a. How many books should Barnes & Noble order? What is its expected profit? How
many books does it expect to sell at a discount?
b. What is the profit that the publisher makes, given Barnes & Noble’s actions?
Buyback Contracts
Inputs
Mean Demand, μ 20,000
Standard Deviation of demand 5,000
Barnes & Noble's Cost, c = $ 12
Barnes & Noble's Sale price, p = $ 24
Barnes & Noble's Salvage value, s = b = $ 3
Publisher's Cost, v $ 1
Publisher's Sale price, c $ 12
Publisher's buyback price, b $ -
Intermediate Calculations
Cost of Understocking, Cu $ 12
Cost of Overstocking, Co $ 9
Outputs
Order size, O* 20,900
Expected overstock 2,477
Expected understock 1,577
Barnes & Noble's Expected Profit $ 198,784
Publisher's E(Profit) $ 229,901
Total Supply Chain Profit = $ 428,685
A publisher sells books to Barnes & Noble at $12 each. The marginal production cost for
the publisher is $1 per book. Barnes & Noble prices the book to its customers at $24 and
expects demand over the next two months to be normally distributed, with a mean of
20,000 and a standard deviation of 5,000. Barnes & Noble places a single order with the
publisher for delivery at the beginning of the two-month period. Currently, Barnes & Noble
discounts any unsold books at the end of two months down to $3, and any books that did
not sell at full price sell at this price.
(c) A plan under discussion is to refund Barnes & Noble's $5 per unsold book. As before
Barnes & Noble will discount them to $3 and sell any that remain. Under this plan how
many books will Barnes & Noble order? What is the expected profit for Barnes & Noble?
How many books are expected to be unsold? What is the expected profit for the publisher?
What should the publisher do?
Buyback Contracts
Inputs
Mean Demand, μ 20,000
Standard Deviation of demand 5,000
Barnes & Noble's Cost, c = $ 12
Barnes & Noble's Sale price, p = $ 24
Barnes & Noble's Salvage value, s = b = $ 8
Publisher's Cost, v $ 1
Publisher's Sale price, c $ 12
Publisher's buyback price, b $ 5
Intermediate Calculations
Cost of Understocking, Cu $ 12
Cost of Overstocking, Co $ 4
Outputs
Barnes & Noble's order size, O* 23,372
Expected overstock 4,118
Expected understock 746
Barnes & Noble's Expected Profit $ 214,578
Publisher's E(Profit) $ 236,506
Total Supply Chain Profit = $ 451,084
