if The publisher is thinking of offering a buy-back contract to the book store. According to this contract, it will sell books to the book store at a price of w per copy; but at the end of the season, it will buy back unsold copies at a price of b per copy. The publisher will dispose all unsold copies at 50% off the retail price. 

When w = 25, what is the buy-back price b that the publisher should use to induce a critical ratio = 80%? What is the new optimal quantity Q that the book store should order now, to maximize his expected profits? Round up Q to integer if necessary. 

 

Detail for question and answers to first two: 

 

Purdue Book Store is trying to decide on how many copies of a book to purchase from the McGraw Hill publisher at the start of a selling season.  The book retails at $28 per copy at the book store, and costs $15 for the book publisher to produce each copy. Purdue Book Store will dispose of all of the unsold copies of the book at 50% off the retail price at the end of the season. 

It is estimated that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250. 

We consider the book publisher ("supplier") and the book store ("retailer") as a simple supply chain.

1. First, consider the centralized case where the supplier and retailer belong to the same company. What is the optimal quantity Q that the book store should order from the publisher to maximize the total supply chain's profit? Round upQ to integer if necessary. 

 

1. Then, consider the decentralized case without any coordination. The publisher sells the book to the book store at $21 per copy. Now, what is the optimal quantity Q that the book store should order from the publisher to maximize his own expected profits? Round up Q to integer if necessary. 

 

15 Purchase Cost 28 Selling Price O Salvage 1000 Mean 250 Std. Deviation 15 Overage cost (Co) 13 Underage cost (Cu) 46% Critical Ratio Purchase cost minus salvage Selling Price Purchase cost Underage / Overage + Underage) -0.090 Z Value 978 Decision based on Newsvendor solution = mean + z value * Std. Deviation