The IMU bookstore needs your help to determine the number of Cachon and Terwiesc

Question

The IMU bookstore needs your help to determine the number of Cachon and Terwiesch’s book (our textbook) to purchase before the 2018 summer session opens. The book retails at $100. McGraw Hill sells the book to IMU for $75. IMU will dispose of all the unsold copies of the book at 85% off the retail price at the end of the summer session. IMU estimates that demand for this book is Poisson with mean of 9 units. As an incentive for IMU to order more of Cachon and Terwiesch’s book, McGraw Hill is offering the following deal. At the end of the summer session, McGraw Hill will buy back unsold copies of the book for $35. However, IMU would have to bear the cost of shipping unsold copies back to McGraw Hill at $2.00 per copy. Find the expected profit maximizing answers to the following questions.

How many books should the IMU store order assuming McGraw Hill does not offer the buy back incentive?

a. 5

b. 6

c. 7

d. 8

e. 9

Explanation / Answer

Considering that McGraw Hill does not offer buyback incentive

Underage/shortage cost, Cu = Retail selling price - Cost = 100 - 75 = $ 25

Overage/excess cost, Co = Cost - discounted selling price = 75 - 100*(1-85%) = $ 60

Optimal service level = Cu/(Cu+Co) = 25/(25+60) = 0.2941

F(x) = 0.2941

Demand is poisson distributed with mean of 9 units. .

F(x) = 0.2941 (as determined above )

Therefore, using inverse poisson function, we get, x = 9 units

ANSWER: e) 9.

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