Troy McClure owns a bookshop in Springfield (Kentucky). In a few weeks from now, the biography of energy tycoon C.M. Burns will be published and Troy has to decide, how much of his book “Power and Destruction” should be ordered. Usually, the demand for a new book is especially large at the beginning; hence it is reasonable to take only one single ordering decision. The selling price of the book is $20 whereas the purchasing price is $12. Manufacturing costs for the publisher amount to $5. The salvage value for the publisher is $2. If at the end of the selling season, there are still books remaining at Troy McClure’s bookshop, he can send them back to the publisher. In return, the publisher will return the whole purchasing price of $12 to Troy. However, Troy has to bear the transportation costs of $4.5 per book. Demand is assumed to be normally distributed with mean 200 books and standard deviation 80 books.
a) Determine Troy McClure’s optimal order quantity, his expected profit and his fill rate.
b) Determine the expected profit of the publisher and the supply chain efficiency when the transport costs are ignored.
c) To which value must Troy’s transportation costs per book be reduced, in order to achieve a supply chain efficiency of 100%?
d) Independent of c): assume that the transportation costs increase to $11. Numerically show the consequences of this change on Troy’s optimal order quantity and argue verbally why this is the case.
e) Follow d), what would happen or what would Troy do if the transportation costs would be completely omitted (i.e. transportation costs = $0)?