A publisher sells mass-market fiction books to a retailer for $13 each. The publisher's production cost is $2 per book and the retailer sells these books to its customers at a retail price of $28 per book. Over a typical two-month period, demand for these books is normally distributed with an average of 22,000 and a standard deviation of 10,000 books. The retailer places a single order with the publisher, for delivery at the beginning of a two-month period. Currently, the retailer discounts any unsold books at the end of two months down to $4/unit and expects to sell all such left-over books at this marked down price. (a) How many books should the retailer order and what is its expected profit? What is the publisher's profit as a result of the retailer's order? Compute the expected profit for the entire supply chain. (b) A proposal under discussion is for the publisher to refund the retailer $5 per book that do not sell during the two-month period. As before, the retailer will discount these to $4 per book and sell any that remain. Under this plan, how many books will the retailer order? Compute the expected profits for the retailer, the publisher and the total supply chain. Should the publisher adopt this proposal? Is this proposal acceptable from the perspective of the retailer? What is the effect of this policy on the total supply chain expected profit?
