Question

On consecutive Sundays, Mac, the owner of a local newsstand, purchases a number of The Supply Chain Digest, a popular weekly magazine. He pays $25 for each copy and sells it for $75 per copy. Copies he has not sold during the week can be salvaged for $2 each. Mac’s newsstand sees a weekly demand for the magazine to be approximately uniformly distributed with the range [50, 75]. Since Mac is a very close associate of his publisher, he conveys to the publisher that the risk of an exvess copy is high in comparison to the loss due to shortage. The publisher of the SC Digest, who incurs only $13 to publish a copy of the magazine, suggests Mac that she in fact can offer a buy-back price b on any left-over units and asks Mac to determine the best for both the publisher and Mac’s profit. The publisher will then salvage the excess units returned by Mac (if any) at a value of $2 each. The publisher claims that this mechanism will let Mac buy more magazines and ultimately improve the product availability. Develop a simulation model with 1 million trials to optimize the total supply chain profit (the sum of Mac’s profit and the publisher’s profit) and find the optimal order quantity Q and buy ? back price b on the excess number of units. Note that there are two decision variables. You can design a table with the first row representing different buy-back price p on the left-overs, and first column representing different purchase quantity Q. The cells of the table should be filled with E[Supply Chain Profit] from the simulation and the optimal values can be found from the table.