Freddie the newsboy runs a newstand. Because of a nearby financial services office, one of the newspapers he sells is the daily Financial Journal. He purchases copies of this newspaper from its distributor at the beginning of each day for $1.50 per copy, sells it for $2.50 each, and then receives a refund of $0.50 from the distributor the next morning for each unsold copy. The number of requests for this newspaper range from 15 to 18 copies per day. Freddie estimates that there are 15 requests on 40 percent of the days, 16 requests on 20 percent of the days, 17 requests on 30 percent of the days, and 18 requests on the remaining days.
(a) Use Bayes’ decision rule presented in Sec. 16.2 to determine what Freddie’s new order quantity should be to maximize his expected daily profit.
(b) Apply Bayes’ decision rule again, but this time with the criterion of minimizing Freddie’s expected daily cost of underordering or overordering.
(c) Use the stochastic single-period model for perishable products to determine Freddie’s optimal order quantity.
(d) Draw the cumulative distribution function of demand and then show graphically how the model in part (c) finds the optimal order quantity.