Because of the industrious nature of the faculty members involved, the Department of Management Sciences at a well-known university consumes a large amount of 81/2 × 11 lined paper. One of the secretaries, with the aid of a graduate student, has developed the following procedure: Once a week (at 5 p.m. on Friday), she reviews the stock level. If there are 20 or fewer pads, she orders 100 additional pads, which always arrive late on the next Tuesday. If there are more than 20 pads on the shelf, she does nothing until at least the next Friday. Assume that the faculty’s needs follow a Poisson distribution with the following rates

(in pads/day):

Day Sun Mon Tue Wed Thu Fri Sat Mean 0.5 2 2 2 2 2 0.5 If a professor needs a pad of paper and none are available, he rushes over to the university bookstore (or to an outlet in the local community) and buys the pad.

a. Indicate how one might arrive at the cost per unit short.

b. Make a crude estimate of each of (i) the safety stock, (ii) the probability of stockout per replenishment cycle, and (iii) the expected number of pads short per year. lpo897