33 Erik Marshall owns and operates one of the largest BMW auto dealerships in St. Louis. In the past 36 months, his weekly sales of Z3s have ranged from a low of 6 to a high of 12, as reflected in the following table:

Z3 SALES PER WEEK FREQUENCY 6 3 7 4 8 6 9 12 10 9 11 1 12 1 Erik believes that sales will continue during the next 24 months at about the same rate and that delivery lead times will also continue to follow this pace (stated in probability form):

DELIVERY TIME

(weeks) PROBABILITY 1 0.44 2 0.33 3 0.16 4 0.07 Erik’s current policy is to order 14 autos at a time

(two full truckloads, with 7 autos on each truck)

and to place a new order whenever the stock on hand reaches 12 autos. Beginning inventory is 14 autos. Erik establishes the following relevant costs:

(i) The carrying cost per Z3 per week is $400, (ii)

the cost of a lost sale averages $7,500, and (iii) the cost of placing an order is $1,000.

(a) Simulate Erik’s inventory policy for the next two years. What is the total weekly cost of this policy? Also, what is the average number of stockouts per week? Use N replications of your model.

(b) Erik wishes to evaluate several different ordering quantities—12, 14, 16, 18, and 20. Based on the total weekly cost, what would you recommend?

Why? Set R = 12 in each case.