Question: Henry Edsel is the owner of Honest Henry's, the largest car dealership in its part of the country. His most popular car model is the Triton, so his largest costs are those associated with ordering these cars from the factory and maintaining an inventory of Tritons on the lot. Therefore, Henry has asked his general manager, Ruby Willis, who once took a course in operations research, to use this background to develop a cost-effective policy for when to place these orders for Tritons and how many to order each time. Ruby decides to use the stochastic continuous-review model to determine an (r, Q) policy. After some investigation, she estimates that the administrative cost for placing each order is $1, 500 (a lot of paperwork is needed for ordering cars), the holding cost for each car is $3,000 per year (15 percent of the agency's purchase price of $20,000), and the shortage cost per car short is $1,000 per year (an estimated probability of 1/3 of losing a car sale and its profit of about $3,000). After considering both the seriousness of incurring shortages and the high holding cost, Ruby and Henry agree to use a 75 percent service level (a probability of 0.75 of not incurring a shortage between the time an order is placed and the delivery of the cars ordered). Based on previous experience, they also estimate that the Tritons sell at a relatively uniform rate of about 900 per year. After an order is placed, the cars are delivered in about two thirds of a month. Ruby's best estimate of the probability distribution of demand during the lead time before a delivery arrives is a normal distribution with a mean of 50 and a standard deviation of 15.

(a) Find the order quantity.

(b) Use a table for the normal distribution to solve for the reorder point.

(c) Given your previous answers, how much safety stock does this inventory policy provide?

(d) This policy can lead to placing a new order before the delivery from the preceding order arrives. Indicate when this would happen.