# 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 presented in Sec. 18.6 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 twothirds 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) Solve by hand for the order quantity.

(b) Use a table for the normal distribution (Appendix 5) to solve for the reorder point.

T (c) Use the Excel template for this model in your OR Courseware to check your answers in parts (a) and (b).

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

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

Ruby decides to use the stochastic continuous-review model presented in Sec. 18.6 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 twothirds 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) Solve by hand for the order quantity.

(b) Use a table for the normal distribution (Appendix 5) to solve for the reorder point.

T (c) Use the Excel template for this model in your OR Courseware to check your answers in parts (a) and (b).

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

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

## Answer to relevant Questions

Tim Madsen is the purchasing agent for Computer Center, a large discount computer store. He has recently added the hottest new computer, the Power model, to the store’s stock of goods. Sales of this model now are running ...Jed Walker is the manager of Have a Cow, a hamburger restaurant in the downtown area. Jed has been purchasing all the restaurant’s beef from Ground Chuck (a local supplier) but is considering switching to Chuck Wagon (a ...Consider the overbooking model presented in Sec. 18.8. For a specific application, suppose that the parameters of the model are p = 0.5, r = $1,000, s = $5,000, and L = 3. Use the binomial distribution directly (not the ...Swanson’s Bakery is well known for producing the best fresh bread in the city, so the sales are very substantial. The daily demand for its fresh bread has a uniform distribution between 300 and 600 loaves. The bread is ...Consider Example 1 (manufacturing speakers for TV sets) introduced in Sec. 18.1 and used in Sec. 18.3 to illustrate the EOQ models. Use the EOQ model with planned shortages to solve this example when the unit shortage cost ...Post your question

0