Please Ignore Part C. Thank you! 18.6-1. Henry Edsel is the owner of Honest Henr
ID: 360746 • Letter: P
Question
Please Ignore Part C. Thank you!
18.6-1. 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 order- ing these cars from the factory and maintaining an inventory of Intons on the lot. Therefore, Henry has asked his general man research, ager, Rub to use this background to develop to place these orders for Tritons and how many to order y Willis, who once took a course in operations a cost-effective policy for when each time. Ruby decides to use the presented in Sec. 18.6 to determine an (R, Q) policy. After some invest stochastic continuous-review model gation, she estimates that the administrative cost for placing each order is $1,500 (a lot of paperwork is needed for ordering ar the holding cost for each car is $3,000 per year (15 percent or the agency's purchase price of $20,000), and the shortage cost ar short is $1,000 per year (an estimated probability of j of Ing a car sale and its profit of about $3,000). After considering e 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) 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 Course ware to check your answers in parts (a) and (b). inventory policy provide? ery from the preceding order arrives. Indicate when this would (d) Given your previous answers, how much safety stock does this (e) This policy can lead to placing a new order before the deliv- happen.Explanation / Answer
Ans....
a) Order quantity = [(2 * avg.demand per year * fixed setup cost per unit per year)/(holding cost per unit per year)]1/2 * [(shortage cost +holding cost) / (shortage cost)]1/2
= [(2*900*1500) / (3000)]1/2 * [(1000 + 3000) / (1000)]1/2 = 30 X 2 = 60
b) Re-order point = mean + K1-L * std. deviation where K is found out using normal distribution table and is the z value, L is service level, here L = 0.75, therefore K1-L = K.25 , now using normal distribution table, we find the value of K.25 = .0675
So, re-order point = 50 + (.675) * 15 = 50 +10.125 = 60.125
c) Safety Stock = K1-L * std. deviation = .675 * 15 = 10.125
d) Placing a new order before the delivery from the preceding order arrives can happen in a situation of stockout. In this case, the excess demand is backlogged, so that the backorders are filled once the order arrives.