Reconsider Prob. 18.6-1 involving Henry Edsel’s car dealership. The current model year is almost over, but the Tritons are selling so well that the current inventory will be depleted before the end-of-year demand can be satisfied. Fortunately, there still is time to place one more order with the factory to replenish the inventory of Tritons just about when the current supply will be gone.
The general manager, Ruby Willis, now needs to decide how many Tritons to order from the factory. Each one costs $20,000. She then is able to sell them at an average price of $23,000, provided they are sold before the end of the model year. However, any of these Tritons left at the end of the model year would then need to be sold at a special sale price of $19,500. Furthermore, Ruby estimates that the extra cost of the capital tied up by holding these cars such an unusually long time would be $500 per car, so the net revenue would be only $19,000. Since she would lose $1,000 on each of these cars left at the end of the model year, Ruby concludes that she needs to be cautious to avoid ordering too many cars, but she also wants to avoid running out of cars to sell before the end of the model year if possible. Therefore, she decides to use the stochastic single-period model for perishable products to select the order quantity. To do this, she estimates that the number of Tritons being ordered now that could be sold before the end of the model year has a normal distribution with a mean of 50 and a standard deviation of 15.
(a) Determine the optimal service level.
(b) Determine the number of Tritons that Ruby should order from the factory.