The penalty cost p used in the shortage model might be very difficult to estimate. Instead, a company might use a service-level constraint, such as, “95% of all demand must be met from on-hand...

The penalty cost p used in the shortage model might be very difficult to estimate. Instead, a company might use a service-level constraint, such as, “95% of all demand must be met from on-hand inventory.” Solve Problem 35 with this constraint instead of the $20,000 penalty cost. Now the problem is to minimize the total annual ordering and holding costs subject to meeting the service-level constraint.

Problem 35

A luxury car dealer must pay $20,000 for each car purchased. The annual holding cost is estimated to be 25% of the dollar value of inventory. The dealer sells an average of 500 cars per year. He is willing to backlog some demand but estimates that if he is short one car for one year, he will lose $20,000 worth of future profits.


Each time the dealer places an order for cars, the ordering cost is $10,000. Determine the luxury car dealer’s optimal ordering policy. What is the maximum shortage that will occur? Assume it costs $5000 to store a car for a year (this is in addition to the holding cost above).