TrustCar is a firm that rents cars in a small island in the Mediterranean sea. Customers of TrustCar aim to get a car for the weekend they visit the island (Friday night to Sunday evening). The firm offers two types of cars for renting: (i) 50 Basic cars (such as Renault and Ford) and (ii) 7 Luxury cars (such as Mercedes Benz and BMW). Of course, the price for renting a Luxury car is much higher than for the Basic cars: for Luxury cars the renting price per weekend is 600 EUR and 200 EUR for basic cars. TrustCar offers their cars through only one channel, the web-page of the firm. In that website the potential clients can book cars up to 90 days before picking-up the cars. During the last months, TrustCar faces many problems with the demand for Basic cars. First, the number of customers interested on this type of car largely exceeds the capacity. Second, although the demand is high, there are many cancellations for Basic cars. To deal with these issues, Mr. Drof, the owner of TrustCar, has collected information about the frequency of such loss demand. Based on such data, he estimated the cancellation rate for the 90 days in the booking horizon. The table below is an example of the cancellation rates for 8 days.

Day 1 2 3 4 5 6 7 8 Cancelation rate 0.30 0.27 0.21 0.16 0.12 0.09 0.05 0.03

Based on this information, Mr. Dorf aims to set an overbooking policy that leads to higher revenues for the firm.

2 Discussion

1. What are the elements that Mr. Dorf should consider when denying the services to some customers? What is your advise for dealing with the potential issues that may arise when implementing an overbooking policy?

2 2. Mr. Dorf is convinced that he should set an overbooking policy in such a way the probability of denying a service is at most 7%. What should be the booking limit? Plot the overbooking limit.

3. An assistant of Mr. Dorf advised him to change the performance measure of the booking policy. Instead of using the probability of denying a service, he proposes to use the proportion of customer that effectively can take a car. Mr. Dorf decides to set the targeted proportion of satisfied customer to 0.95. What should be the booking limit? Plot the overbooking limit.

4. Beside the ideas of Mr. Dorf, you want to propose a booking limit that maximizes the expected profit of the firm. If the compensation policy of TrustCar is to return the full-fare and to provide additional services, such as a night in a hotel close to the store (whose cost is 100 EUR) and a dinner for 2 persons (50 EUR), what is your proposal for the booking limit? Plot the overbooking limit.

5. Mr. Dorf likes your proposal, but he does not consider interesting the way you compute the compensation cost. Moreover, he really appreciate the idea of his assistant (to set the targeted proportion of satisfied customers in 0.95). Based on those two proposals, could you provide an estimation of the marginal cost of a denied service?

6. Now, Mr. Dorf would like to test the overbooking limits of questions 2, 3 and 4 and to compare them with the policy of working without overbooking. To do so, he would like to check how these proposed limits could perform with the data of the last booking horizon. What could be the indicators to measure the quality of the policies? Provide a comparison. Be clear in your reasoning and assumptions.