Optimal overbooking model for car rental business with two levels of prices having stochastic joint booking and show-up levels

Abstract

Overbooking is a technique in revenue management which offers products or services more than the amount available because there is a possibility that some purchasers may later cancel their purchases. In car rental overbooking problem, overbooking model is complicated because in car rental business, different types of car must be taken into account. This paper presents a mathematical overbooking model for car rental business with two levels of prices in order to find the optimal overbooking levels which minimize the total cost, consisting of opportunity cost, outsourcing cost, and upgrading cost. Booking requests and show-up customers are joint random variables which follow some known joint distributions. Sensitivity analysis is performed to examine the effects of parameters in the overbooking model on the optimal overbooking levels. Due to the complication of the overbooking model, several simplified models are presented as alternative methods for estimating the solutions of the overbooking problem. The results show that the total cost difference between the optimal model and the proposed regression models is in the range of about 3.2–14.09%. The expected total cost when the overbooking policy is implemented is also compared to the total cost when there is no overbooking policy to explore how overbooking decision is significant in minimizing total cost.