A co-evolutionary matheuristic for the car rental capacity-pricing stochastic problem

Abstract When planning a selling season, a car rental company must decide on the number and type of vehicles in the fleet to meet demand. The demand for the rental products is uncertain and highly price-sensitive, and thus capacity and pricing decisions are interconnected. Moreover, since the products are rentals, capacity “returns”. This creates a link between capacity with fleet deployment and other tools that allow the company to meet demand, such as upgrades, transferring vehicles between locations or temporarily leasing additional vehicles. We propose a methodology that aims to support decision-makers with different risk profiles plan a season, providing good solutions and outlining their ability to deal with uncertainty when little information about it is available. This matheuristic is based on a co-evolutionary genetic algorithm, where parallel populations of solutions and scenarios co-evolve. The fitness of a solution depends on the risk profile of the decision-maker and its performance against the scenarios, which is obtained by solving a mathematical programming model. The fitness of a scenario is based on its contribution in making the scenario population representative and diverse. This is measured by the impact the scenarios have on the solutions. Computational experiments show the potential of this methodology regarding the quality of the solutions obtained and the diversity and representativeness of the set of scenarios generated. Its main advantages are that no information regarding probability distributions is required, it supports different decision-making risk profiles, and it provides a set of good solutions for an innovative complex application.