Abstract

Abstract
Empty repositions are a major problem for car rental companies that deal with special types of vehicles whose number of units is small. In order to meet reservation requirements concerning time and location, companies are forced to transfer cars between rental stations, bearing significant costs and increasing the environmental impact of their activity due to the fuel consumption and CO2 emission. In this paper, this problem is tackled under a vehicle-reservation assignment framework as a network-flow model in which the profit is maximized. The reservations are allocated considering the initial and future availability of each car, interdependencies between rental groups, and different reservation priorities. To solve this model, a relax-and-fix heuristic procedure is proposed, including a constraint based on local branching that enables and controls modifications between iterations. Using real instances, the value of this approach is established and an improvement of 33% was achieved when compared to the company's current practices.

Abstract
This paper aims to present, define and structure the car rental fleet management problem, which includes operational fleet management issues and problems traditionally studied under the revenue management framework. The car rental business has challenging and distinctive characteristics, which are mainly related with fleet and decision-making flexibility, and that render this problem relevant for academic research and practical applications. Three main contributions are presented: an in-depth literature review and discussion on car rental fleet and revenue management issues, a novel integrating conceptual framework for this problem, and the identification of research directions for the future development of the field.

Abstract
Internet sales channels, especially e-brokers that compare prices in the market, have a major impact on car rentals. As costs are heavily correlated with unoccupied fleet, occupation considerations should be integrated with swift responses to the market prices. This work was developed alongside Guerin, a Portuguese car rental, to build a tool that quickly updates prices on e-brokers websites to increase total value. This paper describes the specificities of the problem and their implication on the solution, and presents an adaptative heuristic to update prices and the system’s architecture. © 2015, Springer International Publishing Switzerland.

Abstract
Car rental companies have the ability and potential to integrate their dynamic pricing decisions with their capacity decisions. Pricing has a significant impact on demand, while capacity, which translates fleet size, acquisition planning and fleet deployment throughout the network, can be used to meet this price-sensitive demand. Dynamic programming has been often used to tackle dynamic pricing problems and also to deal with similar integrated problems, yet with some significant differences as far as the inventory depletion and replenishment are considered. The goal of this work is to understand what makes the car rental problem different and hinders the application of more common methods. To do so, a discrete dynamic programming framework is proposed, with two different approaches to calculate the optimal-value function: one based on a Mixed Integer Non Linear Program (MINLP) and one based on a Constraint Programming (CP) model. These two approaches are analyzed and relevant insights are derived regarding the (in)ability of discrete dynamic programming to effectively tackle this problem within a rental context when realistically sized instances are considered.

Abstract
Optimization problems that are motivated by real-world settings are often complex to solve. Bridging the gap between theory and practice in this field starts by understanding the causes of complexity of each problem and measuring its impact in order to make better decisions on approaches and methods. The Job-Shop Scheduling Problem (JSSP) is a well-known complex combinatorial problem with several industrial applications. This problem is used to analyse what makes some instances difficult to solve for a commonly used solution approach - Mathematical Integer Programming (MIP) - and to compare the power of an alternative approach: Constraint Programming (CP). The causes of complexity are analysed and compared for both approaches and a measure of MIP complexity is proposed, based on the concept of load per machine. Also, the impact of problem-specific global constraints in CP modelling is analysed, making proof of the industrial practical interest of commercially available CP models for the JSSP.