Abstract
In the Container Loading Problem literature, the cargo dynamic stability constraint has been evaluated by the percentage of boxes with insufficient lateral support. This metric has been used as a proxy for the real-world dynamic stability constraint and has conditioned the algorithms developed for this problem. It has the advantage of not being expensive from a computation perspective. However, guaranteeing that at least three sides of a box are in contact with another box or with the container wall does not necessarily ensure stability during transportation. In this paper we propose a physics simulation tool based on a physics engine that will be used in the evaluation of the dynamic stability constraint. We compare the results of our physics simulation tool with the state-of-the-art simulation engineering software Abaqus Unified FEA, and conclude that our tool is a promising alternative.

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
The load balance aspect of the Container Loading Problem (CLP) has been handled in an simplified way in the literature. Either load balance has been treated as a soft constraint or the geometrical centre of the container has been assumed to be the ideal location for the centre of gravity of the cargo, or both, which does not meet regulatory directives and transportation legislation. In this paper, we treat load balance as a 'hard constraint and adopt vehicle specific diagrams that define the feasibility domain for the location of the centre of gravity of the cargo, according to the vehicle specific technical characteristics, thus fulfilling and complying with real-world regulations and legislation. We propose a multi-population biased random-key genetic algorithm (BRKGA), with a new fitness function that takes static stability and load balance into account. Extensive computational experiments were performed with different variants of the proposed approach. Also solutions taken from the literature were evaluated in terms of load balance. The computational results show that it is possible to obtain stable and load balanced solutions without compromising the performance in terms of container volume utilization, and demonstrate also the advantage in incorporating load balance in the packing generation algorithm.

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
Solving nesting problems involves the waste minimisation in cutting processes, and therefore it is not only economically relevant for many industries but has also an important environmental impact, as the raw materials that are cut are usually a natural resource. However, very few exact approaches have been proposed in the literature for the nesting problem (also known as irregular packing problem), and the majority of the known approaches are heuristic algorithms, leading to suboptimal solutions. The few mathematical programming models known for this problem can be divided into discrete and continuous models, based on how the placement coordinates of the pieces to be cut are dealt with. In this paper, we propose an innovative semi-continuous mixed-integer programming model for two-dimensional cutting and packing problems with irregular shaped pieces. The model aims to exploit the advantages of the two previous classes of approaches and discretises the [GRAPHICS] -axis while keeping the [GRAPHICS] -coordinate continuous. The board can therefore be seen as a set of stripes. Computational results show that the model, when solved by a commercial solver, can deal with large problems and determine the optimal solution for smaller instances, but as it happens with discrete models, the optimal solution value depends on the discretisation step that is used.