Abstract
Pricing and capacity decisions in car rental companies are characterized by high flexibility and interdependence. When planning a selling season, tackling these two types of decisions in an integrated way has a significant impact. This paper tackles the integration of capacity and pricing problems for car rental companies. These problems include decisions on fleet size and mix, acquisitions and removals, fleet deployment and repositioning, as well as pricing strategies for the different rental requests. A novel mathematical model is proposed, which considers the specific dynamics of rentals on the relationship between inventory and pricing as well as realistic requirements from the flexible car rental business, such as upgrades. Moreover, a solution procedure that is able to solve real-sized instances within a reasonable time frame is developed. The solution procedure is a matheuristic based on the decomposition of the model, guided by a biased random-key genetic algorithm (BRKGA) boosted by heuristically generated initial solutions. The positive impact on profit, of integrating capacity and pricing decisions versus a hierarchical/sequential approach, is validated.

Abstract
As in many other combinatorial optimisation problems, research on nesting problems (aka irregular packing problems) has evolved around the dichotomy between continuous (time consuming) and discrete (memory consuming) representations of the solution space. Recent research has been devoting increasing attention to discrete representations for the geometric layer of nesting problems, namely in mathematical programming-based approaches. These approaches employ conventional regular meshes, and an increase in their precision has a high computational cost. In this paper, we propose a data structure to represent non-regular meshes, based on the geometry of each piece. It supports non-regular discrete geometric representations of the shapes, and by means of the proposed data structure, the discretisation can be easily adapted to the instances, thus overcoming the precision loss associated with discrete representations and consequently allowing for a more efficient implementation of search methods for the nesting problem. Experiments are conducted with the dotted-board model - a recently published mesh-based binary programming model for nesting problems. In the light of both the scale of the instances, which are now solvable, and the quality of the solutions obtained, the results are very promising.

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.

Abstract
Cutting and Packing (C & P) problems arise in many industrial and logistics applications, whenever a set of small items, with different shapes, has to be assigned to large objects with specific shapes so as to optimize some objective function. Besides some characteristics common to combinatorial optimization problems, the distinctive feature of this field is the existence of a geometric subproblem, to ensure that the items do not overlap and are completely contained in the large objects. The geometric tools required to deal with this subproblem depend on the shapes (rectangles, circles, irregular) and on the specific conditions of the problem being solved. In this chapter, after an introduction that describes and classifies Cutting and Packing problems, we review the basic strategies that have appeared in the literature for designing constructive algorithms, local search procedures, and metaheuristics for problems with regular and irregular shapes.

Abstract
In this paper we present a Benders decomposition approach for the Berth Allocation Problem (BAP). Benders decomposition is a cutting plane method that has been widely used for solving large-scale mixed integer linear optimization problems. On the other hand, the Berth Allocation Problem is a NP-hard and large-scale problem that has been gaining relevance both from the practical and scientific points of view. In this work we address the discrete and dynamic version of the problem, and develop a new decomposition approach and apply it to a reformulation of the BAP based on the Heterogeneous Vehicle Routing Problem with Time Windows (HVRPTW) model. In a discrete and dynamic BAP each berth can moor one vessel at a time, and the vessels are not all available to moor at the beginning of the planning horizon (there is an availability time window). Computational tests are run to compare the proposed Benders Decomposition with a state-of-the-art commercial solver. © 2019, Springer Nature Switzerland AG.

Abstract
In two-dimensional nesting problems (irregular packing problems) small pieces with irregular shapes must be packed in large objects. A small number of exact methods have been proposed to solve nesting problems, typically focusing on a single problem variant, the strip packing problem. There are however several other variants of the nesting problem which were identified in the literature and are very relevant in the industry. In this paper, constraint programming (CP) is used to model and solve all the variants of irregular cutting and packing problems proposed in the literature. Three approaches, which differ in the representation of the variable domains, in the way they deal with the core constraints and in the objective functions, are the basis for the three models proposed for each variant of the problem. The non-overlap among pieces, which must be enforced for all the problem variants, is guaranteed through the new global constraint NoOverlap in one of the proposed approaches. Taking the benchmark instances for the strip-packing problem, new instances were generated for each problem variant. Extensive computational experiments were run with these problem instances from the literature to evaluate the performance of each approach applied to each problem variant. The models based on the global constraint NoOverlap performed consistently better for all variants due to the increased propagation and to the low memory usage. The performance of the CP model for the strip packing problem with the global constraint NoOverlap was then compared with the Dotted Board with Rotations using larger instances from the literature. The experiments show that the CP model with global constraint NoOverlap can quickly find good quality solutions in shorter computational times even for large instances.