Abstract
Cutting and packing problems have been widely studied in the last decades, mainly due to the variety of industrial applications where the problems emerge. This paper presents an overview of the solution approaches that have been proposed for solving two-dimensional rectangular cutting and packing problems. The main emphasis of this work is on two distinct problems that belong to the cutting and packing problem family. The first problem aims to place onto an object the maximum-profit subset of items, that is, output maximization, while the second one aims to place all the items using as few identical objects as possible, that is, input minimization. The objective of this paper is not to be exhaustive but to provide a solid grasp on two-dimensional rectangular cutting and packing problems by describing their most important solution approaches.

Abstract
Interest in integrating lot-sizing and cutting stock problems has been increasing over the years. This integrated problem has been applied in many industries, such as paper, textile and furniture. Yet, there are only a few studies that acknowledge the importance of uncertainty to optimise these integrated decisions. This work aims to address this gap by incorporating demand uncertainty through stochastic programming and robust optimisation approaches. Both robust and stochastic models were specifically conceived to be solved by a column generation method. In addition, both models are embedded in a rolling-horizon procedure in order to incorporate dynamic reaction to demand realisation and adapt the models to a multistage stochastic setting. Computational experiments are proposed to test the efficiency of the column generation method and include a Monte Carlo simulation to assess both stochastic programming and robust optimisation for the integrated problem. Results suggest that acknowledging uncertainty can cut costs by up to 39.7%, while maintaining or reducing variability at the same time.

Abstract
The implementation of novel regulatory and technical requirements for the distribution of vehicle axle weights in road freight transport introduces a new set of constraints on vehicle routing. Until now, axle weight distribution in determining the load plan for freight transport units has been overlooked in the vehicle routing process. Compliance with these axle weight constraints has become paramount for road freight transport companies, since noncompliance with the axle weight distribution legislation translates into heavy fines. This work aims to provide a tool capable of generating cargo loading plans and routing sequences for a palletised cargo distribution problem. The problem addressed integrates the capacitated vehicle routing problem with time window and the two-dimensional loading problem with load balance constraints. Two integrative solution approaches are proposed, one giving greater importance to the routing and the other prioritising the loading. In addition, a novel MILP model is proposed for the 2D pallet loading problem with load-balance constraints that take advantage of the standard dimension of the pallets. Extensive computational experiments were performed with a set of well-known literature benchmark instances, extended to incorporate additional features. The computational results show the effectiveness of the proposed approaches.