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.

Abstract
This paper describes the results of our collaboration with the leading Portuguese food retailer to address the shelf-space planning problem of allocating products to shop-floor shelves. Our challenge was to introduce analytical methods into the shelf-space planning process to improve the return on space and automate a process heavily dependent on the experience of the retailer's space managers. This led to the creation of GAP, a decision support system that the company's space-management team uses daily. We developed a modular operations research approach that systematically applies mathematical programming models and heuristics to determine the best layout of products on the shelves. GAP combines its analytical strength with an ability to incorporate different types of merchandising rules to balance the tradeoff between optimization and customization.

Abstract
The manufacturer's pallet loading problem (MPLP) has been widely studied during the past 50 years. It consists of placing a maximum number of identical rectangular boxes onto a single rectangular pallet. In this paper, we have reviewed the methods that have been proposed for the solution of this problem. Furthermore, the various problem instances and data sets are analyzed that have been used in computational experiments for the evaluation of these methods. The most challenging and yet unsolved methods are identified. By doing so, areas of future research concerning the MPLP can be highlighted.

Abstract

Abstract
The irregular strip packing problem is a common variant of cutting and packing problems. Only a few exact methods have been proposed to solve this problem in the literature. However, several heuristics have been proposed to solve it. Despite the number of proposed heuristics, only a few methods that combine exact and heuristic approaches to solve the problem can be found in the literature. In this paper, a matheuristic is proposed to solve the irregular strip packing problem. The method has three phases in which exact mixed integer programming models from the literature are used to solve the sub-problems. The results show that the matheuristic is less dependent on the instance size and finds equal or better solutions in 87,5% of the cases in shorter computational times compared with the results of other models in the literature. Furthermore, the matheuristic is faster than other heuristics from the literature. © 2016 Brazilian Operations Research Society.

Abstract
The integration of wind power in electricity generation brings new challenges to the unit commitment problem, as a result of the random nature of the wind speed. The scheduling of thermal generation units at the day-ahead stage is usually based on wind power forecasts. Due to technical limitations of thermal units, deviations from those forecasts during intra-day operations may lead to unwanted consequences, such as load shedding and increased operating costs. Wind power forecasting uncertainty has been handled in practice by means of conservative stochastic scenario-based optimization models, or through additional operating reserve settings. However, generation companies may have different attitudes towards the risks associated to wind power variability. In this paper, operating costs and load shedding are modeled by non-linear utility functions aggregated into a single additive utility function of a multi-objective model. Computational experiments have been done to validate the approach: firstly we test our model for the wind-thermal unit commitment problem and, in a second stage, pumped storage hydro units are added, leading to a model with wind-hydro-thermal coordination. Results have shown that the proposed methodology is able to correctly reflect different risk profiles of decision makers for both models.