Abstract
Two-dimensional rectangular strip packing problems belong to the broader class of Cutting and Packing (C&P) problems, in which small items are required to be cut from or packed on a larger object, so that the waste (unused regions of the large object) is minimized. C&P problems differ from other combinatorial optimization problems by the intrinsic geometric constraints: items may not overlap and have to be fully contained in the large object. This survey approaches the specific C&P problem in which all items are rectangles, therefore fully characterized by a width and a height, and the large object is a strip, i.e. a rectangle with a fixed width but an infinite height, being the problem’s goal to place all rectangles on the strip so that the height is minimized. These problems have been intensively and extensively tackled in the literature and this paper will focus on heuristic resolution methods. Both the seminal and the most recent approaches (from the last decade) will be reviewed, in a rather tutorial flavor, and classified according to their type: constructive heuristics, improvement heuristics with search over sequences and improvement heuristics with search over layouts. Building on this review, research gaps are identified and the most interesting research directions pointed out. © 2016 Brazilian Operations Research Society.

Abstract
In this paper we consider the problem of minimizing the waste of textile material in a Portuguese home textile manufacturing company. The company has a vertical structure covering the different production stages of the home textile, from weaving until the finished products. Production planning comprises different decisions: the definition of the widths and lengths of the fabric rolls to be produced, the number of fabric rolls to be used from stock or purchased and the definition of the cutting patterns to be applied to each width of the fabric roll, so that the waste is minimized. We propose a MIP model, solved by a column generation method, to tackle the problem.

Abstract
Cutting and packing problems have been extensively studied in the literature in recent decades, mainly due to their numerous real-world applications while at the same time exhibiting intrinsic computational complexity. However, a major limitation has been the lack of problem generators that can be widely and commonly used by all researchers in their computational experiments. In this paper, a problem generator for every type of two-dimensional rectangular cutting and packing problems is proposed. The problems are defined according to the recent typology for cutting and packing problems proposed by Wascher, Haussner, and Schumann (2007) and the relevant problem parameters are identified. The proposed problem generator can significantly contribute to the quality of the computational experiments run with cutting and packing problems and therefore will help improve the quality of the papers published in this 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
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
This paper addresses the problem of determining the cutting patterns of metal sheets, which arises in a manufacturer of metal cages, in order to minimize the waste, the number of cuts performed, the number of metal sheets used or a weighted combination of the three. A two stage approach, to solve a 2D guillotine cutting stock problem with single and multiple stock sizes, is presented and compared with the company approach and state-of-the-art algorithms. The results show great improvement compared to the company approach and a very good performance compared to state-of-the-art algorithms.