Abstract
The retail shelf space planning problem has long been addressed by Marketing and Operations Research (OR) professionals and researchers, with the first empirical studies tracing back to the 1960s and the first modelling approaches back to the 1970s. Due to this long history, this field presents a wide range of different mathematical modelling approaches that deal with the decisions surrounding a set of products and not only define their space assignment and related quantity, but also their vertical and horizontal positioning within a retail shelf. These decisions affect customer demand, namely in the form of space- and position-dependent demand and replenishment requirements. Current literature provides either more comprehensive decision models with a wide range of demand effects but limited practical applicability, or more simplistic model formulations with greater practical application but limited consideration of the associated demand. Despite the recent progress seen in this research area, no work has yet systematised published research with a clear focus on shelf space planning. As a result, there is neither any up-to-date structured literature nor a unique model approach, and no benchmark sets are available. This paper provides a description and a state-of-the-art literature review of this problem, focusing on optimisation models. Based on this review, a classification framework is proposed to systematise the research into a set of sub-problems, followed by a unified approach with a univocal notation of model classes. Future lines of research point to the most promising open questions in this field.

Abstract
The irregular strip packing problem arises in a wide variety of industrial sectors, from garment and footwear to the metal industry, and has a substantial impact in raw-material waste minimization. The goal of this problem is to find a layout for a large object to be cut into smaller pieces. What differentiates this problem from all the other cutting and packing problems, and is its primary source of complexity, is the irregular (non-rectangular) shape of the small pieces. However, in practical applications, after a layout has been determined, a second problem arises: finding the path that the cutting tool has to follow to actually cut the pieces, as previously planned. This second problem is known as the cutting path determination problem. Although the solution of the first problem strongly influences the resolution of the second one, only a few studies are dealing with cutting/packing and cutting path determination together, and, to the best of the authors' knowledge, none of them considers the irregular strip packing problem. In this paper, we propose the first mathematical programming model that integrates the irregular strip packing and the cutting path determination problems. Computational experiments were run to show the correctness of the proposed model and the advantage of tackling the two problems together. Two variants of the cutting path determination problem were considered, the fixed vertex and the free cut models. The strengths and drawbacks of these two variants are also established through computational experiments. Overall, the computational results show that the integration of these problems is advantageous, even if only small instances could be solved to optimality, given that solving to optimality the integrated is at least as difficult as solving each one of the other problems individually. As future research, it should be highlighted that the proposed integrated model is a solid basis for the development of matheuristics aiming at tackling real-world size problems.

Abstract
Solving nesting problems or irregular strip packing problems is to position polygons on a fixed width and unlimited length strip, obeying polygon integrity containment constraints and non-overlapping constraints, in order to minimize the used length of the strip. To ensure non-overlapping, we use separation lines, i.e., straight lines that separate polygons. We present a nonlinear programming model that considers free rotations of the polygons and of the separation lines. This model uses a considerable smaller number of variables than the few other approaches proposed in the literature. We use the nonlinear programming solver IPOPT (an algorithm of interior points type), which is part of COIN-OR. Computational tests were run using established benchmark instances and the results were compared with the ones obtained with other methodologies in the literature that use free rotations. © 2018 Brazilian Operations Research Society.

Abstract
In this paper, we address the Constrained Three-dimensional Guillotine Cutting Problem (C3GCP), which consists of cutting a larger cuboid block (object) to produce a limited number of smaller cuboid pieces (items) using orthogonal guillotine cuts only. This way, all cuts must be parallel to the object's walls and generate two cuboid sub-blocks, and there is a maximum number of copies that can be manufactured for each item type. The C3GCP arises in industrial manufacturing settings, such as the cutting of steel and foam for mattresses. To model this problem, we propose a new compact mixed-integer non-linear programming (MINLP) formulation by extending its two-dimensional version, and develop a mixed-integer linear programming (MILP) version. We also propose a new model for a particular case of the problem which considers 3-staged patterns. As a solution method, we extend the algorithm of Wang (1983) to the three-dimensional case. We emphasise that the C3GCP is different from 3D packing problems, namely from the Container Loading Problem, because of the guillotine cut constraints. All proposed approaches are evaluated through computational experiments using benchmark instances. The results show that the approaches are effective on different types of instances, mainly when the maximum number of copies per item type is small, a situation typically encountered in practical settings with low demand for each item type. These approaches can be easily embedded into existing expert systems for supporting the decision-making process.

Abstract
Designing a viable carsharing system in a competitive environment is challenging and often dependent on a myriad of decisions. This paper establishes and presents an integrated conceptual decision-support framework for carsharing systems, encompassing critical decisions that should be made by carsharing organizations and users. To identify the main decisions in a carsharing system, and the inputs and interactions among them, it is crucial to obtain a comprehensive understanding of the current state of the literature as well as the business practices and context. To this aim, a holistic and in-depth literature review is conducted to structure distinct streams of literature and their main findings. Then, we describe some of the key decisions and business practices that are often oversimplified in the literature. Finally, we propose a conceptual decision-support framework that systematizes the interactions between the usually isolated problems in the academic literature and business practices, integrating the perspectives of carsharing organizations and of their users. From the proposed framework, we identify relevant research gaps and ways to bridge them in the future, toward more realistic and applicable research.

Abstract
The carsharing market has never been as competitive as it is now, and during the last years, we have been witnessing a boom in the number of carsharing organizations that appear, often accompanied by an also booming number of companies that disappear. Designing a viable carsharing system is challenging and often depends on local conditions as well as on a myriad of operational decisions that need to be supported by suitable decision support systems. Therefore, carsharing is being increasingly studied in the Operations Management (OM) literature. Nevertheless, often due to the limited transparency of this highly competitive sector and the recency of this business, there is still a "gap of understanding" of the scientific community concerning the business practices and contexts, often resulting in over-simplifications and relevant problems being overlooked. In this paper, we aim to close this "gap of understanding" by describing, conceptualizing, and analyzing the reality of 34 business to-consumer carsharing organizations. With the data collected, we propose a detailed description of the current business practices, such as the ones concerning pricing. From this, we highlight relevant "research insights" and structure all collected data organized by different OM topics, enabling knowledge to be further developed in this field.