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 nesting problem, also known as irregular packing problem, belongs to the generic class of cutting and packing (C&P) problems. It differs from other 2-D C&P problems in the irregular shape of the pieces. This paper proposes a new mixed-integer model in which binary decision variables are associated with each discrete point of the board (a dot) and with each piece type. It is much more flexible than previously proposed formulations and solves to optimality larger instances of the nesting problem, at the cost of having its precision dependent on board discretization. To date no results have been published concerning optimal solutions for nesting problems with more than 7 pieces. We ran computational experiments on 45 problem instances with the new model, solving to optimality 34 instances with a total number of pieces ranging from 16 to 56, depending on the number of piece types, grid resolution and the size of the board. A strong advantage of the model is its insensitivity to piece and board geometry, making it easy to extend to more complex problems such as non-convex boards, possibly with defects. Additionally, the number of binary variables does not depend on the total number of pieces but on the number of piece types, making the model particularly suitable for problems with few piece types. The discrete nature of the model requires a trade-off between grid resolution and problem size, as the number of binary variables grows with the square of the selected grid resolution and with board size.

Abstract
Retailers' individual products are categorized as part of product families. Merchandising rules specify how the products should be arranged on the shelves using product families, creating more structured displays capable of increasing the viewers' attention. This paper presents a novel mixed integer programming formulation for the Shelf Space Allocation Problem considering two innovative features emerging from merchandising rules: hierarchical product families and display directions. The formulation uses single commodity flow constraints to model product sequencing and explores the product families' hierarchy to reduce the combinatorial nature of the problem. Based on the formulation, a mathematical programming-based heuristic was also developed that uses product families to decompose the problem into a sequence of sub-problems. To improve performance, its original design was adapted following two directions: recovery from infeasible solutions and reduction of solution times. A new set of real case benchmark instances is also provided, which was used to assess the formulation and the matheuristic. This approach will allow retailers to efficiently create planograms capable of following merchandising rules and optimizing shelf space revenue.

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
Operations Research/Management Science (OR/MS) can be described as the discipline of applying advanced analytical methods to help making better decisions and has been around in the agricultural and forestry management sectors since the fifties, approaching decision problems that range from more strategic sectorlevel planning to farm operation issues and integrated supply chain management. In this paper insights are given on the use of OR/MS in agriculture, illustrating them with cases drawn from the literature on this topic while keeping the descriptions accessible to uninitiated readers. The presence of OR/MS in Agriculture and Forest Management applications is already extensive but the potential for development is huge in times where resources are becoming increasingly scarce and more has to be done with less, in a sustainable way.