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
The purpose of this paper is to present the current understanding and con-ceptualization of the cargo stability constraint within the context of the Container Loading Problem. This problem is highly relevant in the transportation industry due to the increasing pressure for a more economically, environmentally and socially efficient and sustainable cargo transportation. Stability is one the most important practical relevant constraints in the Container Loading Problem due to its strong influence on the cargo arrangement. Stability is usually divided into stability during loading operations (static) and stability during transportation (dynamic). Two main contributions are made. Firstly, an overview of recent developments in the literature on the two types of stability, static and dynamic, is provided. Secondly, of opportunities for future research are identified.

Abstract
This work addresses a case study in an intercontinental supply chain. The problem emerges in a company in Angola dedicated to the trade of consumable goods for construction building and industrial maintenance. The company in Angola sends the replenishment needs to a Portuguese company, which takes the decision of which products and in which quantities will be sent by shipping container to the company in Angola. The replenishment needs include the list of products that reached the corresponding reorder point. The decision of which products and in which quantity should take into consideration a set of practical constraints: the maximum weight of the cargo, the maximum volume the cargo and financial constraints related with the minimum value that guarantees the profitability of the business and a maximum value associated with shipping insurance. A 2-stage hybrid method is proposed. In the first stage, an integer linear programming model is used to select the products that maximise the sales potential. In the second stage, a Container Loading Algorithm is used to effectively pack the selected products in the shipping container ensuring the geometrical constraints, and safety constraints such as weight limit and stability. A new set of problem instances was generated with the 2DCPackGen problem generator, using as inputs the data collected in the company. Computational results for the algorithm are presented and discussed. Good results were obtained with the solution approach proposed, with an average occupation ratio of 92% of the container and an average gap of 4% for the solution of the integer linear programming model.

Abstract
Car rental companies have the ability and potential to integrate their dynamic pricing decisions with their capacity decisions. Pricing has a significant impact on demand, while capacity, which translates fleet size, acquisition planning and fleet deployment throughout the network, can be used to meet this price-sensitive demand. Dynamic programming has been often used to tackle dynamic pricing problems and also to deal with similar integrated problems, yet with some significant differences as far as the inventory depletion and replenishment are considered. The goal of this work is to understand what makes the car rental problem different and hinders the application of more common methods. To do so, a discrete dynamic programming framework is proposed, with two different approaches to calculate the optimal-value function: one based on a Mixed Integer Non Linear Program (MINLP) and one based on a Constraint Programming (CP) model. These two approaches are analyzed and relevant insights are derived regarding the (in)ability of discrete dynamic programming to effectively tackle this problem within a rental context when realistically sized instances are considered.

Abstract
This paper presents an exploratory approach to study and identify the main characteristics of the two-dimensional strip packing problem (2D-SPP). A large number of variables was defined to represent the main problem characteristics, aggregated in six groups, established through qualitative knowledge about the context of the problem. Coefficient correlation are used as a quantitative measure to validate the assignment of variables to groups. A principal component analysis (PCA) is used to reduce the dimensions of each group, taking advantage of the relations between variables from the same group. Our analysis indicates that the problem can be reduced to 19 characteristics, retaining most part of the total variance. These characteristics can be used to fit regression models to estimate the strip height necessary to position all items inside the strip.

Abstract
Cutting raw-material into smaller parts is a fundamental phase of many production processes. These operations originate raw-material waste that can be minimised. These problems have a strong economic and ecological impact and their proper solving is essential to many sectors of the economy, such as the textile, footwear, automotive and shipbuilding industries, to mention only a few. Two-dimensional (2D) nesting problems, in particular, deal with the cutting of irregularly shaped pieces from a set of larger containers, so that either the waste is minimised or the value of the pieces actually cut from the containers is maximised. Despite the real-world practical relevance of these problems, very few approaches have been proposed capable of dealing with concrete characteristics that arise in practice. In this paper, we propose a new general heuristic (H4NP) for all 2D nesting problems with limited-size containers: the Placement problem, the Knapsack problem, the Cutting Stock problem, and the Bin Packing problem. Extensive computational experiments were run on a total of 1100 instances. H4NP obtained equal or better solutions for 73% of the instances for which there were previous results against which to compare, and new benchmarks are proposed.