Abstract
In the last years, the paradigm of the Portuguese footwear industry has improved drastically to become one of the main world players. In fact, a lot has changed, from low-cost mass production to serving clients consisting of small retail chains, where orders are small and models are varied. In order to deal with such modifications, the footwear industry started investing in technological solutions. The industrial case presented in this paper fits that purpose. The goal is to contribute to the solution of complex scheduling problems arising in the new mixed-model flexible automatic stitching systems of an important footwear factory. The project starts by building an optimization model. Although the model has its own usefulness, the CPLEX program is only capable of reaching optimal solutions for small problem instances. Therefore, a recent metaheuristic, the Imperialist Competitive Algorithm (ICA), has been chosen to tackle larger problems. The ICA is capable of finding optimal results for smaller instances and achieving adequate solutions for real problems in short periods of time. Moreover, ICA improves the results obtained so far by the method currently used in the factory.

Abstract
Sectorization refers to partitioning a large territory, network, or area into smaller parts or sectors considering one or more objectives. Sectorization problems appear in diverse realities and applications. For instance, political districting, waste collection, maintenance operations, forest planning, health or school districting are only some of the application fields. Commonly, sectorization problems respect a set of features necessary to be preserved to evaluate the solutions. These features change for different sectorization applications. Thus, it is important to conceive the needs and the preferences of the decision-makers about the solutions. In the current paper, we solve sectorization problems using the Genetic Algorithm by considering three objectives: equilibrium, compactness, and contiguity. These objectives are collected within a single composite objective function to evaluate the solutions over generations. Moreover, the Analytical Hierarchy Process, a powerful method to perceive the relative importance of several objectives regarding decision makers' preferences, is used to construct the weights. We observe the changes in the solutions by considering different sectorization problems that prioritize various objectives. The results show that the solutions' progress changed accurately to the given importance of each objective over generations.

Abstract
Many models have been proposed for the location-allocation problem. In this study, based on sectorization concept, we propose a new single-objective model of this problem, in which, there is a set of customers to be assigned to distribution centres (DCs). In sectorization problems there are two important criteria as compactness and equilibrium, which can be defined as constraints as well as objective functions. In this study, the objective function is defined based on the equilibrium of distances in sectors. The concept of compactness is closely related to the accessibility of customers from DCs. As a new approach, instead of compactness, we define the accessibility of customers from DCs based on the covering radius concept. The interpretation of this definition in real life is explained. As another contribution, in the model, a method is used for the selection of DCs, and a comparison is made with another method from the literature, then the advantages of each are discussed. We generate benchmarks for the problem and we solve it with a solver available in Python’s Pulp library. Implemented codes are presented in brief.

Abstract
One of the most widely used methods in multi-objective optimization problems is the weighted sum method. However, in this method, defining the weights of objectives is always a challenge. Various methods have been suggested to achieve the weights, one of which is Shannon’s entropy method. In this study, a bi-objective model is introduced to solve the sectorization problem. As a solution method, the model is transformed into two single-objective ones. Also, the bi-objective model is solved for the case where the weights are equal to one. The gained three results from a benchmark are supposed as alternatives in a decision matrix. After the limitation of this approach appears, solutions from different benchmarks are added to the matrix. With Shannon’s entropy method, the weights of the objective functions are got from the decision matrix. The limitations of the approach and possible causes are discussed.

Abstract
In sectorization problems (SPs), a large area is divided into smaller regions for administrative purposes. SPs have applications in many fields. Since real-life problems are often dynamic, in this study, a new model for dynamic SP is proposed. In the problem, points are assigned to service centres and in this way sectors are formed. The sectors must be balanced in terms of distance and demand, which is defined in the objective function and constraints of the model. In the problem, in a certain time period, the coordinates and demands of some points change according to certain statistical distributions. A two-stage solution method is suggested for this problem. In the first stage, the expected values of coordinates and demands of the points are estimated by a Monte Carlo simulation, and in the second stage, the problem is solved like a deterministic optimization problem. The model is nonlinear, but after linearization, it is solved in Python’s Pulp library for benchmarks of different sizes and the results are discussed.

Abstract
The manufacturing industry faces a new revolution, grounded on the intense digitalization of assets and industrial processes and the increasing computation capabilities imposed by the new data-driven digital architectures. This reality has been promoting the Digital Twin (DT) concept and its importance on the industrial companies' business models. However, with these new opportunities, also new threads may rise, mainly related to industrial data protection and sovereignty. Therefore, this research paper will demonstrate the International Data Spaces (IDS) reference model's application to overcome these limitations. Following a pilot study with a Portuguese machine manufacturing company, this paper will demonstrate the development of a cutting and bending machines DT, leveraged on an IDS infrastructure for interoperability, for the plastic and metal industry and its importance to introduce this machine manufacturing company in a new B2B marketplace from the EU project Market 4.0.