Abstract
This paper addresses a new Mixed-model Assembly Line Sequencing Problem in the Footwear industry. This problem emerges in a large company, which benefits from advanced automated stitching systems. However, these systems need to be managed and optimised. Operators with varied abilities operate machines of various types, placed throughout the stitching lines. In different quantities, the components of the various shoe models, placed in boxes, move along the lines in either direction. The work assumes that the associated balancing problems have already been solved, thus solely concentrating on the sequencing procedures to minimise the makespan. An optimisation model is presented, but it has just been useful to structure the problems and test small instances due to the practical problems' complexity and dimension. Consequently, two methods were developed, one based on Variable Neighbourhood Descent, named VND-MSeq, and the other based on Genetic Algorithms, referred to as GA-MSeq. Computational results are included, referring to diverse instances and real large-size problems. These results allow for a comparison of the novel methods and to ascertain their effectiveness. We obtained better solutions than those available in the company.

Abstract
In this study, two novel stochastic models are introduced to solve the dynamic sectorization problem, in which sectors are created by assigning points to service centres. The objective function of the first model is defined based on the equilibration of the distance in the sectors, while in the second one, it is based on the equilibration of the demands of the sectors. Both models impose constraints on assignments and compactness of sectors. In the problem, the coordinates of the points and their demand change over time, hence it is called a dynamic problem. A new solution method is used to solve the models, in which expected values of the coordinates of the points and their demand are assessed by using the Monte Carlo simulation. Thus, the problem is converted into a deterministic one. The linear and deterministic type of the model, which is originally non-linear is implemented in Python's Pulp library and in this way the generated benchmarks are solved. Information about how benchmarks are derived and the obtained solutions are presented.

Abstract
This paper deals with multi-objective location-routing problems involving distribution centres and a set of customers. It proposes a new two-stage solution method that comprehends the concept of sectorization. Distribution centres are opened, and the corresponding opening cost is calculated. A subset of customers is assigned to each of them and, in this way, sectors are formed. The objective functions in assigning customers to distribution centres are the total deviation in demands of sectors and the total deviation in total distance of customers from centroid of sectors, which must be minimized Afterward, a route is determined for each sector to meet the demands of customers. At this stage, the objective function is the total distance on the routes in the sectors, that must be minimized Benchmarks are defined for the problem and the results acquired with the two-stage method are compared to those obtained with NSGA-II. It is observed that NSGA-II can achieve many non-dominated solutions.

Abstract
The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.

Abstract
In sectorization problems, a large district is split into small ones, usually meeting certain criteria. In this study, at first, two single-objective integer programming models for sectorization are presented. Models contain sector centers and customers, which are known beforehand. Sectors are established by assigning a subset of customers to each center, regarding objective functions like equilibrium and compactness. Pulp and Pyomo libraries available in Python are utilised to solve related benchmarks. The problems are then solved using a genetic algorithm available in Pymoo, which is a library in Python that contains evolutionary algorithms. Furthermore, the multi-objective versions of the models are solved with NSGA-II and RNSGA-II from Pymoo. A comparison is made among solution approaches. Between solvers, Gurobi performs better, while in the case of setting proper parameters and operators the evolutionary algorithm in Pymoo is better in terms of solution time, particularly for larger benchmarks. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

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.