Abstract
Sectorization consists of grouping the basic units of a large territory to deal with a complex problem involving different criteria. Resectorization rearranges a current sectorization avoiding substantial changes, given a set of conditions. The paper considers the case of the distribution of geographic areas of fire brigades in the north of Portugal so that they can protect and rescue the population surrounding the fire stations. Starting from a current sectorization, assuming the geographic and population characteristics of the areas and the fire brigades’ response capacity, we provide an optimized resectorization considering two objectives: to reduce the rescue time by maximizing the compactness criterion, and to avoid overload situations by maximizing the equilibrium criterion. The solution method is based on the Non-dominated Sorting Genetic Algorithm (NSGA-II). Finally, computational results are presented and discussed. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Sectorization is the partition of a set or region into smaller parts, taking into account certain objectives. Sectorization problems appear in real-life situations, such as school or health districting, logistic planning, maintenance operations or transportation. The diversity of applications, the complexity of the problems and the difficulty in finding good solutions warrant sectorization as a relevant research area. Decision Support Systems (DSS) are computerised information systems that may provide quick solutions to decision-makers and researchers and allow for observing differences between various scenarios. The paper is an overview of the development of a DSS for Sectorization, its extent, architecture, implementation steps and benefits. It constitutes a quite general system, for it handles various types of problems, which the authors grouped as (i) basic sectorization problems; (ii) sectorization problems with service centres; (iii) re-sectorization problems; and (iv) dynamic sectorization problems. The new DSS is expected to facilitate the resolution of various practitioners’ problems and support researchers, academics and students in sectorization. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Sectorization is the division of a large area, territory or network into smaller parts considering one or more objectives. Dynamic sectorization deals with situations where it is convenient to discretize the time horizon in a certain number of periods. The decisions will not be isolated, and they will consider the past. The application areas are diverse and increasing due to uncertain times. This work proposes a conceptualization of dynamic sectorization and applies it to a distribution problem with variable demand. Furthermore, Genetic Algorithm is used to obtain solutions for the problem since it has several criteria; Analytical Hierarchy Process is used for the weighting procedure. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract
Sectorization is concerned with dividing a large territory into smaller areas, also known as sectors. This process usually simplifies a complex problem, leading to easier solution approaches to solving the resulting subproblems. Sectors are built with several criteria in mind, such as equilibrium, compactness, contiguity, and desirability, which vary with the applications. Sectorization appears in different contexts: sales territory design, political districting, healthcare logistics, and vehicle routing problems (agrifood distribution, winter road maintenance, parcel delivery). Environmental problems can also be tackled with a sectorization approach; for example, in municipal waste collection, water distribution networks, and even in finding more sustainable transportation routes. This work focuses on sectorization concerning the location of the area's centers and allocating basic units to each sector. Integer programming models address the location-allocation problems, and various formulations implementing different criteria are compared. Methods to deal with multiobjective optimization problems, such as the e-constraint, the lexicographic, and the weighted sum methods, are applied and compared. Computational results obtained for a set of benchmarking instances of sectorization problems are also presented.

Abstract

Abstract
Sectorisation refers to dividing a whole into smaller parts, the sectors, to facilitate an activity or achieve some goals. The paper proposes a new matrix form genetic encoding system, called matrix form binary grouping (MFBG), specifically designed for sectorisation and related problems. In MFBG representation, the columns and rows represent sectors and nodes, respectively. As a solution procedure, we followed NSGA-II by contemplating adapted measures for three commonly used criteria (equilibrium, compactness, contiguity) for sectorisation problems. The performance of the MFBG within the NSGA-II is tested from two perspectives: 1) through several experiments on the set of instances; 2) by its comparison with the group-oriented genetic encoding system under the grouping GA. Results showed that the MFBG could find good quality solutions and outperforms the GGA. This confirms that the MFBG is an innovative procedure for dealing with sectorisation problems and an excellent contribution as an alternative encoding technique. © 2023 Inderscience Enterprises Ltd.