Abstract

Abstract
Multi-objective optimization (MOO) considers several objectives to find a feasible set of solutions. Selecting a solution from Pareto frontier (PF) solutions requires further effort. This work proposes a new classification procedure that fits into the analytic hierarchy Process (AHP) to pick the best solution. The method classifies PF solutions using pairwise comparison matrices for each objective. Sectorization is the problem of splitting a region into smaller sectors based on multiple objectives. The efficacy of the proposed method is tested in such problems using our instances and real data from a Portuguese delivery company. A non-dominated sorting genetic algorithm (NSGA-II) is used to obtain PF solutions based on three objectives. The proposed method rapidly selects an appropriate solution. The method was assessed by comparing it with a method based on a weighted composite single-objective function.

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
This paper explores the problem of sectorization of a parcel delivery service that wants to assign an action region to each of its teams, regarding the number of deliveries scheduled for each zone, so that there is a balanced service amongst sectors, covering contiguous zones, and considering limited capacities for the teams. Besides being relatively easy to model, the available optimization tools and software provide poor results when dimension increases in these types of problems, with computational capacity exceeding. In this paper an integer programming model, combined with an heuristic to return a faster solution, was implemented to solve a sectorization problem in two different situations. The main advantage of the strategy proposed, compared to previous ones, is its simplicity and easy implementation while still returning an optimal solution. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Abstract