In this paper, we study a new Workforce Scheduling and Routing Problem, denoted Multiperiod Workforce Scheduling and Routing Problem with Dependent Tasks. In this problem, customers request services from a company. Each service is composed of dependent tasks, which are executed by teams of varying skills along one or more days. Tasks belonging to a service may be executed by different teams, and customers may be visited more than once a day, as long as precedences are not violated. The objective is to schedule and route teams so that the makespan is minimized, i.e., all services are completed in the minimum number of days. In order to solve this problem, we propose a Mixed-Integer Programming model, a constructive algorithm and heuristic algorithms based on the Ant Colony Optimization (ACO) metaheuristic. The presence of precedence constraints makes it difficult to develop efficient local search algorithms. This motivates the choice of the ACO metaheuristic, which is effective in guiding the construction process towards good solutions. Computational results show that the model is capable of consistently solving problems with up to about 20 customers and 60 tasks. In most cases, the best performing ACO algorithm was able to match the best solution provided by the model in a fraction of its computational time.

A definição das parcelas familiares em projetos de reforma agrária envolve questões técnicas e sociais. Essas questões estão associadas principalmente às diferentes aptidões agrícolas do solo nestes projetos. O objetivo deste trabalho foi apresentar método para realizar o processo de ordenamento territorial em assentamentos de reforma agrária empregando Algoritmo Genético (AG). O AG foi testado no Projeto de Assentamento Veredas, em Minas Gerais, e implementado com base no sistema de aptidão agrícola das terras.

Moreira. 2011. Optimal subdivision of land in agrarian reform projects: an analysis using genetic algorithms. Cien. Inv. Agr. 38(2): 169-178. The objective of this manuscript is to develop a new procedure to achieve optimal land subdivision using genetic algorithms (GA). The genetic algorithm was tested in the rural settlement of Veredas, located in Minas Gerais, Brazil. This implementation was based on the land aptitude and its productivity index. The sequence of tests in the study was carried out in two areas with eight different agricultural aptitude classes, including one area of 391.88 ha subdivided into 12 lots and another of 404.1763 ha subdivided into 14 lots. The effectiveness of the method was measured using the shunting line standard value of a parceled area lot's productivity index. To evaluate each parameter, a sequence of 15 calculations was performed to record the best individual fitness average (MMI) found for each parameter variation. The best parameter combination found in testing and used to generate the new parceling with the GA was the following: 320 as the generation number, a population of 40 individuals, 0.8 mutation tax, and a 0.3 renewal tax. The solution generated rather homogeneous lots in terms of productive capacity.

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