Otimização da atribuição de condutores em clínicas no Detran-AL

Abstract

In compliance with art. 3 of resolution 1636/2002 of the Federal Council of Medicine, clinical and/or psychological examinations belonging to the processes of the State Department of Traffic of Alagoas (Detran-AL) must be distributed, in an equitable and impartial way in relation to the clinics accredited to the agency, therefore generating the Detran Attribution Problem (PAD). In order to better allocate candidates for exams in an equitable manner in clinics, in this work studied a variant of the Attribution Problem (Assignment Problem), a classic optimization problem, which aims to allocate n tasks to m agents, in order to minimize the total cost of assignments. In the case of PAD, a set of clinics C and a set of conductors M are entered and the objective is to assign each driver to exactly one clinic in order to minimize the total cost of travel. What differentiates PAD from the classic attribution problem is the constraint created by the equitable division between clinics. Let k = [|M||C|] be the ratio between the number of drivers and the number of clinics, in the PAD all clinics should receive exactly k or k +1 drivers. Two optimization models have been proposed, the first one solves the PAD by allocating drivers in clinics, minimizing the total distance. From a theoretical point of view, it was proved that the PAD coefficient matrix is totally unimodular, implying that the problem can be solved in polynomial time. The second model, named PAD+, aims to suggest the location of a new clinic to be accredited to DETRAN. Due to typing errors in the driver’s addresses, a classification model was proposed based on recurrent neural network techniques to infer each driver’s neighborhood. It was found that the model used of neural networks managed to achieve an accuracy of approximately 92% on the validation basis. Regarding the optimization models, the first model proposed reduced by 30.07% the total cost of displacing candidates to the allocated clinics. The suggestion of a location, made by the second model, reduced the total cost by up to 67.16% in relation to the original allocation. Finally, through a sensitivity analysis, the effect on the solution obtained from the PAD in case of variation in the input parameters is investigated. Therefore, it was possible to determine the locations of the clinics that most influence the displacement of the candidates.