O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.

O objetivo deste trabalho é testar um modelo de distribuição de viagens do tipo gravitacional para a calibração de matrizes origem/destino (O/D) em linhas de transporte público por ônibus a partir de dados de pesquisa de contagem de embarque/desembarque (E/D). A metodologia proposta possibilita a obtenção de matrizes O/D de forma rápida e barata, pois combina um método de pesquisa simples e de baixo custo (pesquisa de contagem de usuários) com um modelo de distribuição de viagens. O modelo associa a cada ponto de origem um valor de parâmetro. A utilização de um valor de parâmetro associado a cada origem busca neste caso reproduzir o custo médio de distribuição de viagens de uma origem em relação aos seus diferentes destinos. O modelo incorpora ainda como restrição a probabilidade de um passageiro desembarcar no ponto seguinte ao seu ponto de embarque. Os dados de pesquisa foram cedidos pelo Departamento de Transportes da Universidade Federal do Paraná. O teste de desempenho do modelo foi realizado através da comparação entre matrizes O/D observadas e simuladas para as cidades de Curitiba e Paranaguá. / The aim of this work is to test a gravity model for trip distribution designed to estimate bus routes origin/destination (O/D) matrices based on boarding and alighting data. The proposed method combines a simple and low-cost survey method (on/off passenger counting) with a mathematical model for trip distribution, which enables the estimation of an O/D matrix in a fast and inexpensive manner. The model assumption that each origin point is associated to a parameter value tries to reproduce the average costs of the actual trip distribution from each origin to every single destination along the bus route. The model brings also as a built-in restriction an expected (usually low) probability of passengers getting off the vehicle in the bus stop following the boarding point. The survey data used in this work have been collected by researchers of the Transportation Department at the Federal University of Paraná. The model performance has been tested by the comparison of observed and simulated O/D matrices in the cities of Curitiba and Paranaguá. The results found in most of the simulations showed that for an estimated trip frequencies did not statistically differ from the actual values for a required level of significance.

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.

We have considered the bilevel programming problem in the case where the lower-level problem admits more than one optimal solution. It is well-known in the literature that in such a situation, the problem is ill-posed from the view point of scalar objective optimization. Thus the optimistic and pessimistic approaches have been suggested earlier in the literature to deal with it in this case. In the thesis, we have developed a unified approach to derive necessary optimality conditions for both the optimistic and pessimistic bilevel programs, which is based on advanced tools from variational analysis. We have obtained various constraint qualifications and stationarity conditions depending on some constructive representations of the solution set-valued mapping of the follower’s problem. In the auxiliary developments, we have provided rules for the generalized differentiation and robust Lipschitzian properties for the lower-level solution setvalued map, which are of a fundamental interest for other areas of nonlinear and nonsmooth optimization. Some of the results of the aforementioned theory have then been applied to derive stationarity conditions for some well-known transportation problems having the bilevel structure.