ABSTRACT In this work, the presence of cut nodes in a network is exploited to propose a competitive method for the multi-terminal maximum flow problem. The main idea of the method is based on the relation between cut-trees and cut nodes, which is observed in the context of sensitivity analysis on the variation of edges capacities. Computational experiments were conducted with the proposed algorithm, whose results were compared with the ones of Gusfield, for randomly generated and well-known instances of the literature. The numerical results demonstrate the potential of the method for some classes of instances. Moreover, the proposed method was adapted for the single maximum flow problem, but failed to improve existing running times for the very same classes of instances.

Este artigo apresenta um modelo de equilíbrio espacial de preços em um mercado oligopolizado de derivados de petróleo. Até o ano de 1997, o mercado brasileiro era caracterizado pelo monopólio estatal da Petrobrás, a qual permaneceu, até 2001, como a única empresa autorizada a importar derivados de petróleo. Com vários agentes operando no mercado, o governo deixou de fixar os preços para a Petrobrás, que passou a determinar os preços baseada na competição com outros agentes. Neste cenário, surgem algumas questões relativas aos níveis de preços a serem oferecidos no mercado e relativas à capacidade das refinarias nacionais de competir com produtos importados. Para responder a estas e outras questões, um novo modelo de equilíbrio espacial de preços para um mercado oligopolizado foi desenvolvido, considerando as características especiais da produção de derivados. Um algoritmo iterativo do tipo Gauss-Seidel, com ajustes seqüenciais, foi desenvolvido e aplicado com dados do mercado brasileiro. O modelo proposto, o algoritmo e a aplicação são discutidos no trabalho. Este modelo pode ser usado por autoridades reguladoras e pelas companhias do setor.

This paper presents a spatial price equilibrium model in an oligopoly market for refined oil products. Till 1997 the Brazilian oil market was characterized by the state monopoly of Petrobras, which up to 2001 remained the only firm authorized to import oil derivatives. With several agents operating in the primary oil supply market, the government stopped fixing the prices for Petrobras, which started to determine the prices based on competition with other players. In this new scenario some questions arise regarding the price levels at which refined products will be supplied in different regions across Brazil as well as the capacity of national refineries to compete with imported products. To answer those and other questions, a new oligopoly spatial equilibrium model is herein proposed, taking into account the special characteristics of production of refined oil products. An iterative Gauss-Seidel-like algorithm with sequential adjustments was developed and applied to Brazilian market data. The model, the algorithm and its application are described in this work. Such a model may be used both by regulatory authorities and by companies in the sector.

As grandes metrópoles do mundo enfrentam-se diariamente com problemas de transporte. Para planejar o sistema os tomadores de decisão necessitam de instrumentos capazes de simular, com uma boa aproximação, o processo de escolha de caminhos de todos os usuários nas suas viagens. O trabalho apresenta a formulação e implementação de um modelo de alocação de fluxos de passageiros, sobre uma rede de transporte público. O modelo foi formulado como um problema de inequação variacional. O algoritmo de solução considera algumas hipóteses sobre o processo de partição de fluxos pelos trechos de linhas alternativas. O procedimento foi implementado usando a linguagem Delphi e aplicado em testes com redes divulgadas na literatura. Um grande experimento foi feito com a rede de transporte da cidade do Rio de Janeiro.

The biggest cities in the world faced problems in the transportation system. In order to plan the system, decision makers need tools, which enable them to make good approximate simulations of the routing choice process for all the users. The work presents the formulation and implementation of a passenger flow assignment model for a transit transportation network. The model has been stated as a variational inequality problem. The solution algorithm makes some assumptions about the process of flow partition between alternative line segments. The procedure has been implemented using Delphi language and applied in tests with small networks published in the literature. A bigger experiment has been conducted with the transit network of Rio de Janeiro city.