In this chapter, you will see how the simplex method simplifies when it is applied to a class of optimization problems that are known as “network flow models.” You will also see that if a network flow model has “integer-valued data,” the simplex method finds an optimal solution that is integer-valued.

Flows in Networks

A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

A Theory of Graphs

This chapter provides an overview and examples of transportation demand analysis, from specification of the characteristics of the urban area in which the project is located to estimation of the vehicle volumes on individual links of the network. It describes a basis for the data selected and the methods used in Chapter 4, where a plan, design, and impact estimation procedure is conducted in the example project.

Transportation Demand Analysis

An approach to assess the impact of the creation or either the expansion of an air transport infrastructure over regional development is proposed in this paper. Effective long term planning of this investment requires performing an overall analysis of socio-economic consequences through long term forecasting, scenario generation and risk analysis. One of main aspects of this task is related with the estimation of future demand over the modified transportation network which attends the considered region. The proposed approach makes use of two complementary models: One model is devoted to demand forecasting taking into account the modified accessibility of the multimodal transportation network, the other one defines the economic performance of local activity sectors and transportation modalities. The demand forecasting process is based on an entropy maximization approach with flexible origin-destination levels to determine the intensity and the distribution of new origin-destination vectors. A two level analysis considering passengers and freight flows at the first level and activity flows at the second level is made possible and becomes available to process the assessment of different regional development scenarios. The proposed approach is illustrated in the case of a fast developing rural agro-industrial area in central Brazil, where the consequences of the installation of a medium size airport are assessed.

http://www-sre.wu.ac.at/ersa/ersaconfs/ersa11/ersa11acfinal00891.pdf

Luis Gustavo

Papers

A bi-level scheme for assessing the impact of air transportation on local development