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

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

In this communication is proposed an appraisal tool for measuring the impacts of the installation of a new airport within a region already connected by a multimodal transportation network. This problem is crucial when choosing location for airports and then when planning the investments in terminals, connection links and fleets. One of the main difficulties of this task is related with the estimation of future demand over the modified transportation network which has direct influence on the evaluation of operational conditions, revenues and costs of the new airport. The proposed approach makes use of two different optimization models: One model is devoted to passenger and freight demand forecasting taking into account the modified accessibility of the multimodal transportation network, the other one defines the global transport supply according with a profit maximization behavior for the involved transport system. The demand forecasting process is based on an entropy maximization approach with distinct urban centers? economic activities generated or attracted constraints levels to determine the intensity and the distribution of origin-destination matrices by the kind of product and transport modality. The proposed solution scheme is composed of an iterative process between the current solution for demand forecasting and the supply optimization problem: the entropy maximizing distribution problem provides the origin-destination matrix given a cost/capacity structure, while the supply optimization problem provides this cost/capacity structure characterizing accessibility, given the origin-destination matrices. The proposed approach is illustrated with the case of the study of the insertion of a new airport of medium size in a rapid developing rural area.

https://hal-enac.archives-ouvertes.fr/hal-00938516/document

Planning airports within regional multimodal transportation systems

In this communication is considered the problem of long term forecasting of the traffic growth in a large transportation network. This problem is crucial when planning the necessary investments in terminals, fleets and traffic control equipments. The proposed approach makes use of two different optimization models: One model is devoted to freight demand forecasting, the other one defines the transport supply on a multimodal basis. A general framework is proposed and a solution scheme composed of an iterative process between the current solutions of the demand and the supply optimization problems, is introduced. Convergence conditions are discussed for this iterative process between these two problems which can be seen as inverse of each other.

https://hal-enac.archives-ouvertes.fr/hal-00939226/document

A global model for long term planning of multimodal freight transportation systems

In this communication is considered the problem of long term forecasting of the freight traffic growth in a large transportation network. This problem is crucial when planning the necessary investments in terminals, transportation links and fleets. One of the main difficulty of this task is related with the estimation of future demand over the network which has direct influence on the operational conditions and costs. The proposed approach makes use of two different optimization models: One model is devoted to freight demand forecasting, the other one defines the global transport supply according with a profit maximization behavior for the whole freight transport sector . The freight demand forecasting process is based a new entropy maximization approach to determine the distribution of origin-destination matrices. A two level solution technique considering vehicle flows at the first level and the freight flows at the second level is introduced. The proposed solution scheme is composed of an iterative process between the current solution for freight demand forecasting and the supply optimization problem: the entropy maximizing freight distribution problem provides the freight origin-destination matrix given a fare structure, while the supply optimization problem provides the fare structure given a freight origin-destination matrix.

https://hal-enac.archives-ouvertes.fr/hal-00938288/document

An Optimization Approach for Long Term Planning of Multimodal Freight Transportation Systems

Cette recherche s'interesse a l'optimisation de l'organisation des systemes multimodaux de transport de marchandises qui font appel de facon significative au transport aerien. Au cours des dernieres decennies de nombreuses etudes dans le domaine de la Recherche Operationnelle et de l'Aide a la Decision ont traite de problemes de planification des activites de transport de marchandises. Ce probleme a ete aborde suivant differentes approches mettant en avant des caracteristiques diverses (choix d'itineraires, localisation des depots, choix de flotte, contraintes temporelles, gestion des stocks, aspects stochastiques, etc.) neanmoins, en ce qui nous concerne, peu de travaux se sont focalises sur le transport aerien comme element central d'un systeme intermodal de transport de marchandises. Par ailleurs, dans la majorite des etudes consultees, l'un des elements essentiels de la prise de decision, la demande, est consideree figee, ce qui limite la prise en compte de la concurrence entre les differents agents economiques participant au transport.

https://hal-enac.archives-ouvertes.fr/hal-00934803/document

Amaranto Lopes Pereira

Papers

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

A global model for long term planning of multimodal freight transportation systems

An Optimization Approach for Long Term Planning of Multimodal Freight Transportation Systems

Planning airports within regional multimodal transportation systems

Une approche de modélisation d'un système multimodal de transport de marchandise en vue de son optimisation