Using emission functions in mathematical programming models for sustainable urban transportation: an application in bilevel optimization

Abstract

Sustainability is an emerging issue as a direct consequence of the population increase in the world. Urban transport systems play a crucial role in maintaining sustainability. Recently, sustainable urban transportation has become a major research area. Most of these studies propose evaluation methods that use simulation tools to assess the sustainability of different transportation policies. Despite all studies, there seems to be lack of mathematical programming models to determine the optimal policies. Conventional mathematical programming techniques have been used in several transportation problems such as toll pricing and traffic assignment problems. To demonstrate the possible applications of mathematical programming within sustainability, we propose a bi-level structure for several optimization models that incorporate the measurement of gas emissions throughout a traffic network. The upper level of the problem represents the decisions of transportation managers who aim to make the transport systems sustainable, whereas the lower level problem represents the decisions of the network users that are assumed to choose their routes to minimize their total travel cost. By using emission factor tables provided by several institutions, we determine the emission functions in terms of traffic flow to reflect the real emission values in case of congestion. Proposed emission functions are plugged into different proposed mathematical programming models that incorporate different policies or actions for sustainability. Among the incorporated policies are toll pricing, district pricing and capacity enhancement. We conduct a thorough computational study with the proposed models on a testing network by a state-of-the-art solver. The thesis ends with a thorough discussion of the solution effort as well as the interpretation of the results.

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