Evaluation of the most suitable mode of transport under Uncertainty. Dempster Shafer Theory applied to Analytical Hierarchy Process and Transformable Belief Model

The main goal of this work is to formulate a mathematical model of a decision support system for choosing the most suitable mode of transport to implement within a metropolitan context, considering uncertainty and ambiguity embedded in transportation problems. The model should consider not only economic parameters such as transport costs, production costs, and transport demand but, above all, environmental and social parameters, which define the quality of the transport service. The study applies a hybrid approach based on two different theories: the Analytical Hierarchy Process (AHP) (Saaty, 1980) and the Evidence- or Dempster-Shafer-Theory (DST) (Dempster 1967; 1968; Shafer, 1976). This is the first time that this methodology is used in the field of local public transport. AHP is used to structure the transportation problem and to define the criteria and alternatives. We used the AHP along with the mathematical Theory of Evidence, called also Dempster-Shafer Theory (DST), to evaluate the users' uncertainty in judgments, and to fuse data coming from diverse sources. Finally, we used the Transformable Belief Model (Smets, 1999) to quantify the probability embedded in belief functions. In the first part of this study, we have carried out a survey to investigate the users‟ point of view about the quality of transport, expressed through fifteen criteria, representative of the transport quality. The criteria were chosen according to the set proposed by Prioni and Hensher (2000), to the criteria included in the Transportation Research Board Handbook (1999) and to the European Standard EN13816. In particular, the chosen criteria are: Accessibility; Security; Cleanliness; Number of offered seats; Crowding; Frequency; Travel Time; Punctuality; Regularity of trips; Flexibility; Information; Single ticket(one ticket for all modes of transport, like a transport card); Intermodality; Pollution; Travel fares. In order to obtain more efficient results, we have divided these fifteen criteria into three macro categories. Each categories is composed of five criteria, and that are: Service Criteria, Time Criteria and External Criteria. Within the proposed survey, shared on the web, the users were asked to rank the chosen criteria. To investigate the transport company‟s point of view, we have extrapolated data, about costs and demand for transport, from financial statements. Among the transport companies that work into the metropolitan city of Bari, we have chosen the Ferrovie Appulo Lucane, which uses both Railway and Roadway transport. Starting from the data about costs and demand of transport, we have obtained the Average Cost curves for Railways and Road Transport. In this way, we have calculated the break-even point between the two curves. Due to the complexity of the transport problem, we have used the Analytical Hierarchy Process to decompose the problem in different levels. Because of the decomposition, we have obtained priority vectors, both for the pairwise comparison matrix of criteria and for the knowledge matrix, which we have taken as basic probability assignments (bpa) for application of the Dempster-Shafer Theory (DST). The DST is used to fuse different users‟ opinions, and to fuse users and company points of view, using the Dempster Rule of Combination. Moreover, the DST is used to take into account Uncertainty embedded in human judgment, thanks to the Belief and Plausibility measures, which are respectively the lower and upper bound of likelihood. Finally, in order to obtain the probability measures, we have used the Pigistic Trasnformation by Smets. The results show which alternatives users and transport company consider the best in relation to analyzed criteria.