A novel dynamic fare pricing model based on fuzzy bi-level programming for subway systems with heterogeneous passengers

Abstract

We propose a dynamic fare pricing model based on demand prediction to mitigate peak hours’ congestion in public transportation. To deal with demand uncertainties, we propose the Kumaraswamy membership function (KMF) as a flexible membership function. The proposed KMF is applied to construct the new KMF-TSK fuzzy logic system (FLS) for passenger demand prediction and the new fuzzy bi-level programming model (KMF-FBP) for fare price determination. We also introduce a new fare structure based on smooth function considering passenger demand and travel distances. The fare structure is a combination of peak hours charging and off-peak hours discounting. We consider passengers' heterogeneity according to their income levels to improve equity in pricing and to increase the acceptance rate of pricing policies. Applying the proposed model, passengers could be informed about the ticket prices for the upcoming week, which helps to mitigate peak congestion. Data for Tehran subway system is utilized as a case study to verify our proposed fare pricing model. The experimental results demonstrate the superiority of the proposed KMF-FBP model over both conventional bi-level and Triangular fuzzy bi-level programming models. Physical distancing is also taken into account in a simulation experiment to assess the effects of the COVID-19 situation.