Joint optimisation of transfer location and capacity for a capacitated multimodal transport network with elastic demand: a bi-level programming model and paradoxes

With the growing attention toward developing a multimodal transport system to enhance urban mobility, there is an increasing need construct new infrastructures, rebuild or expand existing ones, accommodate current and newly generated travel demand. Therefore, this study develops bi-level model that simultaneously determines location capacity of transfer infrastructure be built considering elastic demand in network. The upper-level problem formulated as mixed-integer linear programming problem, whereas lower-level combined trip distribution/modal split/assignment depicts both destination route choices travellers via multinomial logit model. Numerical studies are conducted demonstrate occurrence two Braess-like paradox phenomena first one states under fixed demand, constructing parking spaces provide usage park-and-ride services could deteriorate performance measured by total passengers’ time, while second reveals for promote its may fail, which would represented decline their modal share. Meanwhile, numerical example also suggests infrastructures at distributed stations outperforms building large centre terms attracting using sustainable transit modes.