Maximum capture problem based on paired combinatorial weibit model to determine park-and-ride facility locations

Park-and-ride (P&R) facilities are key components in encouraging people to use the transit system by allowing them to leave their private vehicles at certain locations. The well-known multinomial logit (MNL) model is often used to develop a random utility maximization–based mathematical programming formulation to determine P&R facility locations. According to the independently and identically distributed (IID) assumption, the MNL model cannot account for the route similarity and user heterogeneity. This study provides a new mixed integer linear programming (MILP) formulation by incorporating a newly developed paired combinatorial weibit (PCW) model to relax the IID assumption for determining the optimal P&R facility location. Specifically, the incorporation of a copula derived from a generalized extreme value (GEV) model addresses the issue of route overlap within the context of the PCW model. In addition, using the Weibull distribution permits the consideration of heterogeneous perception variance. Its two-level tree structure for evaluating the marginal and conditional probabilities allows a linearization scheme to obtain a set of linear constraints. Numerical examples reveal the influence of the IID assumption relaxation on the results. The two probabilities from the tree structure and the binary location variables are combined to present a corresponding PCW model under open/close P&R facility solution. According to the degree of route overlapping and route-specific perception variance, the fare structure, particularly the distance-based scheme, has an impact on the number of P&R users and location at optimum.