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.

停车换乘 (P&R) 设施是鼓励人们使用交通系统的关键组成部分，允许人们将私家车停放在特定地点。众所周知的多项 Logit (MNL) 模型通常用于开发基于随机效用最大化的数学规划公式来确定 P&R 设施位置。根据独立同分布（IID）假设，MNL模型无法考虑路线相似性和用户异质性。本研究通过结合新开发的配对组合 weibit (PCW) 模型提供了一种新的混合整数线性规划 (MILP) 公式，以放宽用于确定最佳 P&R 设施位置的 IID 假设。具体来说，结合从广义极值 (GEV) 模型导出的联结可以解决 PCW 模型上下文中的路线重叠问题。此外，使用威布尔分布可以考虑异质感知方差。其用于评估边际概率和条件概率的两级树结构允许线性化方案获得一组线性约束。数值例子揭示了IID假设松弛对结果的影响。将来自树结构和二元位置变量的两个概率组合起来，在打开/关闭 P&R 设施解决方案下呈现相应的 PCW 模型。根据路线重叠程度和特定路线的感知差异，票价结构，特别是基于距离的方案，对 P&R 用户数量和最佳位置有影响。