A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is defined through a novel supernetwork approach where users' daily trip chains are represented to model the mobility services used to reach each destination. At the upper level, a profit maximization formulation is introduced to describe each MSPs' behaviour. At the lower level, users within a class choose minimum cost routes, according to Wardrop's first equilibrium principle. To consider the interactions between modes, non-separable costs between supernetwork links are defined, and users' equilibrium conditions are formulated as a Variational Inequality (VI). To solve the MPEC, an iterative solution algorithm based on a Modified Projection Method is proposed. Numerical examples are presented to illustrate properties of the model, and to examine scenarios showcasing cooperation or competition strategies between MSPs.

翻译：本文构建了一个具有均衡约束的数学规划（MPEC）模型，以刻画多式联运网络中多个出行服务提供商（MSP）与用户之间的互动关系。网络供应结构通过一种新颖的超网络方法进行定义，其中用户的日常出行链被表示出来，以模拟其抵达各目的地所使用的出行服务。在上层，引入利润最大化公式来描述每个MSP的行为。在下层，用户类别根据Wardrop第一均衡原理选择最小成本路径。为考虑各交通方式间的相互作用，定义了超网络链路上的不可分离成本，并将用户的均衡条件表述为变分不等式（VI）。为求解该MPEC，提出了一种基于修正投影法的迭代求解算法。通过数值算例展示了模型的性质，并检验了MSP之间合作或竞争策略下的场景。