A Multi-Modal Network Equilibrium Model with Interacting Mobility Service Providers'Strategies

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.