Regulating mobility-on-demand services: Tri-level model and Bayesian optimization solution approach

The goal of this paper is to develop a modeling framework that captures the inter-decision dynamics between mobility service providers (MSPs) and travelers that can be used to optimize and analyze policies/regulations related to MSPs. To meet this goal, the paper proposes a tri-level mathematical programming model with a public-sector decision maker (i.e. a policymaker/regulator) at the highest level, the MSP in the middle level, and travelers at the lowest level. The public-sector decision maker aims to maximize social welfare via implementing regulations, policies, plans, transit service designs, etc. The MSP aims to maximize profit by adjusting its service designs. Travelers aim to maximize utility by changing their modes and routes. The travelers’ decisions depend on the regulator and MSP's decisions while the MSP decisions themselves depend on the regulator's decisions. To solve the tri-level mathematical program, the study employs Bayesian optimization (BO) within a simulation–optimization solution approach. At the lowest level, the solution approach includes an agent-based transportation system simulation model to capture travelers’ behavior subject to specific decisions made by the regulator and MSP. At the middle and highest levels, the solution approach employs BO for the MSP to maximize profit and for the regulator to maximize social welfare. The agent-based transportation simulation model includes a mode choice model, a road network, a transit network, and an MSP providing automated mobility-on-demand (AMOD) service with shared rides. The modeling and solution approaches are applied to Munich, Germany in order to validate the model. The case study investigates the tolls and parking costs the city administration should set, as well as changes in the public transport budget and a limitation of the AMOD fleet size. Best policy settings are derived for two social welfare definitions, in both of which the AMOD fleet size is not regulated as the shared-ride AMOD service provides significant value to travelers in Munich.