Integrating passenger transportation costs into service network design: A bilevel optimal control approach using macroscopic fundamental diagram

Abstract

Service Network Design (SND) problem traditionally focuses on optimizing scheduling and routing costs of freight vehicles. However, it often overlooks the costs related to passenger vehicles. This study addresses this gap by proposing a bilevel optimal control framework that integrates the Macroscopic Fundamental Diagram (MFD) to estimate passenger transportation costs due to freight traffic movement. The lower-level aims at maximizing passenger vehicles while reducing freight vehicle accumulation. The upper-level ensures the total vehicle accumulation is regulated under a predefined threshold. A Model Predictive Controller (MPC) approach is used to solve the optimal control problem. A framework is presented to use the accumulation results for the calculation of passenger transportation costs along with travelled distance and time spent by vehicles in the traffic network. This change in passenger transportation costs due to freight vehicles is integrated into SND objective function. The methodology is implemented on Islamabad's Road network, estimating passenger transportation costs for various freight and passenger traffic mixes. The results indicate that as the number of passenger vehicles increases, the impact of freight vehicles on the passenger transportation costs is minimized. This SND-MFD integration presents significant potential for urban planners and logistics firms, facilitating informed decisions for optimizing the transportation mix, enhancing traffic flow and reducing costs.