Joint Optimization of Pattern, Headway, and Fleet Size of Multiple Urban Transit Lines with Perceived Headway Consideration and Passenger Flow Allocation

TL;DR

This paper presents a comprehensive optimization model for urban transit planning that simultaneously designs routes, headways, and fleet sizes, considering passenger perceptions and flow allocations to enhance service quality and efficiency.

Contribution

It introduces a large-scale, flexible MCNF-based MILP model that integrates multiple operational strategies and passenger perceptions for transit system design.

Findings

Achieved near-optimal solutions for a city-sized network in hours.

Reduced total weighted journey times by up to 5.76%.

Provided an efficient planning tool for transit agencies.

Abstract

This study addresses the urban transit pattern design problem, optimizing stop sequences, headways, and fleet sizes across multiple routes and periods simultaneously to minimize user costs (composed of riding, waiting, and transfer times) under operational constraints (e.g., vehicle capacity and fleet size). A destination-labeled multi-commodity network flow (MCNF) formulation is developed to solve the problem at a large scale more efficiently compared to the previous literature. The model allows for flexible pattern options without relying on pre-defined candidate sets and simultaneously considers multiple operational strategies such as express/local services, short-turning, and deadheading. It evaluates perceived headways of joint patterns for passengers, assigns passenger flows to each pattern accordingly, and allows transfers across patterns in different directions. The mixed-integer linear programming (MILP) model is demonstrated with a city-sized network of metro lines in Chicago, IL, USA, achieving near-optimal solutions in hours. The total weighted journey times are reduced by 0.61% and 5.76% under single-route and multi-period multi-route scenarios respectively. The model provides transit agencies with an efficient tool for comprehensive service design and resource allocation, improving service quality and resource utilization without additional operational costs.