Multi-period bus frequency optimization and fleet rebalancing based on equity over time

Abstract

The equity-efficiency tradeoff is a perpetual challenge in public transport planning. There is a strong need to integrate equity considerations into transit planning, while respecting the long-term financial sustainability of the public transport system. We introduce an ‘Equity over Time (EoT)’ multi-period, biobjective, bilevel frequency optimization framework, to integrate fairness metrics into bus allocation, while incorporating practical considerations such as fleet rebalancing costs and transfers. By changing the recipient of benefits or penalties over time, the multi-period allocation perspective allows the model to improve the tradeoff between efficiency and equity. We use Pareto-front analysis to demonstrate the improved tradeoffs between efficiency and equity of the EoT approach, then show through numerical experiments that the EoT framework is able to achieve better or equal solutions than its single period counterpart in all instances. We propose a customized matheuristic combining pattern generation and scheduling to solve larger instances. Numerical experiments show that the heuristic is on average 99.03% faster than the exact method for instances that return a solution. The EoT framework is then applied to the southern suburbs in Canberra, Australia. We introduce an Efficiency-Equity Tradeoff Index to support the selection of a suitable planning horizon duration.