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The equity-efficiency trade-off 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. This thesis introduces a novel multi-period optimisation framework called “Equity over Time (EoT)” aiming to balance efficiency and equity without introducing new resources. The concept of EoT is applied through a multi-period, bilevel frequency optimisation framework which integrates equity 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 trade-off between efficiency and equity.
Various equity metrics based on justice theories, including Utilitarianism, Prioritarianism, Capabilitarian Sufficiency and Rawls' Egalitarianism, are integrated into the optimisation framework to guide resource allocation. The resultant network performances are assessed against different justice theory-driven metrics to highlight the multi-dimensionality of equity analysis, and how different equity principles could lead to distinct policy recommendations. This thesis uses Pareto-front analysis to demonstrate the improved trade-offs 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.
The thesis proposes a customised matheuristic combining pattern generation and scheduling to improve computational tractability of the multi-period model. Specifically, it introduces a symmetry-breaking term to reduce the solution space and proposes two variations of the matheuristic for single-objective and biobjective optimisation models. Within allowable run time, the matheuristic consistently achieved solutions that were equal to or better than those from the exact method in every instance with run times that were on average 96.78% (single-objective) and 99.03% (biobjective) faster. The EoT framework is then applied to the southern suburbs in Canberra, Australia to demonstrate the scalability of the proposed framework and consistency of the findings regardless of the size of the network.