W ith growing dependence of many cities on urban mass transit, even limited disruptions of public transportation networks can lead to widespread confusion and significant productivity losses. A need exists for systematic approaches to developing efficient responses to minimize such negative impacts. We present an optimization-based approach that responds to degradations of urban transit rail networks by introducing smartly designed bus bridging services that take into consideration commuter travel demand at the time of the disruption. The approach consists of three fundamental steps, namely, (1) a column generation procedure to dynamically generate demand-responsive candidate bus routes, (2) a path-based multicommodity network flow model to identify the most effective combination of these candidate bus routes, and (3) another optimizationbased procedure to determine simultaneously the optimal allocation of available vehicle resources among the selected routes and corresponding headways. The approach is applied to two case studies defined using actual data. The results show that the proposed approach can be carried out efficiently and that adding nonintuitive bus routes to the standard bus bridging services can significantly reduce the average travel delay. Moreover, the approach distributes delay more equitably. Many realistic operating constraints can also be handled.
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