A Double Decomposition Algorithm for Network Planning and Operations in Deviated Fixed-route Microtransit

Abstract

Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system that relies on reference lines but can deviate on demand in response to passenger requests. We formulate a Microtransit Network Design (MiND) model via two-stage stochastic integer optimization, with a first-stage network design and service scheduling structure and a second-stage vehicle routing structure. We derive a tight second-stage relaxation using a subpath-based representation of microtransit operations in a load-expanded network. We develop a double-decomposition algorithm combining Benders decomposition and subpath-based column generation. We prove that the algorithm maintains a valid optimality gap and converges to an optimal solution in a finite number of iterations. Results obtained with real-world data from Manhattan show that the methodology scales to large and otherwise-intractable instances, with up to 10-100 candidate lines and hundreds of stops. Comparisons with transit and ride-sharing suggest that microtransit can provide win-win outcomes toward efficient mobility (high demand coverage, low costs, high level of service), equitable mobility (broad geographic reach) and sustainable mobility (limited environmental footprint). We provide an open-source implementation to enable replication.