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Many transit agencies operating paratransit and microtransit services have torespond to trip requests that arrive in real-time, which entails solving hardcombinatorial and sequential decision-making problems under uncertainty. Toavoid decisions that lead to significant inefficiency in the long term,vehicles should be allocated to requests by optimizing a non-myopic utilityfunction or by batching requests together and optimizing a myopic utilityfunction. While the former approach is typically offline, the latter can beperformed online. We point out two major issues with such approaches whenapplied to paratransit services in practice. First, it is difficult to batchparatransit requests together as they are temporally sparse. Second, theenvironment in which transit agencies operate changes dynamically (e.g.,traffic conditions), causing estimates that are learned offline to becomestale. To address these challenges, we propose a fully online approach to solvethe dynamic vehicle routing problem (DVRP) with time windows and stochastictrip requests that is robust to changing environmental dynamics byconstruction. We focus on scenarios where requests are relatively sparse - ourproblem is motivated by applications to paratransit services. We formulate DVRPas a Markov decision process and use Monte Carlo tree search to evaluateactions for any given state. Accounting for stochastic requests whileoptimizing a non-myopic utility function is computationally challenging;indeed, the action space for such a problem is intractably large in practice.To tackle the large action space, we leverage the structure of the problem todesign heuristics that can sample promising actions for the tree search. Ourexperiments using real-world data from our partner agency show that theproposed approach outperforms existing state-of-the-art approaches both interms of performance and robustness.

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services