Adaptive scheduling of mixed bus services with flexible fleet size assignment under demand uncertainty

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This paper presents an optimization framework for adaptive scheduling of mixed bus services with flexible fleet size assignment under demand uncertainty. The service scheduling plans are driven by prevailing stochastic passenger demand subject to operational constraints. The optimization problem is formulated as a Markov decision process which aims to minimize passengers’ in-vehicle and waiting times, as well as the operator’s cost via use of services with different routes, schedules, and fleet sizes. To address the computational challenges, the solutions to the problem are to be calculated with use of reinforcement learning techniques. The proposed framework is implemented and tested using real-world scenarios configured from actual bus service route in Hong Kong. Experiment results reveals the benefits of the proposed bus service scheduling framework with use of flexible routes and fleet sizes in saving passengers’ and operator’s costs. This study contributes to real time transit operational planning with advanced computing and optimization techniques.