  The multi-depot vehicle scheduling problem (MDVSP) is a critical planning
challenge for transit agencies. We introduce a novel approach to MDVSP by
incorporating service reliability through chance-constrained programming (CCP),
targeting the pivotal issue of travel time uncertainty and its impact on
transit service quality. Our model guarantees service reliability measured by
on-time performance (OTP), a primary metric for transit agencies, and fairness
across different service areas.We propose an exact branch-and-cut (B&C) scheme
to solve our CCP model. We present several cut-generation procedures that
exploit the underlying problem structure and analyze the relationship between
the obtained cut families. Additionally, we design a Lagrangian-based heuristic
to handle large-scale instances reflective of real-world transit operations.
Our approach partitions the set of trips, each subset leading to a subproblem
that can be efficiently solved with our B&C algorithm, and then employs a
procedure to combine the subproblem solutions to create a vehicle schedule that
satisfies all the planning constraints of the MDVSP. Our empirical evaluation
demonstrates the superiority of our stochastic variant in achieving
cost-effective schedules with reliable OTP guarantees compared to alternatives
commonly used by practitioners, as well as the computational benefits of our
methodologies.
