Vehicle dispatching plan for minimizing passenger waiting time in a corridor with buses of different sizes: Model formulation and solution approaches

Urban public transportation agencies sometimes have to operate mixing vehicles of different sizes on their routes, due to resource limitations or historical reasons. Services with different passenger-carrying capacities are provided to passengers during a mixed-fleet operation. A fundamental question arising here is how to optimally deploy a given fleet of different bus sizes to provide services that minimize passenger waiting time. We formulate a mixed-fleet vehicle dispatching problem as a Mixed-Integer Nonlinear Programming (MINLP) model to optimize dispatching schemes (dispatching orders and times) when a given set of buses of different sizes are available to serve demand along a route. The objective is to minimize the average passenger waiting time under time-dependent demand volumes. Stochastic travel times between stops and vehicle capacity constraints (i.e., introducing extra waiting time due to denied boarding) are explicitly modeled. A Simulated Annealing (SA) algorithm coupled with a Monte Carlo simulation framework is developed to solve large real-world instances in the presence of stochastic travel times. Results show that, in addition to dispatching headway, bus dispatching sequence can strongly affect waiting times under a mixed-fleet operation. Indeed, with an optimal dispatching sequence, a more accurate adjustment of supply to demand is possible in accordance with time-dependent demand conditions, and the total savings in waiting time are mainly driven by a further reduction in the number of passengers left behind. The optimality of uneven dispatching headways stems from two elements: having a mixed fleet and having localized peaks on demand that make buses run full.