Mixed optimization for constrained resource allocation, an application to a local bus service

The present paper follows up on Vázquez-Abad (2013), where we applied the ghost simulation model to a public transportation problem. The ghost simulation model replaces faster point processes (passenger arrivals) with a “fluid” model while retaining a discrete event simulation for the rest of the processes (bus dynamics). This is not an approximation, but an exact conditional expectation when the fast process is Poisson. It can be interpreted as a Filtered Monte Carlo method for fast simulation. In the current paper we develop the required theory to implement a mixed optimization procedure to find the optimal fleet size under a stationary probability constraint. It is a hybrid optimization because for each fleet size, the optimal headway is real-valued, while the fleet size is integer-valued. We exploit the structure of the problem to implement a stopped target tracking method combined with stochastic binary search.