Adaptive variable neighbourhood search approach for time-dependent joint location and dispatching problem in a multi-tier ambulance system

Location-allocation of ambulances is a critical planning problem in the efficient operation of an emergency medical services system. This work considers a joint ambulance location and dispatch problem for a multi-tier ambulance system. The proposed problem addresses three key decisions: the location of ambulance stations, allocation of ambulances to these stations, and the preference order of stations for dispatching ambulances. We consider various other important factors, such as temporal variation in demand and travel time, station-specific ambulance busy probabilities and possible relocation of ambulances over the day. A mixed-integer non-linear programming model is formulated with a survival probability-based objective function to represent the problem. A queueing-based iterative approximation approach is presented to estimate the station-level dispatch probability of ambulances. We propose an adaptive variable neighbourhood search approach to solve the problem that utilises the approximation approach to obtain the objective function. A relaxed station location problem combined with a particle swarm approach for ambulance allocation is solved to obtain an initial solution. The effectiveness of the proposed approach is validated using a dataset generated based on the city of Kolkata in India.