Operation of an ambulance fleet under uncertainty

We introduce two new optimization models for the dispatch of ambulances. The first model, called the ambulance selection problem, is used when an emergency call arrives to decide whether an ambulance should be dispatched for that call, and if so, which ambulance should be dispatched, or whether the request should be put in a queue of waiting requests. The second model, called the ambulance reassignment problem, is used when an ambulance finishes its current task to decide whether the ambulance should be dispatched to a request waiting in queue, and if so, which request, or whether the ambulance should be dispatched to an ambulance staging location, and if so, which ambulance staging location. These decisions affect not only the emergency call and ambulance under consideration, but also the ability of the ambulance fleet to service future calls. There is uncertainty regarding the locations, arrival times, and types of future calls. We propose a rolling horizon approach that combines the current decisions to be made as first-stage decisions with second-stage models that represent the ability of the ambulance fleet to service future calls. The second-stage optimization problems can be formulated as large-scale deterministic integer linear programs. We propose a column generation algorithm to solve the continuous relaxation of these second-stage problems. The optimal objective values of these second-stage continuous relaxations are used to make approximately optimal first-stage decisions. We compare our resulting dispatch policy with popular decision rules for Rio de Janeiro emergency medical service, based on data of more than 2 years of emergency calls for that service. These tests show that our proposed policy results in smaller response times than the popular decision rules.