  In this paper we discuss optimal dispatching of fire trucks, based on a
particular dispatching problem that arises at the Amsterdam Fire Department,
where two fire trucks are send to the same incident location for a quick
response. We formulate the dispatching problem as a Markov Decision Process,
and numerically obtain the optimal dispatching decisions using policy
iteration. We show that the fraction of late arrivals can be significantly
reduced by deviating from current practice of dispatching the closest available
trucks, with a relative improvement of on average about $20\%$, and over $50\%$
for certain instances. We also show that driving-time correlation has a
non-negligible impact on decision making, and if ignored may lead to
performance decrease of over $20\%$ in certain cases. As the optimal policy
cannot be computed for problems of realistic size due to the computational
complexity of the policy iteration algorithm, we propose a dispatching
heuristic based on a queueing approximation for the state of the network. We
show that the performance of this heuristic is close to the optimal policy, and
requires significantly less computational effort.
