A Markovian Decision Model for Deciding How Many Fire Companies to Dispatch

In deciding how many units to dispatch to an incoming alarm of unknown seventy the fire department is faced with a dilemma: If too few units are sent initially the extra units needed will be delayed; if too many units are sent, the extra units make a needless response and are temporarily unavailable for subsequent alarms. In this paper, we present a Markovian decision model for this problem. The model leads to a simple decision rule that considers three key factors: (1) the probability that the incoming alarm is serious (the greater the probability the more units dispatched); (2) the expected alarm rate in the area surrounding the alarm (the greater the alarm rate, the fewer units dispatched); and (3) the number of units available in the area surrounding the alarm (the more units available, the more units dispatched). We compare the decision rule to policies commonly in use and find that it results in significant improvements in response time to serious fires.