Evacuating an Elementary School Building

Early in our mathematical modeling course, Penelope Smith, the student co-author, fulfilled her library research assignment by investigating existing models of fire evacuation. Although there were a few studies of evacuating adults from public buildings, there were none of moving children out of schools. This seems to be a lamentable oversight, since children often spend long periods of time at pre-assigned places in old wooden buildings.

The problem's definition is not immediately obvious. One could want to minimize the average time in which it takes students to leave, or one could want to minimize the time required to evacuate the entire school. We considered both goals. It is customary to have entire elementary school classes remain supervised by their own teachers, so this study treats each class as a unit. We also assume that only one class can pass through a door at once, that is passing requires non-zero time, and that the classes do not delay each other in the hallways.