Modeling of building evacuation problems by network flows with side constraints

In this paper we model building evacuations by network flows with side constraints. Side constraints come from variable arc capacities on some arcs which are functions of flows in incident arcs. In this context we study maximum flow, minimum cost, and minimax objectives. For some special structured networks we propose ‘greedy’ algorithms for solving these problems. For more general network structures, solution procedures are recommended which take advantage of the network structures of the problems.