Demonstrating one of the most incredible examples of collective behavior among social insects, the self-assembling structures formed by army ants of the species Eciton hamatum provide a clear benefit to the entire colony. In order to navigate the rough and complex terrain of the tropical forests of Central and South America, these nomadic ants use their bodies to create temporary bridges for their nest mates to travel over. These living bridges are uniquely complex in their ability to adapt their size according to traffic and assemble across a wide variety of environments. While these bridges provide a short cut in the foraging trail, the dynamics of their formation suggest the existence of a cost-benefit trade-off, in which the benefit of increased efficiency must be balanced by the cost of removing workers from the foraging pool to form the structure. To examine this trade-off, we extend the work of an existing publication to construct mathematical models of self-assembly which represent different configurations of the local environment. These models will be used to generate predictions about the bridge location that maximizes the foraging rate of the colony.