An Application of Optimal Control to the Economics of Recycling

A city's landfill is an exhaustible resource; recycling is a backstop method of waste disposal. We formulate an optimal control model that maximizes the total utility of a representative consumer by choosing the appropriate levels of the two disposal techniques. The model is simple enough that some general conclusions can be drawn, and yet specific solutions will require some computations that show a few of the possibilities in optimal control problems. Among the primary results is that once recycling begins, it will increase. It is also likely that the level of recycling will assume the values at the endpoints of its domain as well as the more standard values in the interior.