Toward optimal waste management policies for a river basin

Abstract

A mathematical analysis of marginal cost functions, where the total basin-wide treatment cost for a series of users of water in a river basin is to be minimized subject to constraints, is presented. The situation considered is where a series of water-using firms are located along a river; the river being the sole source of water supply and the only place to discharge wastewater. In such a situation, upstream users, if they discharge waste, impose damage costs on those downstream. On the other hand, if the upstream user is restricted in discharging wastes into the river, the costs for withholding or treating of these wastes are imposed on him. This trade-off is the basis for the minimization of the total basin-wide treatment cost. The results of this study show that under most conditions an optimal solution can be found which balances the upstream marginal waste withholding cost with the downstream damage costs. The analysis is concluded with a presentation of conditions which make these marginal cost relationships sufficient as well as necessary for optimally. Although stream-flow, inflow and outflow are treated as deterministic, this model should be valid except during extreme, transient conditions.