A Model for Optimal Wastewater Management in a River Basin

The problem of wastewater management in a river basin has been extensively studied in the operations research literature. Two main trends can be identified in this area : the first attempts to determine the optimal (in the sense of minimal cost) treatment levels to be achieved in a set of treatment plants located along rivers, for which quality standards are specified. Examples of such studies are given in papers by Deininger (1965), Loucks et al. (1967), Ecker (1975) and Fiacco and Ghaemi (1979). The second trend is devoted to the optimal location and design of a wastewater transportation and treatment system in such a way that all wastewaters of the river basin receive some priori specified treatment. This problem was studied by Deininger (1969, 1972), Joeres et al. (1974), Jarvis et al. (1978) and the authors (Smeers and Tyteca, 1982a). Both problems can be brought together and investigates as a more general problem which aims at simultaneously determining the topology and size of the sewage and treatment system as well as the treatment levels to be achieved at each treatment plant, in order to meet some water quality target at overall minimal cost. That problem has only received limited attention in the literature (Graves, 1972; Graves et al., 1972). This is mainly due to the high analytical complexity of the resulting mathematical programming problem, and to practical difficulties of implementation. The authors (Smeers and Tyteca, 1982b) presented a model for solving the global problem, in which, furthermore, the non-homogeneity of the raw wastewater at the various emission points is taken into account. The aim of this paper is to extend this previous work so as to explore a new formulation of the model which exploits the dual formulation of the mathematical progral, and to present some sensitivity analyses with respect to the characteristics of the receiving water bodies.