NONLINEAR PROGRAMMING IN RIVER BASIN MODELING1

ABSTRACT: This paper explores the use of nonlinear programming in river basin water quality modelling. Applications recently reported in the literature, along with the author's experience with nonlinear programming, are reviewed. Results obtained using nonlinear programming are compared with the results obtained by other researchers using linear and dynamic programming to solve river basin water quality optimization problems. These water quality models have objective functions with continuous first partial derivatives, several inequality and variable bound constraints, and are of the form: minizie Σ^j=n_j=1Y_j(X_j) subject to Σ^j=n_j=1a_ijX_jb_i, i=1,2, …, m c_jX_jd_j, j= 1,2, …, n The variable X_i is the maximum allowable ratio of the BOD (biochemical oxygen demand) of the effluent outflow to the BOD of the wastewater inflow for treatment plant j, in the range c_j to d_j. The a_ijd and b_i are constants in the DO (dissolved oxygen) and BOD constraints. The resuks show, given certain assumptions about the data, that nonlinear programming is a better solution method for these problems than is either linear programming or dynamic programming.