Reservoir Operations by Successive Linear Programming

The dynamics of a reservoir system are usually described by the repeated applications of continuity equations. Since the number of variables involved is usually double the number of equations, the feasible solutions of the system are infinite and always lie on the hyperplane determined by the continuity equations. This study shows that the final optimal solutions of SLP can be reached by the introduction of step bounds either on releases or on storages, whichever has the smaller range of variations, and not on both simultaneously, and the continuous reduction of their sizes in the search process. Different search schemes are compared. The search scheme, in which the step sizes ar halved for each new iteration, takes less than half the time to reach an optimum for an example single-resevoir problem than the commonly used search scheme in which the step sizes are only halved when the new solution of LP is less optimal than the previous one.