Optimal management of a multireservoir water supply system

Abstract

This paper presents a pilot study of a method for finding an approximation for the optimal policy of a dynamic system which depends on stochastic state variables. The systems being considered are multi‐reservoir water supply systems whose (stochastic) state variables are the quantities of water in each reservoir and some previous inflows which affect future inflows. Of special importance is the three‐reservoir system which represents the major part of Israel's water supply system: Lake Kinneret and two underground aquifers. This system can be represented by five stochastic state variables: the quantities of water in each of the three reservoirs and the inflows into the Kinneret for the two previous months. Since this system is too large to be solved by the usual dynamic programing approach, a method was devised in this study for obtaining an approximate solution which does not consume too much time or space. This method will be referred to as the parameters iteration method. It has been tested on a smaller system which contains only three stochastic state variables: the amount of water in the Kinneret and two previous monthly inflows. The results were satisfactory in the sense that the approximate solution obtained by this method was as good as the optimal solution obtained by a dynamic programing approach to this problem. Thus it can be expected that the parameter iteration method would be efficient for the three reservoir problems as well and for larger problems.