Hierarchical Algorithm for Water Supply Expansion

Abstract

A computational method is described for finding the approximate optimal capacity expansion plan for a surface‐water supply system. The algorithm determines the estimated least‐costly sizing, sequencing, and operation of surface‐water storage and conveyance facilities over a specified set of staging periods. The expansion problem is separated into capital investment and system operation subproblems. A dynamic programming (DP) algorithm computes the least‐costly capital investment plan, where the optimal operating costs are approximated for each feasible set of projects. Development plans at each stage are then analyzed using a coupled set of network optimization models to compute actual system operating costs. These optimal operating costs are used to update the estimated minimum system costs. When an expansion plan is obtained by DP, which has the true operating costs, then the estimated minimum‐cost policy has been found. This approximate optimal plan is the true optimum if evaporation differences between reservoirs are insignificant. The algorithm is applied to the Guadalupe and San Antonio river basins in Texas to demonstrate its use in regional planning.