Decomposition methods for water resources optimization models with fixed costs

Abstract

This paper illustrates the application of two decomposition algorithms, generalized Benders decomposition (GBD) and outer approximation (OA), to water resources problems involving cost functions with both discrete and nonlinear terms. Each algorithm involves the solution of an alternating finite sequence of nonlinear programming subproblems and relaxed versions of a mixed-integer linear programming master problem. Three example models, involving capacity expansion of a conjunctively managed surface and groundwater system, are formulated and solved to demonstrate the performance of the algorithms. The results show that OA obtains solutions in far fewer iterations than GBD, but OA requires more computational resources per iteration. As a result, depending on the mixed-integer programming and nonlinear programming solvers available, GBD may be better suited for solving larger planning problems.