Mixed Integer Linear Fractional Programming for Conjunctive Use of Surface Water and Groundwater

Abstract

A conjunctive-use model is developed for management of groundwater and surface water resources via mixed integer linear fractional programming (MILFP). The objective of the conjunctive-use model is to maximize the ratio of groundwater usage to surface water usage through a water supply network. A conditional head constraint is imposed to the conjunctive-use model to maintain aquifer sustainability. A transformation approach is introduced to transform the conditional head constraint into a set of mixed integer linear constraints in terms of groundwater head. Groundwater head is further linearized with respect to pumping rates that are decision variables. Eventually, the conjunctive-use model is to solve a successive MILFP problem by updating the response matrix in each iteration. To make an MILFP problem tractable, the study develops a transformation technique along with the Charnes–Cooper transformation approach to transform an MILFP problem into an equivalent problem of mixed integer linear programming (MILP) to be solved by CPLEX. The proposed conjunctive-use model is applied to northern Louisiana. A water supply network is proposed to utilize four existing reservoirs as alternative resources in order to raise groundwater level in the Sparta aquifer to acceptable target level in Ouachita, Lincoln, and Union Parishes while maximizing groundwater pumping. The results show that the conjunctive-use management framework increases groundwater levels by an average of 6.96 m (22.82 ft) from 2001 to 2010 by reducing total groundwater withdrawal 28.93%, which is counterbalanced by reservoir water.