A Mixed Integer Linear Programming Method for Optimizing Layout of Irrigated Pumping Well in Oasis

Optimization of irrigation well layout plays a vital role in the rational utilization of groundwater and to balance the water-energy nexus, especially in arid irrigation districts. This study proposes the mixed integer linear programming model (MILP) for well layout optimization with minimum well irrigation costs. This model efficiently establishes a link between irrigation area and wells to express the constraints of ensuring that irrigation area can be covered with optimal wells by using grid points to represent the irrigation area. It also uses the special ordered sets (SOS) modeling tool to decompose the mixed integer nonlinear programming into a mixed integer linear programming by assigning SOS-constrained weights to discrete points of a nonlinear function. This method was used in Cele Oasis of the Tarim Basin of the Xinjiang Province, an arid region in northwestern China. Since the original well layout was already established, different economic criteria like implicit cost and explicit cost were considered and two optimization results were yielded. The results showed that (1) the implicit cost optimization (ICO) and explicit cost optimization (ECO) reduced total costs by 7.64% and 3.56% compared with the condition of without optimization; and (2) the ICO and ECO reduced the optimal number of wells by 52.89% and 10.74% compared with the existing number of wells. Based on the analysis of the results, it is suggested that the manager should close uneconomical wells after determining the economic criteria. This method for well layout optimization can assist managers to make more rational plans for irrigation systems to exploit groundwater more efficiently, economically, and in a more environmentally friendly manner.