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Open AccessArticle

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

by Teng Ma 1, Jinwen Wang 1,*, Yi Liu 2,3,4, Huaiwei Sun 1, Dongwei Gui 2,3,4,* and Jie Xue 2,3,4
1
College of Hydropower & Information Engineering, Huazhong University of Science & Technology, Wuhan 430074, China
2
State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China
3
Cele National Station of Observation & Research for Desert-Grassland Ecosystem, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, China
4
University of Chinese Academy of Sciences, Beijing 100049, China
*
Authors to whom correspondence should be addressed.
Water 2019, 11(6), 1185; https://doi.org/10.3390/w11061185
Received: 8 May 2019 / Revised: 29 May 2019 / Accepted: 5 June 2019 / Published: 6 June 2019
(This article belongs to the Section Hydrology)
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. View Full-Text
Keywords: well layout optimization; well flow distribution; mixed integer linear programming (MILP); special ordered sets (SOS); Oasis district well layout optimization; well flow distribution; mixed integer linear programming (MILP); special ordered sets (SOS); Oasis district
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Ma, T.; Wang, J.; Liu, Y.; Sun, H.; Gui, D.; Xue, J. A Mixed Integer Linear Programming Method for Optimizing Layout of Irrigated Pumping Well in Oasis. Water 2019, 11, 1185.

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