This paper proposes a hybrid mixed-integer linear programming-linear programming-linear programming (MILP-LP-LP) methodology for simultaneous optimal design and operation of unconfined groundwater utilization systems. The proposed model is an extension to the earlier LP-LP model introduced by the authors for the optimal design and operation of confined groundwater utilization systems. The proposed model can be used to minimize the total cost, including the well drilling, pump installation cost and energy cost, of utilizing a two-dimensional unconfined aquifer under both steady-state and transient flow conditions. The solution of the problem is defined by the well numbers and location, well drilling depth and the corresponding pumping rates, satisfying a downstream demand, lower/upper bound on the pumping rates, and lower/upper bound on the water level drawdown in the wells. A discretized version of the differential equation governing the aquifer is first embedded into the model formulation as additional constraints. The resulting mixed-integer non-linear programming problem is then decomposed into three sub-problems with different sets of decision variables, namely, hydraulic head, well numbers and locations and their pumping rates, and well depths. Starting with a set of random values for all decision variables, the three sub-problems are solved assuming fixed values for the other variables. This process is iterated until convergence is achieved.
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12 May 2016
This article was originally published in
Journal of Water Supply: Research and Technology-Aqua
Article Contents
Research Article|
January 07 2016
A hybrid MILP-LP-LP approach for the optimal design and operation of unconfined groundwater utilization systems
M. Bostan;
1Department of Civil Engineering, College of Agriculture, Kermanshah Branch, Islamic Azad University, PO Box 6718997551, Kermanshah, Iran
E-mail: [email protected]
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M. H. Afshar;
M. H. Afshar
2Civil Engineering Faculty & Enviro-Hydroinformatic COE, Iran University of Science and Technology, PO Box 16765-163, Narmak, Tehran, Iran
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M. Khadem;
M. Khadem
3School of Civil Engineering, Iran University of Science and Technology, Tehran, Iran
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A. A. Akhtari
A. A. Akhtari
4Department of Civil Engineering, College of Engineering, Razi University, PO Box 6734667149, Kermanshah, Iran
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Journal of Water Supply: Research and Technology-Aqua (2016) 65 (3): 208–219.
Article history
Received:
February 26 2015
Accepted:
November 22 2015
Citation
M. Bostan, M. H. Afshar, M. Khadem, A. A. Akhtari; A hybrid MILP-LP-LP approach for the optimal design and operation of unconfined groundwater utilization systems. Journal of Water Supply: Research and Technology-Aqua 12 May 2016; 65 (3): 208–219. doi: https://doi.org/10.2166/aqua.2016.028
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