Application of interactive interval linear programming for optimal water and crop area allocation considering virtual water content and socio-economic factors (Case study: Dorudzan-Korbal Plain)

Document Type : Research Article


1 PhD Candidate in Watershed Sciences & Engineering, Hormozgan University, Bandar-Abbas, Iran

2 Assistant Professor, Department of Watershed Sciences & Engineering, Hormozgan University, Bandar-Abbas, Iran

3 Assistant Professor, Department of Civil and Environmental Engineering, Shiraz University, Shiraz, Iran

4 Professor, Faculty of Environment, University of Tehran, Tehran, Iran.


One of the key issues in the practical planning for water resources is the existence of uncertain factors. One of the approaches for decision making under such circumstances is interval programming. The current study aims to develop an interactive optimization model for water and crop area allocation. The developed model consists of four objectives that take into account socio-economic factors, the virtual water content of crops, and meeting environmental water requirements. For solving the model, four crop area scenarios (assumptions) were considered. Results showed that by raising the level of satisfaction threshold on the constraints, the amount of water allocated to each water user is declined. So that from the satisfaction level of 0.65 to the level of complete satisfaction, the model allocates only the minimum amount of water (40 MCM) to meet the environmental water needs. Based on considered scenarios for solving the model, the largest cultivation areas are allocated to wheat and maize for autumn and spring cultivations, respectively. Solving the model in the absence of upper bound for crop areas revealed that the greatest difference between optimal crop area and the highest cultivation area belong to rice with 2777 and 5821.6 hectares in Dorudzan and Korbal districts, respectively. The main advantage of the developed model in the present study is the linear formulation as well as its ability to deal with uncertain parameters. Outcomes of the model provide information required for the assessment of risk and reliability of planning options for water allocation.


Main Subjects


1.   Han Y, Huang Y-F, Wang G-Q, Maqsood I. A multi-objective linear programming model with interval parameters for water resources allocation in Dalian city. Water resources management. 2011;25(2):449-63.
2.   Nikoo MR, Kerachian R, Poorsepahy-Samian H. An interval parameter model for cooperative inter-basin water resources allocation considering the water quality issues. Water resources management. 2012;26(11):3329-43.
3.   Nikoo MR, Kerachian R, Karimi A. A nonlinear interval model for water and waste load allocation in river basins. Water resources management. 2012;26(10):2911-26.
4.   Nikoo MR, Karimi A, Kerachian R. Optimal long-term operation of reservoir-river systems under hydrologic uncertainties: application of interval programming. Water resources management. 2013;27(11):3865-83.
5.   Bijani M, Hayati D, Abdolvand B. Agricultural Water Conflict in the Doroodzan Dam Irrigation Network, Iran: The Opinion of Regional Water Experts. Environmental Sciences. 2012;10(1):59-78. [Persian]
6.   Maqsood I, Huang G, Huang Y, Chen B. ITOM: an interval-parameter two-stage optimization model for stochastic planning of water resources systems. Stochastic Environmental Research and Risk Assessment. 2005;19(2):125-33.
7.   Wu S, Huang G, Guo H. An interactive inexact-fuzzy approach for multiobjective planning of water resource systems. Water Science and Technology. 1997;36(5):235-42.
8.   Wang L, Meng W, Guo H, Zhang Z, Liu Y, Fan Y. An interval fuzzy multiobjective watershed management model for the Lake Qionghai Watershed, China. Water resources management. 2006;20(5):701-21.
9.   Urli B, Nadeau R. An interactive method to multiobjective linear programming problems with interval coefficients. INFOR: Information Systems and Operational Research. 1992;30(2):127-37.
10.                Han Y, Xu S-g, Xu X-z. Modeling multisource multiuser water resources allocation. Water resources management. 2008;22(7):911-23.
11.                Allan T. Fortunately there are substitutes for water otherwise our hydro-political futures would be impossible. Proceedings of the Conference on Priorities for water resources allocation and management. 1993;Paper 2:13-26.
12.                Allan T. 'Virtual water': a long term solution for water short Middle Eastern economies?. British Association Festival of Science, Water and Development Session, University of Leeds; 1997.
13.                Yang H, Wang L, Zehnder AJ. Water scarcity and food trade in the Southern and Eastern Mediterranean countries. Food Policy. 2007;32(5):585-605.
14.                Verma S, Kampman DA, van der Zaag P, Hoekstra AY. Going against the flow: a critical analysis of inter-state virtual water trade in the context of India’s National River Linking Program. Physics and Chemistry of the Earth, Parts A/B/C. 2009;34(4):261-9.
15.                Velázquez E. Water trade in Andalusia. Virtual water: An alternative way to manage water use. Ecological Economics. 2007;63(1):201-8.
16.                Hoekstra AY, Chapagain AK. The water footprints of Morocco and the Netherlands: Global water use as a result of domestic consumption of agricultural commodities. Ecological Economics. 2007;64(1):143-51.
17.                Kort A. Virtual water trade in the SADC region: a grid-based approach. 2010.
18.                Zeitoun M, Allan JT, Mohieldeen Y. Virtual water ‘flows’ of the Nile Basin, 1998–2004: A first approximation and implications for water security. Global Environmental Change. 2010;20(2):229-42.
19.                Paulsen A. Virtual water: a useful concept for informing land use in New Zealand. 2013.
20.                Wichelns D. Virtual water: A helpful perspective, but not a sufficient policy criterion. Water Resources Management. 2010;24(10):2203-19.
21.                Yang H, Zehnder A. “Virtual water”: an unfolding concept in integrated water resources management. Water Resources Research. 2007;43(12).
22.                Rouhani N, Yang H, Amin Sichani S, Afyuni M, Mousavi S, Kamgar Haghighi A. Assessment of Food Products and Virtual Water Trade as Related to Available Water Resources in Iran. JWSS-Isfahan University of Technology. 2009;12(46):417-32. [Persian]
23.                Sabouhi M, Soltani G. Optimization of Cropping Patterns at Basin Level by Considering Social Profit and Net Virtual Water Import: A Case Study of Khorasan District. JWSS-Isfahan University of Technology. 2008;12(43):297-313. [Persian]
24.                Faramarzi M, Yang H, Mousavi J, Schulin R, Binder C, Abbaspour K. Analysis of intra-country virtual water trade strategy to alleviate water scarcity in Iran. Hydrology and Earth System Sciences Discussions. 2010;7(2):2609-49.
25.                Bakhshoodeh M, Dehghanpur H. Modeling crop cultivation pattern based on virtual water trade: evidence from Marvdasht in southern Iran. Iran Agricultural Research. 2015;34(2):29-34.
26.                Khanjari Sadati S, Speelman S, Sabouhi M, Gitizadeh M, Ghahraman B. Optimal irrigation water allocation using a genetic algorithm under various weather conditions. Water. 2014;6(10):3068-84.
27.                Rabie Z, Honar T, Mehdi Bateni M. Determination of optimal and and water allocation under limited water resources using soil water balance in Ordibehesht canal of Doroodzan water district. Iran Agricultural Research. 2015;34(2):21-28.
28.                Su X, Li J, Singh VP. Optimal allocation of agricultural water resources based on virtual water subdivision in Shiyang River Basin. Water resources management. 2014;28(8):2243-57.
29.Fooladmand HR, Ahmadi SH. Monthly spatial calibration of Blaney–Criddle equation for calculating monthly ETo in south of Iran. Irrigation and Drainage. 2009;58(2):234-45.
30.Tabari H, Hosseinzadeh Talaee P, Shifteh Some'e B. Spatial modelling of reference evapotranspiration using adjusted Blaney-Criddle equation in an arid environment. Hydrological Sciences Journal. 2013;58(2):408-20.
31.                Mohsenpour R, Zibaei M. Determination of optimal crop patterns using nonlinear programming and deficit Irrigation strategies under Dorodzan Dam. Agricultural Economics and Development 2010;18(71):1-23. [Persian]
Volume 4, Issue 2
June 2017
Pages 601-613
  • Receive Date: 22 November 2016
  • Revise Date: 27 February 2017
  • Accept Date: 15 March 2017
  • First Publish Date: 22 June 2017