Two-Stage Stochastic Chance-Constrained Fractional Programming Model for Optimal Agricultural Cultivation Scale in an Arid Area
Publication: Journal of Irrigation and Drainage Engineering
Volume 143, Issue 9
Abstract
In the agricultural irrigation system, agricultural water availability and demand are significantly affected by seasonal variations. Additionally, agricultural land use in arid regions largely depends on water availability rather than on arable land resources only. Thus, in this study, a two-stage stochastic chance-constrained fractional programming (TSCFP) model is developed to address the agricultural cultivation–scale problem under uncertainty. In the developed model, techniques of chance-constrained programming (CCP) and two-stage stochastic programming (TSP) are jointly incorporated into the linear fractional programming (LFP) optimization framework. The model balances the conflicting objectives of two aspects by transforming the problem into a ratio-based problem that reflects land-use efficiency and also analyzes the trade-offs among efficiency, constraint violations, and policy scenarios. The model is applied to determine the agricultural cultivation scale of Linze County in Gansu Province of northwest China, where managers must consider the conflicting objectives of economic benefit and irrigated crop area under stochastic inputs. By providing four scenarios of preregulated irrigation targets, optimal solutions are obtained. The appropriate agricultural cultivation scale in Linze County for the current circumstances are 10,961, 13,171, 15,490, and 16,855 ha under four scenarios. Therefore, the results offer decision support for decision makers to obtain the optimal agricultural cultivation scale under different predetermined irrigation targets and different probabilities of violation.
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Acknowledgments
This research was supported by the National Natural Science Foundation of China (Nos. 51439006 and 91425302), the Governmental Public Research Funds for Projects of Ministry of Water Resources (No. 201501017). The authors are grateful to the editors and the anonymous reviewers for their insightful comments and suggestions.
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Published In
Journal of Irrigation and Drainage Engineering
Volume 143 • Issue 9 • September 2017
Copyright
©2017 American Society of Civil Engineers.
History
Received: Jul 5, 2016
Accepted: Mar 21, 2017
Published online: Jul 12, 2017
Published in print: Sep 1, 2017
Discussion open until: Dec 12, 2017
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