Two-Stage Stochastic Chance-Constrained Fractional Programming Model for Optimal Agricultural Cultivation Scale in an Arid Area

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.