Abstract
Crop planting structure optimization is a significant way to increase agricultural economic benefits and improve agricultural water management. The complexities of fluctuating stream conditions, varying economic profits, and uncertainties and errors in estimated modeling parameters, as well as the complexities among economic, social, natural resources and environmental aspects, have led to the necessity of developing optimization models for crop planting structure which consider uncertainty and multi-objectives elements. In this study, three single-objective programming models under uncertainty for crop planting structure optimization were developed, including an interval linear programming model, an inexact fuzzy chance-constrained programming (IFCCP) model and an inexact fuzzy linear programming (IFLP) model. Each of the three models takes grayness into account. Moreover, the IFCCP model considers fuzzy uncertainty of parameters/variables and stochastic characteristics of constraints, while the IFLP model takes into account the fuzzy uncertainty of both constraints and objective functions. To satisfy the sustainable development of crop planting structure planning, a fuzzy-optimizationtheory-based fuzzy linear multi-objective programming model was developed, which is capable of reflecting both uncertainties and multi-objective. In addition, a multiobjective fractional programming model for crop structure optimization was also developed to quantitatively express the multi-objective in one optimization model with the numerator representing maximum economic benefits and the denominator representing minimum crop planting area allocation. These models better reflect actual situations, considering the uncertainties and multi-objectives of crop planting structure optimization systems. The five models developed were then applied to a real case study in Minqin County, north-west China. The advantages, the applicable conditions and the solution methods of each model are expounded. Detailed analysis of results of each model and their comparisons demonstrate the feasibility and applicability of the models developed, therefore decision makers can choose the appropriate model when making decisions.
Highlights
Crop planting structure optimization is important for both irrigation water management and agricultural management[1], and is increasingly significant in agricultural water management
This paper reports the development of five models for crop planting structure optimization to express multiple objectives and uncertainties from different perspectives, including three single-objective and two multi-objective programming models
Fuzzy linear programming (FLP) blurs the constraints and objective function of Linear programming (LP) to deal with fuzzy uncertainties[15]
Summary
Crop planting structure optimization is important for both irrigation water management and agricultural management[1], and is increasingly significant in agricultural water management. Linear programming (LP) has been a widely used optimization method, but the parameters, constraints and objectives of most LP models for crop planting structure are deterministic. Mo LI et al Crop planting structure optimization under uncertainty interrelationships, constraints and objectives, e.g., the spatial and temporal variations of stream conditions and irrigation quota, the fluctuations of system benefit coefficients, the grayness of system objective and constrains, and the errors in estimated modeling parameters[9]. Crop planting structure optimization involves more than one kind of uncertainty factor, since it involves a complex system with the interaction of multiple uncertainties, e.g., fuzziness and grayness, fuzziness and randomness. This paper reports the development of five models for crop planting structure optimization to express multiple objectives and uncertainties from different perspectives, including three single-objective and two multi-objective programming models. Decision makers can choose the appropriate models based on actual situations, which will help to optimize crop planting structure more effectively in the wake of uncertainty
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