Agricultural production planning approach based on interval fuzzy credibility-constrained bi-level programming and Nerlove supply response theory

Abstract

Abstract: When planning agricultural production, planting area and water allocation are two major subjects faced by decision makers. In this study, a framework integrated Nerlove supply response model (Nerlove model) and interval fuzzy credibility-constraint bi-level programming (IFCBP) model is developed for planning the agricultural production in arid and semi-arid regions. Through Nerlove model, the planning process of crop planting area was described as an economic problem for forecasting farmers' behavior rather than an optimization problem for allocating farmland resources, and the relationship between crop planting area and market price can be obtained and further provide credible future crop planting area information. The IFCBP model can not only deal with uncertainties presented as interval and fuzzy numbers but also examine the credibility of the constraints and handle tradeoffs between two-level decision makers. To solve the IFCBP model, a solution method based on the interval interactive algorithm and credibility-cut method is proposed. Then, to verify the validity of the developed framework and solving method for agricultural production planning, they were applied to a real-case in the middle reaches of the Heihe River basin, northwest China. The forecasting results obtained from Nerlove model have better performance in predicting the future planting area of corn and vegetable than wheat, indicating that wheat plays a more vulnerable role in the decision-making process of planting area owing to its higher substitutability. The results show that the proposed framework can tackle two-level decision makers’ concerns under uncertainties featured as inexact and fuzzy numbers, which can help regional managers plan future resources effectively. Furthermore, a comparison was made between IFCBP and two corresponding single-level models in this study. The comparison indicates that the developed model provides an effective tradeoff between two decision makers from different decision-making levels in IFCBP. The developed framework provides managers an effective way to plan agricultural production in arid and semi-arid regions, and the developed model and related thinking may help solve similar problems.