Solving Cropping Pattern Optimization Problems Using Robust Positive Mathematical Programming

Agricultural activities occur in an environment that is constantly changing. In each cropping season, farmers must make management decisions based on numerous factors, some of which are beyond their control and others which are not. The use of mathematical programming models in determining optimal decisions for farmers, predicting the outcomes of policy effects, and the occurrence of uncontrollable factors in the agriculture sector is beneficial. It can provide planners and farmers with appropriate awareness and understanding of the effects of each decision related to resource allocation and cropping patterns before implementing that decision. One of the problems with some cropping pattern models is the consideration of resource amounts as fixed and certain, neglecting the issue of uncertainty. This results in a significant difference between the estimated model and the behavior of the farmers. In this context, the formulation of a mathematical programming model aligned with the real world and considering its uncertainties is highly important. This chapter aims to present an appropriate mathematical programming model for decision-making in determining cropping patterns and optimal resource allocation. This model should be able to model the uncertainties of the real world in the agriculture sector in the best possible way and provide more desirable and practical results. Therefore, while discussing the generalities related to the features and application of mathematical programming models and their types, the chapter elaborates on the basic and extended models of policy analysis using Positive Mathematical Programming (PMP) and the Robust Optimization (RO) approach. Subsequently, the method and a practical example of the combined model of Robust Positive Mathematical Programming (RPMP) in solving cropping pattern optimization problems is explained.