Advantages of combining linear programming and weighted goal programming for agriculture application

Abstract

The aim of this paper is to present the basic characteristics of linear programing (LP) and weighted goal programming (WGP) to optimize processes on farms. Characteristics of both mathematical techniques are presented through the development of the crop planning model for solving some objective problems: maximizing financial results and minimizing different production costs on agricultural holdings. The model is structured from two sub-models, where the first based on linear programming and the second based on weighted goal programming are supported with penalty functions. The authors dispatch the weaknesses of LP with the application of WGP in the model and support this statement with results in this paper. The model was tested and validated on crop rotation with combinations of different field and vegetable crops in two different scenarios (WGPSC1 and WGPSC2) on a real agricultural holding in Slovenia. The results show that WGP combines more suitable crop rotation from an economic perspective than LP and provides a better solution for diversified and economically feasible crops that are included in the crop rotation. LP gives completely unacceptable results from the aspect of underachievement (for more than 100 %) of the maximum cropping area on a farm, while WGP completely satisfies all goals. From the obtained results in this paper, the authors identify several weaknesses of LP and present how it could be removed by applying the WGP technique.