Cropping-Plan Optimization on Agricultural Holdings with a Combination of Linear and Weighted-goal Programming

Abstract

Abstract.We present a crop plan that aims to maximize farmers’ returns and minimize production costs for the analyzed agricultural holding. This study describes a model that combines linear programming (LP) and the weighted goal programming (WGP) method with penalty functions to simultaneously satisfy a variety of goals within the tolerance interval bounds in terms of their weights. The results indicate that, from an economic perspective, WGP sub-model including LP gives a better solution than using the LP sub-model separately. We designed the model to handle five different types of field and vegetable crops during crop planning and was tested for WGP optimization [WGPSC1, WGPSC2, WGPSC3, and WGPSC4 (SC4 for testing model parameterization)) on four different scenarios. For example, the farmers’ returns in the WGP scenarios were higher or equal as in LP scenario (by approx. €100 to €110) while the costs were reduced (from €2.58 in the case of mechanical labor costs and to €1,376.66 for fertilizer costs). In addition, the combination of both serves as a more viable option for diversified and economically optimized crops to be included in crop plans. It is also important that the WGP calculated higher farmer returns, even though it was run on a cropping area that was 0.02 ha smaller than that in the LP. Further, the model was tested with a parameterization process to determine and explain the role of weights and penalty functions on the quality of the model results. Keywords: Agricultural application, Agricultural economics, Farmer’s return, Mathematical modelling.