Optimization of Rice (Oryza sativa) Crop in Simalungun District using Quadratic Programming Wolfe Model and Exterior Penalty Function Method

Abstract

Optimization is a way of optimizing the objective function while still paying attention to existing constraints. The aim of this research is to form a mathematical model to optimize the average production of lowland and field rice in Simalungun Regency and to complete the model using Wolfe model quadratic programming and the exterior penalty function method. The mathematical model in this research is a nonlinear model created using the least squares method. Quadratic programming solves nonlinear problems by turning them into linear problems using the Kuhn Tucker condition and linear problems are solved using the Wolfe model. Meanwhile, the exterior penalty function method solves limited (constrained) nonlinear problems into unlimited (unconstrained) nonlinear problems. Based on the calculations of the two methods, optimal results were obtained for both the Wolfe quadratic programming model and the exterior penalty function method, where the average production of wetland and field rice in Simalungun Regency was 203.1925 tonnes with a wetland rice harvest area of 90.077 hectares and a field rice harvest area of 13.092. hectare. Optimization testing using this algorithm can be used as a basis for related parties such as the community and government in developing productivity. The implication of this research is an increase in harvested area and average rice production, in this case maintaining productivity stability.