In this paper, we propose a novel methodology to parse the argumentative structures. Firstly, the essays are of the type persuasive essays. They are divided into tokens. Here now we apply new model to detect the argumentative structures. Integer linear programming is used as the proposed model to optimize types of argument components and their argumentative relations. This model will increase the efficiency of the performance of base classifiers and also outperforms the heuristic baselines. Here the corpus is consisting of the persuasive essays having annotated schemes. The corpus is the open source and made available. © 2018 IEEE.