بررسی روش سیمپلکس برای حل مُدل‌های برنامه¬ریزی خطی

Abstract

In the current era, the issue of production mix has not received sufficient attention in the objective functions of linear programming models within operations research. This oversight has often led to increased costs and reduced efficiency in decision-making systems. However, by utilizing linear programming models, such additional costs can be avoided. One of the most effective methods for solving such models is the Simplex method, which is recognized as an advanced and widely used technique in operations research. This method is specifically designed to solve models with linear objective functions and linear constraints, and it is particularly applicable to problems involving more than two decision variables—unlike simpler approaches such as the graphical method, which is limited to two-variable cases. The aim of this study is to introduce and comprehensively examine the Simplex method among other optimization techniques, with the goal of reducing unnecessary expenditures and enhancing the effectiveness of decision-making processes. This research has been conducted through a library-based approach and relies on reputable academic sources. The findings of the study indicate that the Simplex method is one of the key tools in analyzing and presenting information across various scientific fields, with a strong capability to simplify complex concepts and render them comprehensible to a wide audience. As a result, this method is introduced in full detail for solving linear programming models in operations research, aiming to minimize losses and maximize gains in everyday activities.