The **Simplex Method** was developed by George Dantzing in 1947. It is without a doubt the most popular algorithm when it comes to solving a **Linear Programming** (LP) model, and it plays a major role in the introduction to Operations Research (OR).

Today we’re presenting a summary of 10 main concepts about the use and application of the **Simplex Method** for our users to be able to have a first approach to the method, while paying attention to some characteristic aspects:

**Simplex Method (10 Things You need to know)**

**History:**In 1947 it was first published by George Dantzing, an American mathematician.**Standard Form:**The Simplex Method’s application requires the Linear Programming model to be on its standard form.**Basic Feasible Solution (BFS):**A basic feasible solution matches a vertices in domain of a Linear Programming model’s feasible solutions.**Optimality Criterion:**The Basic feasible solution is optimal if and only if the reduced costs of all the nonbasic variables are higher or equal to zero.**Infinite Solutions:**This case is seen when there are reduced costs equal to zero in one or more optimal nonbasic variables.**Unbounded Problem:**This case is seen when, while doing the calculus of the variable which leaves the base, all the elements ykj of the column j in the tableau are negative.**Infeasible Problem:**This is the case when the optimal value of the problem in Phase 1 (in a Two Phase Simplex Method) is nonzero.**Rate of Convergence:**If two or more nonbasic variables have negative reduced cost, the entrance to the base goes to the lowest reduced cost.**Postoptimal Analysis:**Once we achieve the optimal solution through the Simplex Method, we can analyze the impact in the results with the alteration of the parameters.**Excel Solver:**The Excel complementallows us to use the Simplex Method as a solving method (Simplex LP)**Solver**

This review is based on the experience we have teaching Operations Research and on the most frequent questions we receive daily from undergraduate students.

**You can download the infographic as a PDF file here:** **Simplex Method**

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