Unfortunately, the tableau method is often the only method mentioned in classes or texts covering the Simplex Method. Some examples of solving linear programming problems with the tableau method are given here and here. Upon taking classes in operations research or optimization (particularly at the undergraduate level) and reviewing the resources available online that cover the Simplex Method, one will almost certainly be introduced to the tableau method for solving linear programming problems with the Simplex method.
Prediction simplexlp series#
This is hardly a satisfactory description of the Simplex Method, so if the reader wants a more insightful intuition into the method, I recommend visiting this article, or watching the first two short videos on the Simplex Method video series by PatrickJMT, which give a good introduction into the kinds of problems the Method solves and how it works. The Simplex Method starts at some point within the feasible region, and then with each iteration of the algorithm maps from one adjacent corner (representing a possible solution to the problem) of the convex polytope to another, such that each step gives a better or equivalent solution than the one in the previous step. It is with this insight that we can motivate the development of the Simplex Method.
I give a complete reference list of linear programming books at the end of this post.Īs seen in the image, the constraints are linear, so the convex polytope has flat edges, and the feasible region is the interior and boundary of the polytope.Ī key insight is that the optimal solution to any constrained linear optimization problem is always on one of the corners of the convex polytope. The book Linear Programming and Network Flows by Bazaraa, Jarvis, and Sherali is also a great in-depth resource that touches upon many of the ideas mentioned in this post. I avoid the mathematics of the particular matrix operations implementation to keep this post concise, however if the reader wishes to learn more about the mathematics of this particular implementation, they can refer to the book Linear and Nonlinear Programming by Stephen Nash and Ariela Sofer, which gives a great introduction into the Simplex Method and the many ways to implement it. In particular, most computational implementations of the Simplex Method are developed by directly implementing the Simplex tableau method.Īs such, in this post I seek to give an alternative implementation of the Simplex Method by developing a program of the Simplex Method that leverages matrix operations instead of the tableau method. In this post, I seek to address the paucity of resources describing and implementing the Simplex Method from a matrix operations perspective.
Prediction simplexlp code#
The code associated with this post can be found in the Gist linked here.
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