There are many simplex method advantages and disadvantages that make the algorithm popular among linear programming experts. In most cases, the advantages outweigh the negatives, while at other times an adapted version is best. Still, the method has remained the most well used linear programming method for half a century and is still used to solve problems with practical interest in the real world.
Advantage: Easily Programmed on a Computer
The simplex method is popular for many reasons, including the ability to easily program the algorithm on a computer. Any function for the method can be quickly adapted in a software program as only the function evaluation needs to be altered. Although the method can be time consuming when done by hand, the ability to program it on calculators and computers makes it popular in advanced mathematics. In fact, in many courses the method is only used by hand when it is taught, after which a calculator is used to speed up problem solving.
Advantage: Easy to Use
The method is very easy to use, even though it can be difficult to notice mistakes. When compared to the graphical method, the simplex method has the advantage of allowing an individual to address problems with more than two decision variables. It also has an advantage over the least-squares method, which is also popular. Unlike the least-squares method, this algorithm does not require a derivative function and the orthogonality condition is not relevant. The simplex method is fairly easy to implement after the vocabulary is familiar.
Disadvantage: Limited Application
There are limited applications to the use of the simplex method to solve programming problems. When used for business purposes, it only applies in situations where a decimal quantity is appropriate. For example, a fifth of an apple doesn’t work. The simplex method is also only appropriate when a few variables are at play. In these instances, the method is very efficient. Unfortunately, many problems with a real-life practical interest have hundreds of variables.
Disadvantage: Difficult Requirements
The simplex method can only be used in certain linear programming problems, making it difficult to adapt. Only problems that can be expressed in a standard form with three conditions can be solved with the algorithm. One requirement is that the goal is to maximize the linear expression, and this condition is easy to meet. The constraints of the problem must also use non-negative constraints for all variables, and it must be expressed in the form =, where the number on the right side is positive.
Overall, there are many simplex method advantages and disadvantages that have made the method so popular over the past sixty years. The method is commonly taught in college courses because it is fairly straightforward and easy to learn and can be programmed into calculators easily. Linear programming experts appreciate the advantages it offers over other methods like the graphical method. Although it only works for specific problems in standard form, for these problems it is often the best method available.