Introduction

The primal simplex algorithm is one of the best methods for solving linear programming problems. To solve linear models, CPLEX or GAMS software has been implemented. But to solve linear programming models with these softwares, they must be installed on the client and for large models, a valid license must be available. In order to make solving linear programming models simple, the optimization city group has designed and developed an online solver for solving linear programming problems. In the following, we will review how to use this online solver.

Instruction of using online solver of linear program with Primal Simplex Method

The GUI of the online solver of the Primal Simplex method is as follows.

Problem input

To find the optimal solution of the linear programming problem using the basic simplex method, the required inputs are as follows:

n: number of decision variables

m: number of constraints

esp: maximum acceptable error in calculations

a: This matrix has m+1 rows and n+1 columns. a[i,j] for i=1,…,m and j=1,…,n for coefficients of constraints, a[0,j] for j=1,…,n corresponding to coefficients of variables in the objective function, and a[i,0] stores the values on the right side of the constraint.

Note: the components of matrix a can be continuous numbers.

Note: the desired model should be in standard form (each limit is a basic variable) and the values on the right side should be non-negative.

Example: To teach how to use this solver, we use the following example. A linear programming model with seven variables and three constraints is defined as follows.

Solution: The input information for the given model is as follows.

Entering information in the online solver for the linear program with primal simplex method is as follows.

After entering the data, we click on the RUN button.

The result of running the algorithm is as follows.

In the output, the phrase Optimal solution found means that the model has a limited optimal solution.

In the output, it reports only the values of the basic variables and the rest of the variables are equal to zero. In this example, the optimal value of the variables are:

In the last part of the output, the value of the optimal objective function is reported, which is equal to 10 in this example.