Two-phase SIMPLE algorithm for General Linear Programming Problems

5,2-phase simplication of General Linear Programming ProblemsAlgorithm 

The linear programming problem after artificial variables are introduced is not equivalent to the original problem, unless all Zi are 0.
To solve this problem, it must be solved in two phases.
In the first stage, an auxiliary target function is used to replace the original target function.
This linear programming problem is called the secondary Linear Programming Problem corresponding to the original linear programming problem.
Use a simple algorithm to solve the problem of auxiliary linear programming.
If the original linear planning problem has a feasible solution, the problem of secondary Linear Planning has an optimal solution, and its optimal value is 0, that is, all Zi are 0.
In the final form table of the problem of auxiliary linear planning, all Zi are non-basic variables.
Remove all corresponding columns of Zi, and the rest is the constrained standard linear programming problem with only XI and Yi.
The first phase of a simple algorithm is to construct an initial basic feasible solution.
The goal of the second stage is to solve the problem of exporting from the first stage.
In this case, use the original target function to solve the problem.
If Zi is not all 0 in the final form table of the problem of auxiliary linear planning, there is no feasible solution to the problem of the original linear planning, so there is no solution to the problem of the original linear planning.