Linear programming
The mathematical model of linear programming has three elements: a number of linear constraint conditions related to the independent variable; the value limit of the independent variable; the linear objective function value of the independent variable. Its general form is
1. Simplex method
Its basic idea is to convert a basic feasible solution in the feasible domain to a new feasible solution, while improving the value of the objective function. When using the simplex method to solve the linear programming, the general form should be transformed into the standard form before solving, that is, by introducing artificial variables, the inequality constraints are transformed into equality constraints.
2. Modified simplex method
In the simplex algorithm, a base variable matrix B is involved, and the inverse of the matrix needs to be calculated at each step, and the calculation of the inverse matrix takes a lot of time. The modified simplex method obtains the inverse of the new matrix B by performing row transformation on the inverse of the old matrix B. Therefore, it is only necessary to calculate the inverse of matrix B at the beginning of the iteration, and then the inverse can be obtained through row transformation. Shorten the solution time.
3. Big M method
The process of solving linear programming is the same as the simplex method. The difference is the general form of linear programming. It processes linear programming into the following form
4. Variable bounded simplex method
Because the actual linear programming problem takes the value of the independent variable within a certain interval, its general form is
