Parametric programming

From a mathematical point of view, parametric programming acts as one of the means of analyzing the sensitivity of a solution to variations in the source data, and assessing the stability of a solution.

Algorithm for solving parametric linear programming problems

The algorithm for solving parametric linear programming problems in the case of dependence on the parameter of the coefficients of the objective function is slightly different from the usual simplex method (examples of solving such problems are given below).
The process of finding a solution to the problem includes the following steps:
Assuming the value of the parameter λ to be equal to a certain number, we find the optimal plan X * or establish the unsolvability of the obtained linear programming problem.
The set of λ parameter values ​​is determined, for which the optimal plan found is optimal or the problem is unsolvable. These parameter values ​​are excluded from consideration.
The value of the parameter λ is assumed to be equal to a certain number belonging to the remaining part of the interval [α, β], and the solution of the obtained linear programming problem is found.
The set of values ​​of the parameter λ is determined, for which the new optimal plan remains optimal or the problem is unsolvable. Calculations are repeated until all parameter values ​​are examined.