Computing the tolerances in multiobjective linear programming

Abstract

We consider a multiobjective linear program and the coefficients of the multiobjective function are supposed to be uncertain. Let x* be an efficient point. We propose a procedure computing a tolerance for each objective function coefficient, such that all these coefficients may simultaneously and independently vary within their tolerances while preserving the efficiency of x*. If x* is a non-degenerate basic solution, then the procedure runs in a polynomial time. Our method is also applicable for the intervals of multiobjective linear programming for checking the necessary efficiency of x*, i.e. whether x* is efficient for all the realizations of interval values.

Keywords:

• multiobjective linear programming
• interval matrix
• efficient point
• sensitivity analysis
• tolerance analysis

AMS Subject Classification :

• 90C29
• 90C31

Additional information

Notes on contributors

M. Hladík

*Email: [email protected]