Computing the tolerances in multiobjective linear programming

Authors:
M. Hladik
Affiliations:
Department of Applied Mathematics, Charles University, Prague, Czech Republic
Venue:
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
Year:
2008

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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.