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Maximal and supremal tolerances in multiobjective linear programming
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DOI：10.1016/j.ejor.2013.01.045.png)
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Let a multiobjective linear programming problem and any efficient solution be given. Tolerance analysis aims to compute interval tolerances for (possibly all) objective function coefficients such that the efficient solution remains efficient for any perturbation of the coefficients within the computed intervals. The known methods either yield tolerances that are not the maximal possible ones, or they consider perturbations of weights of the weighted sum scalarization only. We focus directly on perturbations of the objective function coefficients, which makes the approach independent on a scalarization technique used. In this paper, we propose a method for calculating the supremal tolerance (the maximal one need not exist). The main disadvantage of the method is the exponential running time in the worst case. Nevertheless, we show that the problem of determining the maximal/supremal tolerance is NP-hard, so an efficient (polynomial time) procedure is not likely to exist. We illustrate our approach on examples and present an application in transportation problems. Since the maximal tolerance may be small, we extend the notion to individual lower and upper tolerances for each objective function coefficient. An algorithm for computing maximal individual tolerances is proposed. (C) 2013 Elsevier B.V. All rights reserved.
Keyword:
Multiobjective linear programming
Efficient solution
Sensitivity analysis
Tolerance analysis
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6
论文数:
2.2W
被引数:
6.4W
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Multiple objective linear programming models with interval coefficients - an illustrated overview具有区间系数的多目标线性规划模型-图解概述
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