Elif Garajová, Miroslav Rada, and Milan Hladík. Outcome range problem in interval linear programming: An exact approach. In V.-N. Huynh et al., editor, Integrated Uncertainty in Knowledge Modelling and Decision Making, LNAI, pp. 3–14, Springer, Cham, 2020.
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Interval programming provides a mathematical model for uncertain optimization problems, in which the input data can be perturbed independently within the given lower and upper bounds. This paper discusses the recently proposed outcome range problem in the context of interval linear programming. The motivation for the outcome range problem is to assess further impacts and consequences of optimal decision making, modeled in the program by an additional linear outcome function. Specifically, the goal is to compute a lower and an upper bound on the value of the given outcome function over the optimal solution set of the interval program. In this paper, we focus mainly on programs with interval coefficients in the objective function and the right-hand-side vector. For this special class of interval programs, we design an algorithm for computing the outcome range exactly, based on complementary slackness and guided basis enumeration. Finally, we perform a series of computational experiments to evaluate the performance of the proposed method.
@inCollection{GarRad2020a,
author = "Elif Garajov\'{a} and Miroslav Rada and Milan Hlad\'{\i}k",
title = "Outcome range problem in interval linear programming: An exact approach",
editor = "Huynh et al., V.-N.",
feditor = "Huynh, Van-Nam and Entani, Tomoe and Jeenanunta, Chawalit and Inuiguchi, Masahiro and Yenradee, Pisal",
booktitle = "Integrated Uncertainty in Knowledge Modelling and Decision Making",
publisher = "Springer",
address = "Cham",
series = "LNAI",
fseries = "Lecture Notes in Artificial Intelligence",
volume = "12482",
pages = "3-14",
year = "2020",
doi = "10.1007/978-3-030-62509-2_1",
isbn = "978-3-030-62509-2",
issn = "0302-9743",
url = "https://doi.org/10.1007/978-3-030-62509-2_1",
bib2html_dl_html = "https://link.springer.com/chapter/10.1007/978-3-030-62509-2_1",
abstract = "Interval programming provides a mathematical model for uncertain optimization problems, in which the input data can be perturbed independently within the given lower and upper bounds. This paper discusses the recently proposed outcome range problem in the context of interval linear programming. The motivation for the outcome range problem is to assess further impacts and consequences of optimal decision making, modeled in the program by an additional linear outcome function. Specifically, the goal is to compute a lower and an upper bound on the value of the given outcome function over the optimal solution set of the interval program. In this paper, we focus mainly on programs with interval coefficients in the objective function and the right-hand-side vector. For this special class of interval programs, we design an algorithm for computing the outcome range exactly, based on complementary slackness and guided basis enumeration. Finally, we perform a series of computational experiments to evaluate the performance of the proposed method.",
keywords = "Interval linear programming; Outcome range problem; Optimal solution set",
}
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