Elif Garajová, Milan Hladík, and Miroslav Rada. Interval transportation problem: The best and the worst (feasible) scenario. In 38th International Conference on Mathematical Methods in Economics 2020 (MME 2020). Conference Proceedings, pp. 122–127, Mendel University in Brno, 2020.
Interval programming presents a powerful mathematical tool for modeling optimization problems affected by uncertainty. We consider an interval linear programming model for the transportation problem with uncertain supply and demand varying within a priori known bounds. We address the problem of computing the optimal value range of an interval transportation problem, i.e. finding the best and the worst possible optimal value, and describing the corresponding scenarios of the problem. Since the worst-case scenario in the traditional sense is often infeasible, thus leading to an infinite bound of the optimal value range, we consider the worst finite optimal value of the problem. We propose a decomposition method based on complementarity for computing the worst finite optimal value exactly. We also study the corresponding best and worst extremal scenarios for which the bounds of the finite optimal value range are attained. Moreover, we derive a description of the structure of the linear program corresponding to the best scenario.
@InProceedings{GarHla2020a,
author = "Elif Garajov\'{a} and Milan Hlad\'{\i}k and Miroslav Rada",
title = "Interval transportation problem: {The} best and the worst (feasible) scenario",
editor = "Svatopluk Kapounek and Hana Vr\'{a}nov\'{a}",
booktitle = "38th International Conference on Mathematical Methods in Economics 2020 (MME 2020). Conference Proceedings",
pages = "122-127",
year = "2020",
publisher = "Mendel University in Brno",
isbn = "978-80-7509-734-7",
url = "https://mme2020.mendelu.cz/wcd/w-rek-mme/mme2020_conference_proceedings_final.pdf",
bib2html_dl_pdf = "https://mme2020.mendelu.cz/wcd/w-rek-mme/mme2020_conference_proceedings_final.pdf",
abstract = "Interval programming presents a powerful mathematical tool for modeling optimization problems affected by uncertainty. We consider an interval linear programming model for the transportation problem with uncertain supply and demand varying within a priori known bounds. We address the problem of computing the optimal value range of an interval transportation problem, i.e. finding the best and the worst possible optimal value, and describing the corresponding scenarios of the problem. Since the worst-case scenario in the traditional sense is often infeasible, thus leading to an infinite bound of the optimal value range, we consider the worst finite optimal value of the problem. We propose a decomposition method based on complementarity for computing the worst finite optimal value exactly. We also study the corresponding best and worst extremal scenarios for which the bounds of the finite optimal value range are attained. Moreover, we derive a description of the structure of the linear program corresponding to the best scenario.",
keywords = "Transportation problem; Interval linear programming; Optimal value range",
}
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