Elif Garajová, Milan Hladík, and Miroslav Rada. Weakly feasible and optimal solution sets in 0-1 interval linear programming. In Proceedings of the 18th International Symposium on Operational Research SOR'25, Bled, Slovenia, September 24-26, 2025, pp. 402–405, Slovenian Society INFORMATIKA, Ljubljana, Slovenia, 2025.
We consider an integer linear programming model with binary variables subject to interval uncertainty, where the data can vary independently within specified lower and upper bounds. Our focus is on the properties of weakly and strongly feasible solution sets, solutions feasible or optimal for at least one realization of the uncertain data. To this end, we formulate a general framework problem for checking whether there exists a scenario admitting prescribed weakly and forbidden feasible solutions. We also propose a mixed-integer model for solving the problem. Then, using this framework, we demonstrate how to characterize the set of all weakly optimal solutions in 0–1 interval linear programming.
@inProceedings{GarHla2025c,
author = "Elif Garajov\'{a} and Milan Hlad\'{\i}k and Miroslav Rada",
title = "Weakly feasible and optimal solution sets in 0-1 interval linear programming",
editor = "S. Drobne and others",
feditor = "S. Drobne and L. Zadnik Stirn and M. Kljajić Borštnar and J. Povh and J. Žerovnik",
booktitle = "Proceedings of the 18th International Symposium on Operational Research SOR'25, Bled, Slovenia, September 24-26, 2025",
publisher = "Slovenian Society INFORMATIKA",
address = "Ljubljana, Slovenia",
pages = "402-405",
year = "2025",
isbn = "978-961-6165-64-8",
url = "https://www.drustvo-informatika.si/sekcije-drustva?stran=publikacije-sor",
bib2html_dl_pdf = "https://drustvo-informatika.si/uploads/documents/d61da7b6-eb3d-4b27-bed5-3c93190ac3de//SOR25Proceeding.pdf",
abstract = "We consider an integer linear programming model with binary variables subject to interval uncertainty, where the data can vary independently within specified lower and upper bounds. Our focus is on the properties of weakly and strongly feasible solution sets, solutions feasible or optimal for at least one realization of the uncertain data. To this end, we formulate a general framework problem for checking whether there exists a scenario admitting prescribed weakly and forbidden feasible solutions. We also propose a mixed-integer model for solving the problem. Then, using this framework, we demonstrate how to characterize the set of all weakly optimal solutions in 0–1 interval linear programming.",
keywords = "Integer programming; interval uncertainty; optimal set",
}
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