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Inside the Box: 0–1 Linear Programming Under Interval Uncertainty

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Numerical Computations: Theory and Algorithms (NUMTA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14476))

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Abstract

Many practical optimization problems require models that are able to reflect uncertainty or inexactness inherently present in the data. Interval linear programming provides a model for handling uncertain optimization problems, in which one assumes that only lower and upper bounds on the input data are available and the data can be independently perturbed within the intervals determined by the given bounds. Apart from the linear programming models with continuous variables, which have been explored by various authors, intervals also often arise in discrete optimization problems.

We adopt the model of integer linear programming with binary variables, in which the constraint matrix, objective vector and right-hand-side vector are affected by interval uncertainty. For this model, only a few works investigating its properties can be found in the literature. In this paper, we discuss the main concepts of feasibility and optimality in the model and discuss their properties. Namely, we address the problem of computing the set and the range of optimal values and characterizing weak optimality of solutions.

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Acknowledgements

The authors were supported by the Czech Science Foundation under Grant P403-22-11117S. The work of the first author was also supported by the grant SVV-2023–260699.

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Authors and Affiliations

  1. Charles University, Faculty of Mathematics and Physics, Department of Applied Mathematics, Malostranské nám. 2/25, 118 00, Prague, Czech Republic

    Elif Garajová & Milan Hladík

  2. Prague University of Economics and Business, Faculty of Informatics and Statistics, Department of Econometrics, nám. W. Churchilla 1938/4, 130 67, Prague, Czech Republic

    Elif Garajová & Milan Hladík

Authors
  1. Elif Garajová
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  2. Milan Hladík
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Correspondence to Elif Garajová .

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Editors and Affiliations

  1. University of Calabria, Rende, Italy

    Yaroslav D. Sergeyev

  2. University of Calabria, Rende, Italy

    Dmitri E. Kvasov

  3. University of Calabria, Rende, Italy

    Annabella Astorino

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Garajová, E., Hladík, M. (2025). Inside the Box: 0–1 Linear Programming Under Interval Uncertainty. In: Sergeyev, Y.D., Kvasov, D.E., Astorino, A. (eds) Numerical Computations: Theory and Algorithms. NUMTA 2023. Lecture Notes in Computer Science, vol 14476. Springer, Cham. https://doi.org/10.1007/978-3-031-81241-5_24

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  • DOI: https://doi.org/10.1007/978-3-031-81241-5_24

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