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Consider a deterministic combinatorial optimization problem \(\mathcal{P}\), which is of the form (1.1). An alternative method of defining scenario set Γ in this problem is applying a discrete scenario representation of uncertainty. In this approach we explicitly list all scenarios, that is we define
If K = 1, then there is only one scenario and the problem boils down to the deterministic problem \(\mathcal{P}\). The maximal regret of a given solution X ∈ Φ is defined in the following way:
Let D-Minmax Regret \(\mathcal{P}\) denote the problem in which we seek a solution that minimizes the maximal regret. The letter ”D” indicates that we deal with the discrete scenario representation of uncertainty. We distinguish two important cases of this problem. In the first case the number of scenarios K is bounded by a constant, for instance we may consider only problems with 2 scenarios. In the second case the number of scenarios is unbounded and K is a part of the input.
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© 2008 Springer-Verlag Berlin Heidelberg
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Kasperski, A. (2008). Discrete Scenario Representation of Uncertainty. In: Discrete Optimization with Interval Data. Studies in Fuzziness and Soft Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78484-5_17
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DOI: https://doi.org/10.1007/978-3-540-78484-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78483-8
Online ISBN: 978-3-540-78484-5
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