Rights statement: This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 265, 2, 2017 DOI: 10.1016/j.ejor.2017.08.013
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - On recoverable and two-stage robust selection problems with budgeted uncertainty
AU - Chassein, André
AU - Goerigk, Marc
AU - Kasperski, Adam
AU - Zielinski, Pawel
N1 - This is the author’s version of a work that was accepted for publication in European Journal of Operational Research. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Operational Research, 265, 2, 2017 DOI: 10.1016/j.ejor.2017.08.013
PY - 2018/3/1
Y1 - 2018/3/1
N2 - In this paper the problem of selecting p out of n available items is discussed, such that their total cost is minimized. We assume that the item costs are not known exactly, but stem from a set of possible outcomes modeled through budgeted uncertainty sets, i.e., the interval uncertainty sets with an additional linear (budget) constraint, in their discrete and continuous variants. Robust recoverable and two-stage models of this selection problem are analyzed through an in-depth discussion of variables at their optimal values. Polynomial algorithms for both models under continuous budgeted uncertainty are proposed. In the case of discrete budgeted uncertainty, compact mixed integer formulations are constructed and some approximation algorithms are proposed. Polynomial combinatorial algorithms for the adversarial and incremental problems (the special cases of the considered robust models) under both discrete and continuous budgeted uncertainty are constructed.
AB - In this paper the problem of selecting p out of n available items is discussed, such that their total cost is minimized. We assume that the item costs are not known exactly, but stem from a set of possible outcomes modeled through budgeted uncertainty sets, i.e., the interval uncertainty sets with an additional linear (budget) constraint, in their discrete and continuous variants. Robust recoverable and two-stage models of this selection problem are analyzed through an in-depth discussion of variables at their optimal values. Polynomial algorithms for both models under continuous budgeted uncertainty are proposed. In the case of discrete budgeted uncertainty, compact mixed integer formulations are constructed and some approximation algorithms are proposed. Polynomial combinatorial algorithms for the adversarial and incremental problems (the special cases of the considered robust models) under both discrete and continuous budgeted uncertainty are constructed.
KW - combinatorial optimization
KW - robust optimization
KW - selection problem
KW - budgeted uncertainty
KW - two-stage robustness
KW - recoverable robustness
U2 - 10.1016/j.ejor.2017.08.013
DO - 10.1016/j.ejor.2017.08.013
M3 - Journal article
VL - 265
SP - 423
EP - 436
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 2
ER -