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@PHDTHESIS{Gersing:986555,
      author       = {Gersing, Timo},
      othercontributors = {Büsing, Christina Maria Katharina and Koster, Arie Marinus
                          and Pferschy, Ulrich},
      title        = {{A}lgorithms for robust combinatorial optimization with
                      budgeted uncertainty and fair planning of the out-of-hours
                      service for pharmacies},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Aachen},
      publisher    = {RWTH Aachen University},
      reportid     = {RWTH-2024-05270},
      pages        = {1 Online-Ressource : Illustrationen},
      year         = {2024},
      note         = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
                      University; Dissertation, RWTH Aachen University, 2024},
      abstract     = {Practical problems usually require robust or fair
                      solutions. However, optimal solutions for classical
                      optimization problems tend to structurally neglect these two
                      criteria. This is due to the promotion of extreme decisions
                      that exhaust the planning constraints and most profitable
                      options as far as possible. Robustness, though, is usually
                      achieved by spreading risks, and fairness by distributing
                      benefits and burdens, which requires diverse solutions
                      rather than extreme ones. Accordingly, both criteria often
                      have to be explicitly integrated into optimization problems.
                      This poses a challenge both from a modeling and an
                      algorithmic point of view. In this thesis, we want to
                      contribute to overcoming this challenge by studying the
                      following problems. In the first part of this thesis, we
                      consider robust optimization with budgeted uncertainty,
                      which is one of the most popular approaches for addressing
                      uncertainty in optimization problems. Positive complexity
                      results as well as the existence of a compact reformulation
                      for (mixed-integer) linear programs suggest that these
                      problems are easy to solve. However, the reformulation as
                      well as the algorithms that provide these complexity results
                      do not perform well when solving robust combinatorial
                      problems in practice. To address this, we propose a new
                      class of valid inequalities to strengthen the reformulation.
                      These inequalities are facet-defining in many cases, and are
                      thus among the theoretically strongest inequalities.
                      Furthermore, we develop a branch-and-bound algorithm based
                      on new formulations and structural results. We show in two
                      extensive computational studies that both approaches
                      facilitate the computation of optimal robust solutions.
                      Especially the branch and bound algorithm outperforms all
                      previous approaches by far. In the second part, we consider
                      the problem of planning the out-of-hours service for
                      pharmacies, which ensures a continuous supply of
                      pharmaceuticals. The problem consists in assigning 24-hour
                      shifts to a subset of pharmacies on each day such that an
                      appropriate supply is guaranteed while the burden on
                      pharmacists is minimized. We present a model for the
                      planning, developed in collaboration with the Chamber of
                      Pharmacists North Rhine, and show that computing a feasible
                      plan is NP-hard. We develop algorithms that nevertheless
                      compute almost optimal plans for the North Rhine area in
                      short time. The computed plans assign fewer shifts in total
                      compared to the real plan of the Chamber of Pharmacists
                      North Rhine, but they exhibit an unfair concentration of
                      shifts. Consequently, we discuss strategies to integrate
                      fairness into the planning. We show theoretical results on
                      fairness in optimization problems, on the basis of which we
                      compute out-of-hours plans that are almost maximally fair.},
      cin          = {125620 / 120000},
      ddc          = {004},
      cid          = {$I:(DE-82)125620_20210528$ / $I:(DE-82)120000_20140620$},
      pnm          = {BMBF 05M16PAA - Verbundprojekt 05M2016 - HealthFaCT:
                      Optimierung der ambulanten medizinischen Versorgung im
                      ländlichen Raum - Teilprojekt 3 (BMBF-05M16PAA)},
      pid          = {G:(BMBF)BMBF-05M16PAA},
      typ          = {PUB:(DE-HGF)11},
      doi          = {10.18154/RWTH-2024-05270},
      url          = {https://publications.rwth-aachen.de/record/986555},
}