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%0 Thesis
%A Schmitz, Sabrina
%T Two-stage robust combinatorial optimization problems with consistent decisions under discrete demand uncertainty and an application to appointment scheduling in primary health care
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2024-03455
%P 1 Online-Ressource : Illustrationen
%D 2024
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University
%Z Dissertation, RWTH Aachen University, 2024
%X In primary health care systems, primary care physicians (PCP) play a pivotal role as they are the initial point of contact for patients seeking medical care and they also coordinate ongoing access to medical care. However, these systems currently face challenges due to declining numbers of PCPs and increasing demand. To address this, the first part of this thesis aims at efficiently managing a PCP's demand for treatment through a tailored appointment scheduling. Using mathematical modeling of combinatorial optimization, we develop a robust appointment scheduling system that incorporates fluctuations in demand for treatment. Motivated by this and further applications, we study a two-stage robust optimization concept for combinatorial optimization problems under discrete demand uncertainty in the second part of the thesis. The contributions of this thesis can be divided into two main parts summarized in the following. In the first part, we study appointment scheduling systems based on so-called masks and focus on the balanced workload of the PCP in form of the mask design problem. Our study considers three different types of patients, including walk-ins who forgo scheduling an appointment and seek immediate care by walking into the practice without prior notice. To account for different uncertainties in demand for treatment, we extend the mask design problem to the robust mask design and the robust multimask design problem. For all three problems, we provide a combinatorial interpretation by a network flow and design model. We use a solution approach that combines binary search with compact formulations (of extensions) of minimum cost flow problems. Finally, we conduct an extensive case study by agent-based simulation, comparing the mask-based appointment scheduling systems with five appointment scheduling systems from the literature. In the second part, we introduce a two-stage robust concept for combinatorial optimization problems under discrete demand uncertainty. Combinatorial optimization problems are based on a finite set of elements for which we decide whether they are part of a solution. We divide the elements into two types, the so-called fixed and free elements. In a first stage, we irrecoverably decide whether some fixed elements are part of a solution despite uncertain demand. In a second stage, we decide whether some free elements complete a solution after a demand scenario is realized. The objective is to find a robust solution that minimizes the worst-case cost over a finite scenario set. We consider this concept both in a general context and for five combinatorial optimization problems: the representative multi-selection, the minimum cost flow, the transshipment, the shortest path, and the minimum weight perfect b-matching problem. We analyze the structure of the problems as well as the complexity depending on different graph classes and obtain some NP-hardness results. In addition, we provide special cases solvable in pseudo-polynomial and polynomial-time.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2024-03455
%U https://publications.rwth-aachen.de/record/983480