@inproceedings{SagnolSchmidtgenanntWaldschmidtTesch2018, author = {Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel and Tesch, Alexander}, title = {The Price of Fixed Assignments in Stochastic Extensible Bin Packing}, volume = {11312}, booktitle = {WAOA 2018: Approximation and Online Algorithms}, doi = {10.1007/978-3-030-04693-4_20}, pages = {327 -- 347}, year = {2018}, abstract = {We consider the stochastic extensible bin packing problem (SEBP) in which n items of stochastic size are packed into m bins of unit capacity. In contrast to the classical bin packing problem, the number of bins is fixed and they can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible. This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of 2. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of (1+e-1)≈1.368 under a reasonable assumption on the distributions of job durations. Furthermore, we prove that the price of fixed assignments, related to the benefit of adaptivity, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for.}, language = {en} } @misc{SagnolBlancoSauvage2017, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {The Cone of Flow Matrices: Approximation Hierarchies and Applications}, issn = {1438-0064}, doi = {10.1002/net.21820}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-64399}, year = {2017}, abstract = {Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices \$\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}\$, where \$\vec{1}_P\in\RR^n\$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over \$\mathcal{K}\$. This cone is intractable: we prove that the membership problem associated to \$\mathcal{K}\$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix \$X\in \operatorname{span} \mathcal{K}\$ as a linear combination of some \$\vec{1}_P\vec{1}_P^T\$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities.}, language = {en} } @article{Tesch2020, author = {Tesch, Alexander}, title = {A Polyhedral Study of Event-Based Models for the Resource-Constrained Project Scheduling Problem}, journal = {Journal of Scheduling}, year = {2020}, abstract = {We consider event-based Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP) that represent an alternative to the common time-indexed model (DDT) of Pritsker et al. (1969) for the case where the underlying time horizon is large or job processing times are subject to huge variations. In contrast to the time-indexed model, the size of event-based models does not depend on the time horizon. For two event-based formulations OOE and SEE of Kon{\´e} et al. (2011) we present new valid inequalities that dominate the original formulation. Additionally, we introduce a new event-based model: the Interval Event-Based Model (IEE). We deduce linear transformations between all three models that yield the strict domination order IEE > SEE > OOE for their linear programming (LP) relaxations, meaning that IEE has the strongest linear relaxation among the event-based models. We further show that the popular DDT formulation can be retrieved from IEE by certain polyhedral operations, thus giving a unifying view on a complete branch of MIP formulations for the RCPSP. In addition, we analyze the computational performance of all presented models on test instances of the PSPLIB (Kolisch and Sprecher 1997).}, language = {en} } @article{DuarteSagnol2020, author = {Duarte, Belmiro and Sagnol, Guillaume}, title = {Approximate and exact optimal designs for 2^k factorial experiments for generalized linear models via second order cone programming}, volume = {61}, journal = {Statistical Papers}, doi = {10.1007/s00362-018-01075-7}, pages = {2737 -- 2767}, year = {2020}, abstract = {Model-based optimal designs of experiments (M-bODE) for nonlinear models are typically hard to compute. The literature on the computation of M-bODE for nonlinear models when the covariates are categorical variables, i.e. factorial experiments, is scarce. We propose second order cone programming (SOCP) and Mixed Integer Second Order Programming (MISOCP) formulations to find, respectively, approximate and exact A- and D-optimal designs for 2𝑘 factorial experiments for Generalized Linear Models (GLMs). First, locally optimal (approximate and exact) designs for GLMs are addressed using the formulation of Sagnol (J Stat Plan Inference 141(5):1684-1708, 2011). Next, we consider the scenario where the parameters are uncertain, and new formulations are proposed to find Bayesian optimal designs using the A- and log det D-optimality criteria. A quasi Monte-Carlo sampling procedure based on the Hammersley sequence is used for computing the expectation in the parametric region of interest. We demonstrate the application of the algorithm with the logistic, probit and complementary log-log models and consider full and fractional factorial designs.}, language = {en} } @misc{BorndoerferTeschSagnol2019, author = {Bornd{\"o}rfer, Ralf and Tesch, Alexander and Sagnol, Guillaume}, title = {Algorithmen unterst{\"u}tzen OP-Planung}, journal = {Management \& Krankenhaus}, number = {12}, publisher = {Wiley}, pages = {20}, year = {2019}, abstract = {Mathematische Algorithmen k{\"o}nnen durch Vorhersage von Unsicherheiten optimierte OP-Pl{\"a}ne berechnen, sodass mehrere Zielkriterien wie {\"U}berstunden, Wartezeit und Ausf{\"a}lle im OP minimiert werden.}, language = {de} } @misc{Tesch2018, author = {Tesch, Alexander}, title = {A Polyhedral Study of Event-Based Models for the Resource-Constrained Project Scheduling Problem}, issn = {1438-0064waoa}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68485}, year = {2018}, abstract = {We consider event-based Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP) that represent an alternative to the common time-indexed model (DDT) of Pritsker et al. (1969) for the case where the underlying time horizon is large or job processing times are subject to huge variations. In contrast to the time-indexed model, the size of event-based models does not depend on the time horizon. For two event-based formulations OOE and SEE of Kon{\´e} et al. (2011) we present new valid inequalities that dominate the original formulation. Additionally, we introduce a new event-based model: the Interval Event-Based Model (IEE). We deduce linear transformations between all three models that yield the strict domination order IEE > SEE > OOE for their linear programming (LP) relaxations, meaning that IEE has the strongest linear relaxation among the event-based models. We further show that the popular DDT formulation can be retrieved from IEE by certain polyhedral operations, thus giving a unifying view on a complete branch of MIP formulations for the RCPSP. In addition, we analyze the computational performance of all presented models on test instances of the PSPLIB (Kolisch and Sprecher 1997).}, language = {en} } @misc{SagnolSchmidtgenanntWaldschmidtTesch2018, author = {Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel and Tesch, Alexander}, title = {The Price of Fixed Assignments in Stochastic Extensible Bin Packing}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68415}, year = {2018}, abstract = {We consider the stochastic extensible bin packing problem (SEBP) in which \$n\$ items of stochastic size are packed into \$m\$ bins of unit capacity. In contrast to the classical bin packing problem, bins can be extended at extra cost. This problem plays an important role in stochastic environments such as in surgery scheduling: Patients must be assigned to operating rooms beforehand, such that the regular capacity is fully utilized while the amount of overtime is as small as possible. This paper focuses on essential ratios between different classes of policies: First, we consider the price of non-splittability, in which we compare the optimal non-anticipatory policy against the optimal fractional assignment policy. We show that this ratio has a tight upper bound of \$2\$. Moreover, we develop an analysis of a fixed assignment variant of the LEPT rule yielding a tight approximation ratio of \$1+1/e \approx 1.368\$ under a reasonable assumption on the distributions of job durations. Furthermore, we prove that the price of fixed assignments, which describes the loss when restricting to fixed assignment policies, is within the same factor. This shows that in some sense, LEPT is the best fixed assignment policy we can hope for.}, language = {en} } @misc{Tesch2016, author = {Tesch, Alexander}, title = {A Nearly Exact Propagation Algorithm for Energetic Reasoning in O(n^2 log n)}, issn = {1438-0064}, doi = {10.1007/978-3-319-44953-1_32}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59332}, year = {2016}, abstract = {In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). In this paper, we first present an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with complexity O(n^2 log n) where n denotes the number of jobs. The key idea is based on a new sweep line subroutine that efficiently evaluates the relevant time intervals for all jobs. In particular, our algorithm yields at least one possible energetic reasoning propagation for each job. Finally, we show that on the vast number of relevant time intervals our approach yields the maximum possible propagation according to the energetic reasoning rule.}, language = {en} } @misc{Tesch2018, author = {Tesch, Alexander}, title = {Improving Energetic Propagations for Cumulative Scheduling}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69331}, year = {2018}, abstract = {We consider the Cumulative Scheduling Problem (CuSP) in which a set of \$n\$ jobs must be scheduled according to release dates, due dates and cumulative resource constraints. In constraint programming, the CuSP is modeled as the cumulative constraint. Among the most common propagation algorithms for the CuSP there is energetic reasoning (Baptiste et al., 1999) with a complexity of O(n^3) and edge-finding (Vilim, 2009) with O(kn log n) where k <= n is the number of different resource demands. We consider the complete versions of the propagators that perform all deductions in one call of the algorithm. In this paper, we introduce the energetic edge-finding rule that is a generalization of both energetic reasoning and edge-finding. Our main result is a complete energetic edge-finding algorithm with a complexity of O(n^2 log n) which improves upon the complexity of energetic reasoning. Moreover, we show that a relaxation of energetic edge-finding with a complexity of O(n^2) subsumes edge-finding while performing stronger propagations from energetic reasoning. A further result shows that energetic edge-finding reaches its fixpoint in strongly polynomial time. Our main insight is that energetic schedules can be interpreted as a single machine scheduling problem from which we deduce a monotonicity property that is exploited in the algorithms. Hence, our algorithms improve upon the strength and the complexity of energetic reasoning and edge-finding whose complexity status seemed widely untouchable for the last decades.}, language = {en} } @inproceedings{Tesch2018, author = {Tesch, Alexander}, title = {Improving Energetic Propagations for Cumulative Scheduling}, booktitle = {Principles and Practice of Constraint Programming (CP 2018)}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69321}, year = {2018}, abstract = {We consider the Cumulative Scheduling Problem (CuSP) in which a set of \$n\$ jobs must be scheduled according to release dates, due dates and cumulative resource constraints. In constraint programming, the CuSP is modeled as the cumulative constraint. Among the most common propagation algorithms for the CuSP there is energetic reasoning (Baptiste et al., 1999) with a complexity of O(n^3) and edge-finding (Vilim, 2009) with O(kn log n) where k <= n is the number of different resource demands. We consider the complete versions of the propagators that perform all deductions in one call of the algorithm. In this paper, we introduce the energetic edge-finding rule that is a generalization of both energetic reasoning and edge-finding. Our main result is a complete energetic edge-finding algorithm with a complexity of O(n^2 log n) which improves upon the complexity of energetic reasoning. Moreover, we show that a relaxation of energetic edge-finding with a complexity of O(n^2) subsumes edge-finding while performing stronger propagations from energetic reasoning. A further result shows that energetic edge-finding reaches its fixpoint in strongly polynomial time. Our main insight is that energetic schedules can be interpreted as a single machine scheduling problem from which we deduce a monotonicity property that is exploited in the algorithms. Hence, our algorithms improve upon the strength and the complexity of energetic reasoning and edge-finding whose complexity status seemed widely untouchable for the last decades.}, language = {en} } @misc{Tesch2016, author = {Tesch, Alexander}, title = {Exact Energetic Reasoning in O(n^2 log^2 n)}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-60367}, year = {2016}, abstract = {In this paper, we address the Energetic Reasoning propagation rule for the Cumulative Scheduling Problem (CuSP). An energetic reasoning propagation algorithm is called exact, if it computes the maximum possible energetic reasoning propagation for all the jobs. The currently best known exact energetic reasoning algorithm has complexity O(n^3). In this paper, we present a new exact energetic reasoning propagation algorithm with improved complexity of O(n^2 \log^2 n).}, language = {en} } @misc{Tesch2016, author = {Tesch, Alexander}, title = {Improved Compact Models for the Resource-Constrained Project Scheduling Problem}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-62891}, year = {2016}, abstract = {In this article, we study compact Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP). Compared to the classical time-indexed formulation, the size of compact models is strongly polynomial in the number of jobs. In addition to two compact models from the literature, we propose a new compact model. We can show that all three compact models are equivalent by successive linear transformations. For their LP-relaxations, however, we state a full inclusion hierarchy where our new model dominates the previous models in terms of polyhedral strength. Moreover, we reveal a polyhedral relationship to the common time-indexed model. Furthermore, a general class of valid cutting planes for the compact models is introduced and finally all models are evaluated by computational experiments.}, language = {en} } @inproceedings{Tesch2016, author = {Tesch, Alexander}, title = {A Nearly Exact Propagation Algorithm for Energetic Reasoning in O(n^2 log n)}, volume = {22}, booktitle = {Principles and Practice of Constraint Programming (CP 2016)}, doi = {10.1007/978-3-319-44953-1_32}, pages = {493 -- 519}, year = {2016}, abstract = {In constraint programming, energetic reasoning constitutes a powerful start time propagation rule for cumulative scheduling problems (CuSP). In this paper, we first present an improved time interval checking algorithm that is derived from a polyhedral model. In a second step, we extend this algorithm to an energetic reasoning propagation algorithm with complexity O(n^2 log n) where n denotes the number of jobs. The key idea is based on a new sweep line subroutine that efficiently evaluates the relevant time intervals for all jobs. In particular, our algorithm yields at least one possible energetic reasoning propagation for each job. Finally, we show that on the vast number of relevant time intervals our approach yields the maximum possible propagation according to the energetic reasoning rule.}, language = {en} } @misc{Mattrisch2018, type = {Master Thesis}, author = {Mattrisch, Lisa}, title = {Optimization of a Master Surgery Schedule}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-69996}, year = {2018}, abstract = {During the past years hospitals saw themselves confronted with increasing economical pressure (WB06, p. V). Therefore, optimizing the general operational procedures has gained in importance. The revenue of a hospital depends on the kinds and quantity of treatments performed and on the effcient use and utilization of the corresponding resources. About 25 - 50\% of the treatment costs of a patient needing surgery incurs in the operating rooms (WB06, p. 58). Hence skillful management of the operating rooms can have a large impact on the overall revenue of a hospital. Belien and Demeulemeester (BD07) describe the planning of operating room (OR) schedules as a multi-stage process. In the first stage OR time is allocated to the hospitals specialties and capacities and resources are adjusted. In the second stage a master surgery schedule (MSS) is developed, that is a timetable for D days that specifies the amount of OR time assigned to the specialties on every individual day. After D days this schedule will be repeated without any changes. Hence, developing an MSS is a long-term problem. Finally, specialties will schedule specific surgeries within their assigned OR time. In this work we will focus on the development of the MSS that maximizes the revenue of the hospital. Our main focus will be to ensure that the capacities of the downstream resources, i.e. the bed capacities in the ICU and ward, will not be exceeded. Additionally, we hope that our formulation of the problem will lead to a leveled bed demand without significant peaks. We will incorporate the uncertainty of patient demand and case mix in our model. There have been several approaches on this subject, for example in (F{\"u}15) and (BD07) and this work is in part in� uenced by these advances.}, language = {en} } @article{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {The Cone of Flow Matrices: Approximation Hierarchies and Applications}, volume = {72}, journal = {Networks}, number = {1}, doi = {10.1002/net.21820}, pages = {128 -- 150}, year = {2018}, abstract = {Let G be a directed acyclic graph with n arcs, a source s and a sink t. We introduce the cone K of flow matrices, which is a polyhedral cone generated by the matrices \$\vec{1}_P\vec{1}_P^T\in\RR^{n\times n}\$, where \$\vec{1}_P\in\RR^n\$ is the incidence vector of the (s,t)-path P. We show that several hard flow (or path) optimization problems, that cannot be solved by using the standard arc-representation of a flow, reduce to a linear optimization problem over \$\mathcal{K}\$. This cone is intractable: we prove that the membership problem associated to \$\mathcal{K}\$ is NP-complete. However, the affine hull of this cone admits a nice description, and we give an algorithm which computes in polynomial-time the decomposition of a matrix \$X\in \operatorname{span} \mathcal{K}\$ as a linear combination of some \$\vec{1}_P\vec{1}_P^T\$'s. Then, we provide two convergent approximation hierarchies, one of them based on a completely positive representation of~K. We illustrate this approach by computing bounds for the quadratic shortest path problem, as well as a maximum flow problem with pairwise arc-capacities.}, language = {en} } @article{PeitzGraelerHenkeetal.2016, author = {Peitz, Sebastian and Gr{\"a}ler, Manuel and Henke, Christian and Hessel-von Molo, Mirko and Dellnitz, Michael and Tr{\"a}chtler, Ansgar}, title = {Multiobjective Model Predictive Control of an Industrial Laundry}, journal = {Procedia Technology}, number = {26}, pages = {483 -- 490}, year = {2016}, abstract = {In a wide range of applications, it is desirable to optimally control a system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a single optimal solution, the set of optimal compromises, the so-called Pareto set, has to be approximated. When it is not possible to compute the entire control trajectory in advance, for instance due to uncertainties or unforeseeable events, model predictive control methods can be applied to control the system during operation in real time. In this article, we present an algorithm for the solution of multiobjective model predictive control problems. In an offline scenario, it can be used to compute the entire set of optimal compromises whereas in a real time scenario, one optimal compromise is computed according to an operator's preference. The results are illustrated using the example of an industrial laundry. A logistics model of the laundry is developed and then utilized in the optimization routine. Results are presented for an offline as well as an online scenario}, language = {en} } @misc{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {Approximation Hierarchies for the cone of flow matrices}, issn = {1438-0064}, doi = {10.1016/j.endm.2018.02.002}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-68424}, year = {2018}, abstract = {Let \$G\$ be a directed acyclic graph with \$n\$ arcs, a source \$s\$ and a sink \$t\$. We introduce the cone \$K\$ of flow matrices, which is a polyhedral cone generated by the matrices \$1_P 1_P^T \in R^{n\times n}\$, where \$1_P\in R^n\$ is the incidence vector of the \$(s,t)\$-path \$P\$. Several combinatorial problems reduce to a linear optimization problem over \$K\$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of \$K\$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities.}, language = {en} } @inproceedings{SagnolBlancoSauvage2018, author = {Sagnol, Guillaume and Blanco, Marco and Sauvage, Thibaut}, title = {Approximation Hierarchies for the cone of flow matrices}, volume = {64}, booktitle = {INOC 2017 - 8th International Network Optimization Conference}, doi = {10.1016/j.endm.2018.02.002}, pages = {275 -- 284}, year = {2018}, abstract = {Let \$G\$ be a directed acyclic graph with \$n\$ arcs, a source \$s\$ and a sink \$t\$. We introduce the cone \$K\$ of flow matrices, which is a polyhedral cone generated by the matrices \$1_P 1_P^T \in R^{n\times n}\$, where \$1_P\in R^n\$ is the incidence vector of the \$(s,t)\$-path \$P\$. Several combinatorial problems reduce to a linear optimization problem over \$K\$. This cone is intractable, but we provide two convergent approximation hierarchies, one of them based on a completely positive representation of \$K\$. We illustrate this approach by computing bounds for a maximum flow problem with pairwise arc-capacities.}, language = {en} } @article{SagnolBarnerBorndoerferetal.2018, author = {Sagnol, Guillaume and Barner, Christoph and Bornd{\"o}rfer, Ralf and Grima, Micka{\"e}l and Seeling, Mathes and Spies, Claudia and Wernecke, Klaus}, title = {Robust Allocation of Operating Rooms: a Cutting Plane Approach to handle Lognormal Case Durations}, volume = {271}, journal = {European Journal of Operational Research}, number = {2}, doi = {10.1016/j.ejor.2018.05.022}, pages = {420 -- 435}, year = {2018}, abstract = {The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.}, language = {en} } @article{ConradGenzelCvetkovicetal.2017, author = {Conrad, Tim and Genzel, Martin and Cvetkovic, Nada and Wulkow, Niklas and Leichtle, Alexander Benedikt and Vybiral, Jan and Kytyniok, Gitta and Sch{\"u}tte, Christof}, title = {Sparse Proteomics Analysis - a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data}, volume = {18}, journal = {BMC Bioinfomatics}, number = {160}, doi = {10.1186/s12859-017-1565-4}, year = {2017}, abstract = {Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. Results: We present a new algorithm, Sparse Proteomics Analysis (SPA),based on thet heory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets.}, language = {en} } @misc{TeschBorndoerfer2025, author = {Tesch, Alexander and Bornd{\"o}rfer, Ralf}, title = {Mathematische Optimierung in der OP-Planung}, volume = {5}, journal = {OP-Management up2date}, number = {1}, publisher = {Thieme}, doi = {10.1055/a-2322-2124}, pages = {21 -- 34}, year = {2025}, abstract = {Deutsche Krankenh{\"a}user sehen sich derzeit mit enormen Schwierigkeiten konfrontiert. Ungef{\"a}hr jede 2. Klinik muss drastische Sparmaßnahmen ergreifen, was auch die Allgemeinversorgung beeintr{\"a}chtigt. Die Gr{\"u}nde daf{\"u}r sind vielschichtig: stark gestiegene Sach- und Personalkosten bei gleicher Finanzierung, teilweiser Patientenr{\"u}ckgang, starke regionale Unterschiede in der Versorgung, Fachkr{\"a}ftemangel und fehlende Investitionen in Kern- und Zukunftsbereiche, insbesondere der Digitalisierung. Das belastet die Haushalte der Kliniken. Insbesondere die Digitalisierung und die Anwendung von Methoden der k{\"u}nstlichen Intelligenz und der mathematischen Optimierung k{\"o}nnten eine Schl{\"u}sselrolle spielen, um die komplexen Krankenhausprozesse mit Kennzahlen qualitativ zu bewerten und zu verbessern. In diesem Artikel stellen wir vier Praxisprobleme aus der OP-Planung vor und benennen welche Entscheidungen, Nebenbedingungen und Zielkriterien mit mathematischen Entscheidungsmodellen dargestellt und optimiert werden k{\"o}nnen. Hierzu erl{\"a}utern wir das erweiterte Potenzial einer umfassenden Anwendung von mathematischer Optimierung im OP-Bereich.}, language = {de} } @misc{SagnolBarnerBorndoerferetal.2016, author = {Sagnol, Guillaume and Barner, Christoph and Bornd{\"o}rfer, Ralf and Grima, Micka{\"e}l and Seeling, Matthes and Spies, Claudia and Wernecke, Klaus}, title = {Robust Allocation of Operating Rooms: a Cutting Plane Approach to handle Lognormal Case Durations}, issn = {1438-0064}, doi = {10.1016/j.ejor.2018.05.022}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-58502}, year = {2016}, abstract = {The problem of allocating operating rooms (OR) to surgical cases is a challenging task, involving both combinatorial aspects and uncertainty handling. We formulate this problem as a parallel machines scheduling problem, in which job durations follow a lognormal distribution, and a fixed assignment of jobs to machines must be computed. We propose a cutting-plane approach to solve the robust counterpart of this optimization problem. To this end, we develop an algorithm based on fixed-point iterations that identifies worst-case scenarios and generates cut inequalities. The main result of this article uses Hilbert's projective geometry to prove the convergence of this procedure under mild conditions. We also propose two exact solution methods for a similar problem, but with a polyhedral uncertainty set, for which only approximation approaches were known. Our model can be extended to balance the load over several planning periods in a rolling horizon. We present extensive numerical experiments for instances based on real data from a major hospital in Berlin. In particular, we find that: (i) our approach performs well compared to a previous model that ignored the distribution of case durations; (ii) compared to an alternative stochastic programming approach, robust optimization yields solutions that are more robust against uncertainty, at a small price in terms of average cost; (iii) the \emph{longest expected processing time first} (LEPT) heuristic performs well and efficiently protects against extreme scenarios, but only if a good prediction model for the durations is available. Finally, we draw a number of managerial implications from these observations.}, language = {en} } @inproceedings{Tesch2017, author = {Tesch, Alexander}, title = {Improved Compact Models for the Resource-Constrained Project Scheduling Problem}, booktitle = {Operations Research Proceedings 2016}, pages = {25 -- 30}, year = {2017}, abstract = {In this article, we study compact Mixed-Integer Programming (MIP) models for the Resource-Constrained Project Scheduling Problem (RCPSP). Compared to the classical time-indexed formulation, the size of compact models is strongly polynomial in the number of jobs. In addition to two compact models from the literature, we propose a new compact model. We can show that all three compact models are equivalent by successive linear transformations. For their LP-relaxations, however, we state a full inclusion hierarchy where our new model dominates the previous models in terms of polyhedral strength. Moreover, we reveal a polyhedral relationship to the common time-indexed model. Furthermore, a general class of valid cutting planes for the compact models is introduced and finally all models are evaluated by computational experiments.}, language = {en} } @article{SagnolSchmidtgenanntWaldschmidt2021, author = {Sagnol, Guillaume and Schmidt genannt Waldschmidt, Daniel}, title = {Restricted Adaptivity in Stochastic Scheduling}, volume = {204}, journal = {29th Annual European Symposium on Algorithms (ESA 2021)}, doi = {10.4230/LIPIcs.ESA.2021.79}, pages = {79:1 -- 79:14}, year = {2021}, abstract = {We consider the stochastic scheduling problem of minimizing the expected makespan on m parallel identical machines. While the (adaptive) list scheduling policy achieves an approximation ratio of 2, any (non-adaptive) fixed assignment policy has performance guarantee Ω(logm/loglogm). Although the performance of the latter class of policies are worse, there are applications in which non-adaptive policies are desired. In this work, we introduce the two classes of δ-delay and τ-shift policies whose degree of adaptivity can be controlled by a parameter. We present a policy - belonging to both classes - which is an O(loglogm)-approximation for reasonably bounded parameters. In other words, an exponential improvement on the performance of any fixed assignment policy can be achieved when allowing a small degree of adaptivity. Moreover, we provide a matching lower bound for any δ-delay and τ-shift policy when both parameters, respectively, are in the order of the expected makespan of an optimal non-anticipatory policy.}, language = {en} } @article{PronzatoSagnol2021, author = {Pronzato, Luc and Sagnol, Guillaume}, title = {Removing inessential points in c- and A-optimal design}, volume = {213}, journal = {Journal of Statistical Planning and Inference}, doi = {10.1016/j.jspi.2020.11.011}, pages = {233 -- 252}, year = {2021}, abstract = {A design point is inessential when it does not contribute to an optimal design, and can therefore be safely discarded from the design space. We derive three inequalities for the detection of such inessential points in c-optimal design: the first two are direct consequences of the equivalence theorem for c-optimality; the third one is derived from a second-order cone programming formulation of c-optimal design. Elimination rules for A-optimal design are obtained as a byproduct. When implemented within an optimization algorithm, each inequality gives a screening test that may provide a substantial acceleration by reducing the size of the problem online. Several examples are presented with a multiplicative algorithm to illustrate the effectiveness of the approach.}, language = {en} }