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Christina Büsing

Publications and source records attributed to Christina Büsing.

17 recordsLinked to original sources

Instance Generation for Patient-to-room Assignment and Admission Scheduling Based on Real Hospital Data

Developing algorithms for real-life problems that perform well in practice depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult, and such data typically cannot be published, which limits reproducibility by other researchers. This is especially true for patient-related problems because of data privacy policies such as the patient-to-room assignment problem. Therefore, artificially generated instances are commonly used. To improve the generation of realistic instances, we develop a configurable instance generator for the patient-to-room assignment problem and other patient-related problems, featuring an easy-to-use graphical user interface. The design of the generator is based on an extensive empirical analysis of real hospital data, which identifies relevant ward-specific patterns such as patients' age and length-of-stay distributions. Moreover, as randomly generated instances are often infeasible, we address this issue in two ways. We implement a dynamic programming approach in the generator to optionally enforce feasibility and extend existing results from the literature to derive new combinatorial insights into patient-to-room feasibility.

math.OC

Robust Capacity Expansion Modelling for Renewable Energy Systems

Future greenhouse gas neutral energy systems will be dominated by renewable energy technologies providing variable supply subject to uncertain weather conditions. For this setting, we propose an algorithm for capacity expansion planning: We evaluate solutions optimised on a single years' data under different input weather years, and iteratively modify solutions whenever supply gaps are detected. These modifications lead to solutions with sufficient capacities to overcome periods of cold dark lulls and seasonal demand/supply fluctuations. A computational study on a German energy system model for 40 operating years shows that preventing supply gaps, i.e. finding a robust system, increases the total annual cost by 1.6-2.9%. In comparison, non-robust systems display loss of load close to 50% of total demand during some periods. Results underline the importance of assessing the feasibility of energy system models using atypical time-series, combining dark lull and cold period effects.

math.OC

Parameterized complexity of scheduling unit-time jobs with generalized precedence constraints

We study the parameterized complexity of scheduling unit-time jobs on parallel, identical machines under generalized precedence constraints for minimization of the makespan and the sum of completion times. In our setting, each job is equipped with a Boolean formula (precedence constraint) over the set of jobs. A schedule satisfies a job's precedence constraint if setting earlier jobs to true satisfies the formula. Our definition generalizes several common types of precedence constraints: classical and-constraints if every formula is a conjunction, or-constraints if every formula is a disjunction, and and/or-constraints if every formula is in conjunctive normal form. We prove fixed-parameter tractability when parameterizing by the number of predecessors. For parameterization by the number of successors, however, the complexity depends on the structure of the precedence constraints. If every constraint is a conjunction or a disjunction, we prove the problem to be fixed-parameter tractable. For constraints in disjunctive normal form, we prove W[1]-hardness. We show that the and/or-constrained problem is NP-hard, even for a single successor. Moreover, we prove NP-hardness on two machines if every constraint is a conjunction or a disjunction. This result not only proves para-NP-hardness for parameterization by the number of machines but also complements the polynomial-time solvability on two machines if every constraint is a conjunction (Coffman and Graham 1972) or if every constraint is a disjunction (Berit 2005).

math.OC

Interval-Constrained Bipartite Matching over Time

Interval-constrained online bipartite matching problem frequently occurs in medical appointment scheduling: Unit-time jobs representing patients arrive online and are assigned to a time slot within their given feasible time interval. We consider a variant of this problem where reassignments are allowed and extend it by a notion of time that is decoupled from the job arrival events. As jobs appear, the current point in time gradually advances, and once the time of a slot is passed, the job assigned to it is fixed and cannot be reassigned anymore. We analyze two algorithms for the problem with respect to the resulting matching size and the number of reassignments they make. We show that FirstFit with reassignments according to the shortest augmenting path rule is $\frac{2}{3}$-competitive with respect to the matching cardinality, and that the bound is tight. For the number of reassignments performed by the algorithm, we show that it is in $Ω(n \log n)$ in the worst case, where $n$ is the number of patients or jobs on the online side. The competitive ratio remains bounded by $\frac{2}{3}$ if we restrict the algorithm to make only up to a constant number $k \geq 1$ of reassignments per job arrival. This fills the gap between the known optimal algorithm that makes no reassignments, which is $\frac{1}{2}$-competitive, on the one hand, and an earliest-deadline-first strategy (EDF), which we prove to obtain a maximum matching in this over-time framework, but which suffers $Ω(n^2)$ reassignments in the worst case, on the other hand. Further, we consider the setting in which the sets of feasible slots per job that are not intervals. We show that FirstFit remains $\frac{2}{3}$-competitive in this case, and that this is the best possible deterministic competitive ratio, while EDF loses its optimality.

cs.DS

Why do women pursue a PhD in Computer Science?

Computer science attracts few women, and their proportion decreases through advancing career stages. Few women progress to PhD studies in CS after completing master's studies. Empowering women at this stage in their careers is essential to unlock untapped potential for society, industry and academia. This paper identifies students' career assumptions and information related to PhD studies focused on gender-based differences. We propose a Women Career Lunch program to inform female master students about PhD studies that explains the process, clarifies misconceptions, and alleviates concerns. An extensive survey was conducted to identify factors that encourage and discourage students from undertaking PhD studies. We identified statistically significant differences between those who undertook PhD studies and those who didn't, as well as gender differences. A catalogue of questions to initiate discussions with potential PhD students which allowed them to explore these factors was developed and translated to 8 languages. Encouraging factors toward PhD study include interest and confidence in research arising from a research involvement during earlier studies; enthusiasm for and self-confidence in CS in addition to an interest in an academic career; encouragement from external sources; and a positive perception towards PhD studies which can involve achieving personal goals. Discouraging factors include uncertainty and lack of knowledge of the PhD process, a perception of lower job flexibility, and the requirement for long-term commitment. Gender differences highlighted that female students who pursue a PhD have less confidence in their technical skills than males but a higher preference for interdisciplinary areas. Female students are less inclined than males to perceive the industry as offering better job opportunities and more flexible career paths than academia.

cs.CY

Minimum-Peak-Cost Flows Over Time

When planning transportation whose operation requires non-consumable resources, the peak demand for allocated resources is often of higher interest than the duration of resource usage. For instance, it is more cost-effective to deliver parcels with a single truck over eight hours than to use two trucks for four hours, as long as the time suffices. To model such scenarios, we introduce the novel minimum peak cost flow over time problem, whose objective is to minimise the maximum cost at all points in time rather than minimising the integral of costs. We focus on minimising peak costs of temporally repeated flows. These are desirable for practical applications due to their simple structure. This yields the minimum-peak-cost temporally repeated flow problem (MPC-TRF). We show that the simple structure of temporally repeated flows comes with the drawback of arbitrarily bad approximation ratios compared to general flows over time. Furthermore, our complexity analysis shows the integral version of MPC-TRF is strongly NP-hard, even under strong restrictions. On the positive side, we identify two benign special cases: unit-cost series-parallel networks and networks with time horizon at least twice as long as the longest path in the network (with respect to the transit time). In both cases, we show that integral optimal flows if the desired flow value equals the maximum flow value and fractional optimal flows for arbitrary flow values can be found in polynomial time. For each of these cases, we provide an explicit algorithm that constructs an optimal solution.

cs.DS

A Faster Parametric Search for the Integral Quickest Transshipment Problem

Algorithms for computing fractional solutions to the quickest transshipment problem have been significantly improved since Hoppe and Tardos first solved the problem in strongly polynomial time. For integral solutions, runtime improvements are limited to general progress on submodular function minimization, which is an integral part of Hoppe and Tardos' algorithm. Yet, no structural improvements on their algorithm itself have been proposed. We replace two central subroutines in the algorithm with methods that require vastly fewer minimizations of submodular functions. This improves the state-of-the-art runtime from $ \tilde{O}(m^4 k^{15}) $ down to $ \tilde{O}(m^2 k^5 + m^4 k^2) $, where $ k $ is the number of terminals and $ m $ is the number of arcs.

cs.DS

Combinatorial and Computational Insights about Patient-to-room Assignment under Consideration of Roommate Compatibility

During a hospital stay, a roommate can significantly influence a patient's overall experience both positivly and negatively. Therefore, hospital staff tries to assign patients together to a room that are likely to be compatible. However, there are more conditions and objectives to be respected by the patient-to-room assignment (PRA), e.g., ensuring gender separated rooms and avoiding transfers. In this paper, we review the literature for reasons why roommate compatibility is important as well as for criteria that can help to increase the probability that two patients are suitable roommates. We further present combinatorial insights about computing patient-to-room assignments with optimal overall roommate compatibility. We then compare different IP-formulations for PRA as well as the influence of different scoring functions for patient compatibility on the runtime of PRA integer programming (IP) optimisation. Using these results and real-world data, we conclude this paper by developing and evaluating a fast IP-based solution approach for the dynamic PRA.

math.OC

Structural Insights and an IP-based Solution Method for Patient-to-room Assignment under Consideration of Single Room Entitlements

Patient-to-room assignment (PRA) is a scheduling problem in decision support for hospitals. It consists of assigning patients to rooms according to certain objectives, e.g., avoiding transfers and respecting single-room requests. This work presents combinatorial insights about the feasibility of PRA and about the assignment of patients to single rooms. We further compare different IP-formulations for PRA as well as the influence of different objectivs on the runtime. Based on these results, we develop a fast IP-based solution approach which obtains high quality solution. The applicability is verified through a computational study with instances derived from real-world data. Results indicate that large, real world instances can be solved to a high degree of optimality within (fractions of) seconds.

math.OC

Robust transshipment problem under consistent flow constraints

In this paper, we study robust transshipment under consistent flow constraints. We consider demand uncertainty represented by a finite set of scenarios and characterize a subset of arcs as so-called fixed arcs. In each scenario, we require an integral flow that satisfies the respective flow balance constraints. In addition, on each fixed arc, we require equal flow for all scenarios. The objective is to minimize the maximum cost occurring among all scenarios. We show that the problem is strongly NP-hard on acyclic digraphs by a reduction from the $(3,B2)$-SAT problem. Furthermore, we prove that the problem is weakly NP-hard on series-parallel digraphs by a reduction from a special case of the \textsc{Partition} problem. If in addition the number of scenarios is constant, we observe the pseudo-polynomial-time solvability of the problem. We provide polynomial-time algorithms for three special cases on series-parallel digraphs. Finally, we present a polynomial-time algorithm for pearl digraphs.

math.OC

The Dial-a-Ride Problem in Primary Care with Flexible Scheduling

Patient transportation systems are instrumental in lowering access barriers in primary care by taking patients to their GPs. As part of this setting, each transportation request of a chronic or walk-in patient consists of an outbound trip to the GP and an inbound trip back home. The economic sustainability of patient transportation systems mainly depends on their utilization and how well transportation requests can be bundled through ride sharing. To ease the latter, we consider a flexible scheduling of chronic patients in which only a certain range for an appointment is fixed a priori while the exact time is determined by the scheduling of the outbound trip. This leads to a novel extension of the dial-a-ride problem that we call the dial-a-ride problem with combined requests and flexible scheduling (DARPCF). In this paper, we introduce two heuristics for the DARPCF that exploit this increased flexibility. Both approaches initially compute so-called mini-clusters of outbound requests. Then, the mini-clusters are linked by (i) solving a traveling salesman problem and creating routes of outbound rides with a splitting procedure or by (ii) using a rolling horizon approach and solving bipartite matching problems for the vehicle assignment. Our computational study shows that by using the presented algorithms with the flexible scheduling of chronic appointments, the average number of served requests can be increased by 16% compared to a non-flexible setting.

math.OC

Robust Minimum Cost Flow Problem Under Consistent Flow Constraints

The robust minimum cost flow problem under consistent flow constraints (RobMCF$\equiv$) is a new extension of the minimum cost flow (MCF) problem. In the RobMCF$\equiv$ problem, we consider demand and supply that are subject to uncertainty. For all demand realizations, however, we require that the flow value on an arc needs to be equal if it is included in the predetermined arc set given. The objective is to find feasible flows that satisfy the equal flow requirements while minimizing the maximum occurring cost among all demand realizations. In the case of a discrete set of scenarios, we derive structural results which point out the differences with the polynomial time solvable MCF problem on networks with integral capacities. In particular, the Integral Flow Theorem of Dantzig and Fulkerson does not hold. For this reason, we require integral flows in the entire paper. We show that the RobMCF$\equiv$ problem is strongly $\mathcal{NP}$-hard on acyclic digraphs by a reduction from the $(3,B2)$-Sat problem. Further, we demonstrate that the RobMCF$\equiv$ problem is weakly $\mathcal{NP}$-hard on series-parallel digraphs by providing a reduction from Partition and a pseudo-polynomial algorithm based on dynamic programming. Finally, we propose a special case on series-parallel digraphs for which we can solve the RobMCF$\equiv$ problem in polynomial time.

math.OC

Robust strategic planning for mobile medical units with steerable and unsteerable demands

Mobile medical units (MMUs) are customized vehicles fitted with medical equipment that are used to provide primary care in rural environments. As MMUs can be easily relocated, they enable a demand-oriented, flexible, and local provision of health services. In this paper, we investigate the strategic planning of an MMU service by deciding where MMU operation sites should be set up and how often these should be serviced. To that end, we study the strategic planning problem for MMUs (SPMMU) $-$ a capacitated set covering problem that includes existing practices and two types of patient demands: (i) steerable demands representing patients who seek health services through a centralized appointment system and can be steered to any treatment facility within a given consideration set and (ii) unsteerable demands representing walk-in patients who always visit the closest available treatment facility. We propose an integer linear program for the SPMMU that can be solved via Benders decomposition and constraint generation. Starting from this formulation, we focus on the uncertain version of the problem in which steerable and unsteerable demands are modeled as random variables that may vary within a given interval. Using methods from robust optimization and duality theory, we devise exact constraint generation methods to solve the robust counterparts for interval and budgeted uncertainty sets. All our results transfer to the session-specific SPMMU and we evaluate our models in a computational study based on a set of instances generated from a rural primary care system in Germany.

math.OC

Patients, Primary Care, and Policy: Simulation Modeling for Health Care Decision Support

Demand for health care is constantly increasing due to the ongoing demographic change, while at the same time health service providers face difficulties in finding skilled personnel. This creates pressure on health care systems around the world, such that the efficient, nationwide provision of primary health care has become one of society's greatest challenges. Due to the complexity of health care systems, unforeseen future events, and a frequent lack of data, analyzing and optimizing the performance of health care systems means tackling a wicked problem. To support this task for primary care, this paper introduces the hybrid agent-based simulation model SiM-Care. SiM-Care models the interactions of patients and primary care physicians on an individual level. By tracking agent interactions, it enables modelers to assess multiple key indicators such as patient waiting times and physician utilization. Based on these indicators, primary care systems can be assessed and compared. Moreover, changes in the infrastructure, patient behavior, and service design can be directly evaluated. To showcase the opportunities offered by SiM-Care and aid model validation, we present a case study for a primary care system in Germany. Specifically, we investigate the effects of an aging population, a decrease in the number of physicians, as well as the combined effects.

cs.MA

Robust Optimization under Multi-band Uncertainty - Part I: Theory

The classical single-band uncertainty model introduced by Bertsimas and Sim has represented a breakthrough in the development of tractable robust counterparts of Linear Programs. However, adopting a single deviation band may be too limitative in practice: in many real-world problems, observed deviations indeed present asymmetric distributions over asymmetric ranges, so that getting a higher modeling resolution by partitioning the band into multiple sub-bands is advisable. The critical aim of our work is to close the knowledge gap on the adoption of multi-band uncertainty in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, interested in getting a better modeling of arbitrary shaped distributions, built on historical data about the uncertainty affecting the considered real-world problems.

math.OC

Reference Point Methods and Approximation in Multicriteria Optimization

Operations research applications often pose multicriteria problems. Mathematical research on multicriteria problems predominantly revolves around the set of Pareto optimal solutions, while in practice, methods that output a single solution are more widespread. In real-world multicriteria optimization, reference point methods are widely used and successful examples of such methods. A reference point solution is the solution closest to a given reference point in the objective space. We study the approximation of reference point solutions. In particular, we establish that approximating reference point solutions is polynomially equivalent to approximating the Pareto set. Complementing these results, we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization. In particular, we lift the link between dynamic programming and FPTAS, as well as oblivious LP-rounding techniques. The latter applies, e.g., to Set Cover and several machine scheduling problems.

cs.DS

New results about multi-band uncertainty in Robust Optimization

"The Price of Robustness" by Bertsimas and Sim represented a breakthrough in the development of a tractable robust counterpart of Linear Programming Problems. However, the central modeling assumption that the deviation band of each uncertain parameter is single may be too limitative in practice: experience indeed suggests that the deviations distribute also internally to the single band, so that getting a higher resolution by partitioning the band into multiple sub-bands seems advisable. The critical aim of our work is to close the knowledge gap about the adoption of a multi-band uncertainty set in Robust Optimization: a general definition and intensive theoretical study of a multi-band model are actually still missing. Our new developments have been also strongly inspired and encouraged by our industrial partners, which have been interested in getting a better modeling of arbitrary distributions, built on historical data of the uncertainty affecting the considered real-world problems. In this paper, we study the robust counterpart of a Linear Programming Problem with uncertain coefficient matrix, when a multi-band uncertainty set is considered. We first show that the robust counterpart corresponds to a compact LP formulation. Then we investigate the problem of separating cuts imposing robustness and we show that the separation can be efficiently operated by solving a min-cost flow problem. Finally, we test the performance of our new approach to Robust Optimization on realistic instances of a Wireless Network Design Problem subject to uncertainty.

math.OC