Queueing and Optimization Models for Hospital Patient Flow

Abstract

Various organizations claim that increasing attention should be put on an efficient use of healthcare resources. The internationally rising life expectancy and population size is accompanied by hospitals that are relying more on short admissions, and thus on limited bed capacity. The international World Health Report published by the World Health Organization shows that 20-40% of all health care resources are not being sufficiently utilized. Thus, tools that benefit an efficient healthcare system is greatly relevant to the present society. The goal of this thesis is to expand methods in the field of modeling and optimizing hospital patient flow with a view to provide management and planners with a range of decision tools for improving the utilization of hospital resources. We elaborate on a number of relevant hospital optimization problems which relate to decision making on both the strategic, tactical and operational level. In addition, we focus on various types of patient flow, from inpatient to acute and surgical admissions, which has led to four different research studies. Methodologically we mainly focus on evaluating the different instances of patient flow based on Markov chain modeling, and employing these models in heuristic search procedures to optimize the configuration of the related hospital resources. We employ this general approach in three studies. Additionally, the fourth study elaborates on a simulation-based Markov decision process. All four studies have been validated with patient data from Danish hospitals. The thesis consists of seven chapters which have been divided into four different parts. The first part consists of two chapters, where Chapter 1 introduces the reader to the concept of hospital patient flow, and presents the motivation for modeling and optimizing the processes that are related hereto. Next, Chapters 2 prepares the reader for the methods that have been employed in our research with particular focus on Markov chain modeling and heuristic optimization. Part II and III contain our contribution to the literature and comprise two chapters each. In Part II we focus exclusively on inpatient flow. Here, Chapter 3 presents a Markov chain model for evaluating the flow of inpatients, and a heuristic search procedure for deriving an improved distribution of the hospital’s bed resources. By employing a heuristic statistical test we find that our approach adequately reflects the behavior of inpatient flow for a specific hospital case, and through additional tests that patient relocations can be reduced by11.8%by re-distributing resources that are already available to the hospital. Next, in Chapter 4 we extend the application of the Markov chain model by introducing patient preferences for room types into the optimization problem. That is, our goal is to maximize the number of patient preference-matches by changing the configuration of room types for the hospital wards. To achieve this we employ a randomized and interpolated search procedure, where solutions are sampled based on an interpolation between the currently known solutions in the search space. Numerical experiments show that this approach is able to derive near-optimal solutions usually within a 1% relative gap from the optimum. In Part III we focus on both acute and surgical patient flow. Chapter 5 presents a method for optimizing emergency department staffing by evaluating the patient flow as a Markov chain model. We employ this model in a search procedure that exploits integer linear programming to minimize the total amount of staff by simultaneously accounting for the patient waiting time. Simulation experiments indicate that our approach is fairly robust to our model assumptions, and that the solutions perform well in emergency departments with multiple triage-classes of patients. Next, in Chapter 6 we present an approach for minimizing the long-term costs related to day-to-day scheduling of surgical patients. Here, we account for the inherent rolling horizon in the problem by employing a simulation-based Markov decision process. By using data from a hospital case, we validate the approach through various simulation experiments, which indicate that distinct improvements can be achieved by employing our approach rather than performing patient scheduling manually. Finally, Part IV comprises a single chapter, namely Chapter 7, where we summarize the findings from each of our studies in a final conclusion to the thesis. In relation hereto, we provide the reader with our reflections and suggestions for future work.