Modelling and solving healthcare decision making problems under uncertainty

The efficient management of healthcare services is a great challenge for healthcare managers because of ageing populations, rising healthcare costs, and complex operation and service delivery systems. The challenge is intensified due to the fact that healthcare systems involve various uncertainties. Operations Research (OR) can be used to model and solve several healthcare decision making problems at strategic, tactical and also operational levels. Among different stages of healthcare decision making, resoure allocation and capacity planning play an important role for the overall performance of the complex systems. This thesis aims to develop modelling and solution tools to support healthcare decision making process within dynamic and stochastic systems. In particular, we are concerned with stochastic optimization problems, namely i) capacity planning in a stem-cell donation network, ii) resource allocation in a healthcare outsourcing network and iii) real-time surgery planning. The patient waiting times and operational costs are considered as the main performance indicators in these healthcare settings. The uncertainties arising in patient arrivals and service durations are integrated into the decision making as the most significant factors affecting the overall performance of the underlying healthcare systems. We use stochastic programming, a collection of OR tools for decision-making under uncertainty, to obtain robust solutions against these uncertainties. Due to complexities of the underlying stochastic optimization models such as large real-life problem instances and non-convexity, these models cannot be solved efficiently by exact methods within reasonable computation time. Thus, we employ approximate solution approaches to obtain feasible decisions close to the optimum. The computational experiments are designed to illustrate the performance of the proposed approximate methods. Moreover, we analyze the numerical results to provide some managerial insights to aid the decision-making processes. The numerical results show the benefits of integrating the uncertainty into decision making process and the impact of various factors in the overall performance of the healthcare systems

Combining Coupled Skorokhod SDEs and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems, one of the major challenges is coming from the fact that corresponding stochastic processes should, in most cases, be considered in bounded domains, possibly with obstacles. This has been known for a long time and yet, very little has been done for the quantification of uncertainties in modelling complex behavioral systems described by such stochastic processes. In this paper, we address this challenge by considering a coupled system of Skorokhod-type stochastic differential equations (SDEs) describing interactions between active and passive participants of a mixed-population group. In developing a multi-fidelity modelling methodology for such behavioral systems, we combine low- and high-fidelity results obtained from (a) the solution of the underlying coupled system of SDEs and (b) simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. Furthermore, we provide representative numerical examples of healthcare systems, subject to an epidemic, where the main focus in our considerations is given to an interacting particle system of asymptomatic and susceptible populations.Comment: 12 pages, 3 figure

Stochastic hybrid system : modelling and verification

Hybrid systems now form a classical computational paradigm unifying discrete and continuous system aspects. The modelling, analysis and verification of these systems are very difficult. One way to reduce the complexity of hybrid system models is to consider randomization. The need for stochastic models has actually multiple motivations. Usually, when building models complete information is not available and we have to consider stochastic versions. Moreover, non-determinism and uncertainty are inherent to complex systems. The stochastic approach can be thought of as a way of quantifying non-determinism (by assigning a probability to each possible execution branch) and managing uncertainty. This is built upon to the - now classical - approach in algorithmics that provides polynomial complexity algorithms via randomization. In this thesis we investigate the stochastic hybrid systems, focused on modelling and analysis. We propose a powerful unifying paradigm that combines analytical and formal methods. Its applications vary from air traffic control to communication networks and healthcare systems. The stochastic hybrid system paradigm has an explosive development. This is because of its very powerful expressivity and the great variety of possible applications. Each hybrid system model can be randomized in different ways, giving rise to many classes of stochastic hybrid systems. Moreover, randomization can change profoundly the mathematical properties of discrete and continuous aspects and also can influence their interaction. Beyond the profound foundational and semantics issues, there is the possibility to combine and cross-fertilize techniques from analytic mathematics (like optimization, control, adaptivity, stability, existence and uniqueness of trajectories, sensitivity analysis) and formal methods (like bisimulation, specification, reachability analysis, model checking). These constitute the major motivations of our research. We investigate new models of stochastic hybrid systems and their associated problems. The main difference from the existing approaches is that we do not follow one way (based only on continuous or discrete mathematics), but their cross-fertilization. For stochastic hybrid systems we introduce concepts that have been defined only for discrete transition systems. Then, techniques that have been used in discrete automata now come in a new analytical fashion. This is partly explained by the fact that popular verification methods (like theorem proving) can hardly work even on probabilistic extensions of discrete systems. When the continuous dimension is added, the idea to use continuous mathematics methods for verification purposes comes in a natural way. The concrete contribution of this thesis has four major milestones: 1. A new and a very general model for stochastic hybrid systems; 2. Stochastic reachability for stochastic hybrid systems is introduced together with an approximating method to compute reach set probabilities; 3. Bisimulation for stochastic hybrid systems is introduced and relationship with reachability analysis is investigated. 4. Considering the communication issue, we extend the modelling paradigm

A decision support system for demand and capacity modelling of an accident and emergency department

© 2019 Operational Research Society.Accident and emergency (A&E) departments in England have been struggling against severe capacity constraints. In addition, A&E demands have been increasing year on year. In this study, our aim was to develop a decision support system combining discrete event simulation and comparative forecasting techniques for the better management of the Princess Alexandra Hospital in England. We used the national hospital episodes statistics data-set including period April, 2009 – January, 2013. Two demand conditions are considered: the expected demand condition is based on A&E demands estimated by comparing forecasting methods, and the unexpected demand is based on the closure of a nearby A&E department due to budgeting constraints. We developed a discrete event simulation model to measure a number of key performance metrics. This paper presents a crucial study which will enable service managers and directors of hospitals to foresee their activities in future and form a strategic plan well in advance.Peer reviewe

Modelling very large complex systems using distributed simulation: A pilot study in a healthcare setting

Modern manufacturing supply chains are hugely complex and like all stochastic systems, can benefit from simulation. Unfortunately supply chain systems often result in massively large and complicated models, which even today’s powerful computers cannot run efficiently. This paper presents one possible solution - distributed simulation. This pilot study is implemented in a healthcare setting, the supply chain of blood from donor to recipient

Dealing with variability in the design, planning and evaluation of Healthcare inpatient units: a modeling methodology for patient dependency variations.

This research addresses the fluctuating demand and high variability in healthcare systems. These system’s variations need to be considered whilst at the same time making efficient use of the systems’ resources. Patient dependency fluctuation, which makes determining the level of adequate staffing highly complex, is among the variations addressed. Dealing with variability is found to be a key feature in the design, planning and evaluation of healthcare systems. Healthcare providers are facing increasing challenges resulting from an aging population, higher patient expectancies, a shortage of healthcare professionals, as well as increasing costs and reduced funding. Despite the accentuated need for effective healthcare systems and efficient use of resources, many healthcare organisations are inadequately designed and, moreover, poorly managed. Hospital systems consist of complex interrelations between relatively small units, each of which is sensitive to stochastic variations in demand. In addition to this aspect of the system view, a critical resource for the patients’ wellbeing and survival is the staffing level of nurses. This puts the planning and scheduling of human resources as one of the system’s foremost aims. Current tools for staffing and personnel planning in healthcare organisations do not take into consideration the workload variations that result from the variable nature of patient dependency levels. The work presents the empirical findings of a number of case studies conducted at a regional hospital in Sweden. Principles and practical suggestions for the robust system design of inpatient wards using Discrete Event Simulation (DES) have been identified. Although DES techniques have, in principle, all the features for modelling the variation and stochastic nature of systems, DES has not been previously used for workload studies of inpatient wards. The main contribution of this work is therefore how a combination of DES and the data of Patient Classification Systems (PCSs) can be used to model workload variations and, subsequently, plan the nurse staffing requirements in systems with high variability. The work presented gives step by step guidance in how the analysis and subsequent modelling of an inpatient ward should be carried out. It defines a novel modelling methodology for patient dependency variations and length of stay modelling of a patient’s dependency progression, including an adaptation to the ward’s discharge figures. The modelling approach opens a novel way of analysing and evaluating the system design of inpatient wards.University of Skövde, Swede

Cost comparison of orthopaedic fracture pathways using discrete event simulation in a Glasgow hospital

Objective: Healthcare faces the continual challenge of improving outcome whilst aiming to reduce cost. The aim of this study was to determine the micro cost differences of the Glasgow non-operative trauma virtual pathway in comparison to a traditional pathway. Design:  Discrete event simulation was used to model and analyse cost and resource utilisation with an activity based costing approach. Data for a full comparison before the process change was unavailable so we utilised a modelling approach, comparing a Virtual Fracture Clinic (VFC) to a simulated Traditional Fracture Clinic (TFC). Setting:  The orthopaedic unit VFC pathway pioneered at Glasgow Royal Infirmary has attracted significant attention and interest and is the focus of this cost study. Outcome measures: Our study focused exclusively on non-operative trauma patients attending Emergency Department or the minor injuries unit and the subsequent step in the patient pathway. Retrospective studies of patient outcomes as a result of the protocol introductions for specific injuries in association with activity costs from the models.ResultsPatients are satisfied with the new pathway, the information provided and the outcome of their injuries (Evidence Level IV). There was a 65% reduction in the number of first outpatient face-to-face attendances in orthopaedics. In the VFC pathway, the resources required per day were significantly lower for all staff groups (p=<0.001). The overall cost per patient of the VFC pathway was £22.84 (95% CI: 21.74, 23.92) per patient compared with £36.81 (95% CI: 35.65, 37.97) for the TFC pathway.  Conclusions:  Our results give a clearer picture of the cost comparison of the virtual pathway over a wholly traditional face-to-face clinic system. The use of simulation-based stochastic costings in healthcare economic analysis has been limited to date, but this study provides evidence for adoption of this method as a basis for its application in other healthcare settings

A survey of simulation techniques in commerce and defence

Despite the developments in Modelling and Simulation (M&S) tools and techniques over the past years, there has been a gap in the M&S research and practice in healthcare on developing a toolkit to assist the modellers and simulation practitioners with selecting an appropriate set of techniques. This study is a preliminary step towards this goal. This paper presents some results from a systematic literature survey on applications of M&S in the commerce and defence domains that could inspire some improvements in the healthcare. Interim results show that in the commercial sector Discrete-Event Simulation (DES) has been the most widely used technique with System Dynamics (SD) in second place. However in the defence sector, SD has gained relatively more attention. SD has been found quite useful for qualitative and soft factors analysis. From both the surveys it becomes clear that there is a growing trend towards using hybrid M&S approaches

Taxonomic classification of planning decisions in health care: a review of the state of the art in OR/MS

We provide a structured overview of the typical decisions to be made in resource capacity planning and control in health care, and a review of relevant OR/MS articles for each planning decision. The contribution of this paper is twofold. First, to position the planning decisions, a taxonomy is presented. This taxonomy provides health care managers and OR/MS researchers with a method to identify, break down and classify planning and control decisions. Second, following the taxonomy, for six health care services, we provide an exhaustive specification of planning and control decisions in resource capacity planning and control. For each planning and control decision, we structurally review the key OR/MS articles and the OR/MS methods and techniques that are applied in the literature to support decision making

Sequential escapes: onset of slow domino regime via a saddle connection

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable "quiescent" equilibrium to a more stable "active" equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper we consider a localized form of non-diffusive (i.e pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation we find increasing coefficient of variation of the subsequent escape times