Flexible hospital-wide elective patient scheduling

In this paper, we build on and extend Gartner and Kolisch (2014)’s hospital-wide patient scheduling problem. Their contribution margin maximizing model decides on the patients' discharge date and therefore the length of stay. Decisions such as the allocation of scarce hospital resources along the clinical pathways are taken. Our extensions which are modeled as a mathematical program include admission decisions and flexible patient-to-specialty assignments to account for multi-morbid patients. Another flexibility extension is that one out of multiple surgical teams can be assigned to each patient. Furthermore, we consider overtime availability of human resources such as residents and nurses. Finally, we include these extensions in the rolling-horizon approach and account for lognormal distributed recovery times and remaining resource capacity for elective patients. Our computational study on real-world instances reveals that, if overtime flexibility is allowed, up to 5% increase in contribution margin can be achieved by reducing length of stay by up to 30%. At the same time, allowing for overtime can reduce waiting times by up to 33%. Our model can be applied in and generalized towards other patient scheduling problems, for example in cancer care where patients may follow defined cancer pathways

Mind the gap: a review of optimisation in mental healthcare service delivery

Well-planned care arrangements with effective distribution of available resources have the potential to address inefficiencies in mental health services. We begin by exploring the complexities associated with mental health and describe how these influence service delivery. We then conduct a scoping literature review of studies employing optimisation techniques that address service delivery issues in mental healthcare. Studies are classified based on criteria such as the type of planning decision addressed, the purpose of the study and care setting. We analyse the modelling methodologies used, objectives, constraints and model solutions. We find that the application of optimisation to mental healthcare is in its early stages compared to the rest of healthcare. Commonalities between mental healthcare service provision and other services are discussed, and the future research agenda is outlined. We find that the existing application of optimisation in specific healthcare settings can be transferred to mental healthcare. Also highlighted are opportunities for addressing specific issues faced by mental healthcare services

Optimizing Resource Allocation in Surgery Delivery Systems

This thesis focuses on developing mathematical models to optimize processes related to surgery delivery systems. Surgical services account for a large portion of hospital revenue and expenses; moreover, increased demand is expected in the future due in part to the aging population in many countries. Achieving high efficiency in this system is challenging due to the uncertain service durations, the interaction of different stages of the system (e.g., surgery, recovery), and competing criteria (e.g., patient wait time, employee satisfaction, the availability and utilization of healthcare professionals, operating rooms (ORs), and recovery beds). Moreover, solutions must overcome an enormous barrier of computational complexity. Considering the complexity of the problem, and the numerous resources involved in delivering surgical care, this thesis focuses on three aspects of surgery delivery systems: short term scheduling (operational level decisions, e.g., daily sequencing of surgeries), service group team design and staff allocation (strategic level team design decisions on the order of years, and tactical level shift allocation decisions, e.g., monthly), and OR capacity reservation (strategic level decisions, e.g., what OR capacity reservation policy to use in the following years). To optimize scheduling policies on an operational level, we developed a 2-phase approximation method, where the first phase determines the number of ORs to open for the day, and assigns surgeons to ORs. The second phase performs surgical case sequencing considering recovery resource availability. For both phases of the approximation, we provide provable worst-case performance guarantees; furthermore, we use numerical experiments to show the methods also have excellent average case performance. We further developed a mixed integer programming (MIP) model for comparison to the approximation method. We evaluated the performance of the approximation compared to the MIP model in deterministic and stochastic settings, using a discrete even simulation (DES) for the latter. On the strategic and tactical levels, we focus on staffing decisions for surgical nurses. These decisions present a challenge due to nurse availability, skill requirements, hospital regulations, and stochastic surgical demand. We present a MIP to group services into teams, and achieve fairness in training time and overnight surgical volume, and balance size across teams. Once teams are created, we use a MIP-based heuristic to assign shifts to services and teams to ensure coverage of surgical demand. We analyze the performance of the heuristic, and present results that provide insight into optimal surgical nurse staff planning decisions. We show that the newly designed teams are more balanced with respect to the performance metrics, and coverage of surgical demand can be improved. Finally, on the strategic level, we use DES to evaluate OR capacity reservation heuristics. OR capacity reservation is a challenging problem due to uncertain demand for surgery and surgery durations. Using our DES model, we evaluate two categories of approximation methods to gain insights into the problem: first come, first served based heuristics, which are used as benchmarks, and appointment slot reservation heuristics, similar to those used in outpatient clinics. We compare the heuristics based on the mean percent of patients that exceed a predefined surgery access target, mean patient wait time, and mean OR utilization. This research was conducted in collaboration with hospitals, and the problems considered are common to many hospitals. Based on data from these hospitals, we provide evidence that significant improvements could be achieved in the three major decision making levels.PHDIndustrial & Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/137041/1/mbam_1.pd

Stochastic Models of Patient Access Management in Healthcare

abstract: This dissertation addresses access management problems that occur in both emergency and outpatient clinics with the objective of allocating the available resources to improve performance measures by considering the trade-offs. Two main settings are considered for estimating patient willingness-to-wait (WtW) behavior for outpatient appointments with statistical analyses of data: allocation of the limited booking horizon to patients of different priorities by using time windows in an outpatient setting considering patient behavior, and allocation of hospital beds to admitted Emergency Department (ED) patients. For each chapter, a different approach based on the problem context is developed and the performance is analyzed by implementing analytical and simulation models. Real hospital data is used in the analyses to provide evidence that the methodologies introduced are beneficial in addressing real life problems, and real improvements can be achievable by using the policies that are suggested. This dissertation starts with studying an outpatient clinic context to develop an effective resource allocation mechanism that can improve patient access to clinic appointments. I first start with identifying patient behavior in terms of willingness-to-wait to an outpatient appointment. Two statistical models are developed to estimate patient WtW distribution by using data on booked appointments and appointment requests. Several analyses are conducted on simulated data to observe effectiveness and accuracy of the estimations. Then, this dissertation introduces a time windows based policy that utilizes patient behavior to improve access by using appointment delay as a lever. The policy improves patient access by allocating the available capacity to the patients from different priorities by dividing the booking horizon into time intervals that can be used by each priority group which strategically delay lower priority patients. Finally, the patient routing between ED and inpatient units to improve the patient access to hospital beds is studied. The strategy that captures the trade-off between patient safety and quality of care is characterized as a threshold type. Through the simulation experiments developed by real data collected from a hospital, the achievable improvement of implementing such a strategy that considers the safety-quality of care trade-off is illustrated.Dissertation/ThesisDoctoral Dissertation Industrial Engineering 201

Towards facilitated optimisation

Optimisation modelling in healthcare has addressed a diverse range of challenges inherent to decision-making and supports decision-makers in determining the best solution under a variety of constraints. In contrast, optimisation models addressing planning and service delivery issues in mental healthcare have received limited attention. Mental healthcare services in England are routinely facing issues relative to scarcity of available resources, inequities in their distribution, and inefficiencies in their use. Optimisation modelling has the potential to support decision making and inform the efficient utilisation of scare resources. Mental healthcare services are a combination of several subsystems and partnerships comprising of numerous stakeholders with a diversity of interests. However, in optimisation literature, the lack of stakeholder involvement in the development process of optimisation models is increasingly identified as a missed opportunity impacting the practical applicability of the models and their results. This thesis argues that simulation modelling literature offers alternative modelling approaches that can be adapted to optimisation modelling to address the shortcoming highlighted. In this study, we adapt PartiSim, a multi-methodology framework to support facilitated simulation modelling in healthcare, towards facilitated optimisation modelling and test it using a real case study in mental healthcare. The case study is concerned with a Primary Care Mental Healthcare (PCMH) service that deploys clinicians with different skills to several General Practice (GP) clinics. The service wanted support to help satisfy increasing demand for appointments and explore the possibility of expanding their workforce. This research puts forward a novel multimethodology framework for participatory optimisation, called PartiOpt. It explores the adaptation and customisation of the and PartiSim framework at each stage of the optimisation modelling lifecycle. The research demonstrates the applicability and relevance of a 'conceptual model' to optimisation modelling, highlighting the potential of facilitated optimisation as a methodology. This thesis argues for the inclusion of conceptual modelling in optimisation when dealing with real world practice-based problems. The thesis proposes an analytics-driven optimisation approach that integrates descriptive, predictive, and prescriptive analytics stages. This approach is utilised to construct a novel multi-skill multi-location optimisation model. By applying the analytics-driven optimisation approach to the case study, previously untapped resource potential is uncovered, leading to the identification of various strategies to improving service efficiency. The successful conceptualisation of an optimisation model and the quantitative decision support requirements that emerged in the initial stages of the study drive the analytics-driven optimisation. Additionally, this research also presents a facilitative approach for stakeholder participation in the validation, experimentation, and implementation of a mathematical optimisation model. Reflecting on the adaptation and subsequent amendments to the modelling stages, the final PartiOpt framework is proposed. It is argued that this framework could reduce the gap between theory and practice for optimisation modelling and offers guidance to optimisation modellers on involving stakeholders in addressing real world problems