Mathematical Modelling and Cluster Analysis in Healthcare Analytics - The Case of Length of Stay Management

Length of Stay (LOS) is an important metric of care quality and efficiency in hospitals that has been studied for decades. Longer stays lead to increased costs and higher burdens on patients, caregivers, clinicians and facilities. Understanding characteristics of LOS outliers is important for developing actionable steps to address LOS reduction. Our study examines clustering of inpatients using key clinical and demographic attributes to identify LOS outliers and investigates the opportunity to reduce their LOS by comparing order sequences with similar non-outliers in the same cluster. Learning from retrospective data, we develop a mathematical model and a two-stage heuristic algorithm. Results indicate that switching orders in homogeneous inpatient sub-populations within the limits of clinical guidelines may be a promising decision support strategy for LOS management. These novel data-driven insights can be offered as suggestions for clinicians to apply new evidence-based, clinical guideline-compliant opportunities for LOS reduction through healthcare analytics

An analytical approach for improving patient-centric delivery of dialysis services

In this paper, we report on the development of an analytical model and a decision support tool for meeting the complex challenge of scheduling dialysis patients. The tool has two optimization objectives: First, waiting times for the start of the dialysis after the patients’ arrivals must be minimized. Second, the minimization of lateness after the scheduled finish time, which is relevant for transport services, are pursued. We model the problem as a mathematical program considering clinical pathways, a limited number of nurses managing the patients, and dialysis stations. Furthermore, information about patients' drop-off and pick-up time windows at/from the dialysis unit are considered. We develop a platform in Microsoft Excel and implement the analytical model using an Open Source optimization solver. A case study from a dialysis unit in the UK shows that a user can compute a schedule efficiently and the results provide useful information for patients, caregivers, clinicians and transport services

E-HOSPITAL – A digital workbench for hospital operations and services planning using information technology and algebraic languages

In this paper, we describe the development of a unified framework and a digital workbench for the strategic, tactical and operational hospital management plan driven by information technology and analytics. The workbench can be used not only by multiple stakeholders in the healthcare delivery setting, but also for pedagogical purposes on topics such as healthcare analytics, services management, and information systems. This tool combines the three classical hierarchical decision-making levels in one integrated environment. At each level, several decision problems can be chosen. Extensions of mathematical models from the literature are presented and incorporated into the digital platform. In a case study using real-world data, we demonstrate how we used the workbench to inform strategic capacity planning decisions in a multi-hospital, multi-stakeholder setting in the United Kingdom

An analytical approach for improving patient-centric delivery of dialysis services

In this paper, we report on the development of an analytical model and a decision support tool for meeting the complex challenge of scheduling dialysis patients. The tool has two optimization objectives: First, waiting times for the start of the dialysis after the patients’ arrivals must be minimized. Second, the minimization of lateness after the scheduled finish time, which is relevant for transport services, are pursued. We model the problem as a mathematical program considering clinical pathways, a limited number of nurses managing the patients, and dialysis stations. Furthermore, information about patients' drop-off and pick-up time windows at/from the dialysis unit are considered. We develop a platform in Microsoft Excel and implement the analytical model using an Open Source optimization solver. A case study from a dialysis unit in the UK shows that a user can compute a schedule efficiently and the results provide useful information for patients, caregivers, clinicians and transport services

Near real-time bed modelling feasibility study

Hospital bed management is crucial to ensure that patients do not have to wait for the right bed for their care. A simulation model has been developed that mimics the bed management rules applied to the Trauma & Orthopaedic wards of a busy Welsh hospital. The model includes forecasting methodologies to predict the number of emergency admissions, split by gender. The model uses near real-time admission data to see whether patients will be admitted to a given ward on a given day in a 7-day planning horizon. The one-week feasibility pilot study examined the accuracy and usability of the tool. The study has shown that it is possible to correctly predict the short-term processes of a Trauma & Orthopaedic bed management system by accurately forecasting arrivals, using known data and statistical distributions to predict patient length of stay, and applying generic bed management rules to dictate their placement

Planning and scheduling of operating theater under resources constraints: State of the art and future trends and impact on energy consumption

The management of operating theaters is currently the subject of considerable discussion, particularly with regard to the use of human and material resources, which are available in limited quantities. The first part of this paper deals with the management of hospital systems and operating theaters. In the second part, we review the main studies on planning surgical procedures under resources constraints, as well as the different methods for solving planning and scheduling problems in operating theaters. A comparative analysis is carried out in order to identify the fundamental ideas leading to the adoption of a new model capable of meeting the needs and satisfying the different constraints of this management. This article shows that planning and scheduling play a major role in the management of an operating theater, which remains difficult given the multiplicity of determinants involved. In this work, we describe the problem of planning and scheduling operating theaters according to several authors, aiming to evaluate and improve existing operating programs to make them feasible and of good quality. The depletion of the world’s available energy resources requires the construction of hospital buildings that respect the environment and take into account energy efficiency while meeting different needs