Improving patient outcomes and reducing healthcare costs
Our researchers have helped to improve patient outcomes in the healthcare sector in the UK and Germany. Using mathematical methods, an increase in efficiency in hospitals and in the delivery of mental health care has been achieved.

Increasing demand on healthcare systems requires innovative resource management to improve patient outcomes while remaining cost-effective. Our research into mathematical modelling techniques has been used by Welsh NHS Health Boards to improve patient outcomes and the delivery of services.
Close collaboration through the Cardiff and NHS Wales innovative researchers-in-residence programme, and via international partnership with University Hospital Munich, enabled efficient design of hospitals, improved the efficiency and effectiveness of mental health outreach teams, and reduced pressure ulcers. This led to significant cost savings in both UK’s NHS and in the German healthcare system.
Research
Healthcare systems typically operate in environments of uncertainty and variability within highly complex and connected networks. Hundreds of patients may pass through different care pathways each day, each of whom require varying resources to treat them efficiently and effectively. Our Operational Research (OR) group has used mathematical modelling to improve health outcomes and service delivery. Our modelling is used to forecast demand, schedule clinics, calculate the required workforce size and mix of skills to correctly roster staff, schedule operating theatres and assignment of surgeons, and reduce waiting times and cancellations.
Meeting healthcare needs
Patient movements through healthcare systems can be represented by networks of queues that are constrained by available resources. Our team’s modelling approach captures resource needs and risk predictors that enable better prediction of service times in healthcare settings. Further research by our team has also helped to determine the required workforce size and mix of skills to correctly roster staff and schedule resources by approximating patient length of stay and resource capacity.
We also optimised the use of equipment in healthcare settings with a strategic decision support tool. Use of our modelling means that processes can be performed quickly, efficiently and in an environmentally friendly way by hospital planners without highly specialised expertise.
E-HOSPITAL
Healthcare settings require decision-making at every level, from strategic decisions around staffing levels and equipment, to effective triaging of patients day-to-day. Our OR group, in collaboration with healthcare providers at Aneurin Bevan University Health Board, have worked extensively since 2014 to develop a software suite able to address the complex needs of healthcare providers. Our research was extended with the creation of a novel comprehensive modelling platform known as E- HOSPITAL which combines strategic, tactical, and operational decision levels for healthcare operations.
This unique and innovative partnership has delivered considerable impact in developing and applying OR methods for improving our NHS services and patient outcomes.
The modelling unit’s work has led to better planning and better analysis: far better decisions are made as a result of the input of the modellers.
Publications
Harper PR, Knight VA and Marshall AH (2012). ‘Discrete Conditional Phase-type Models Utilising Classification Trees: Application to Modelling Health Service Capacities’. European Journal of Operational Research 219(3): 522-530. doi: 10.1016/j.ejor.2011.10.035.
Harper PR, Powell NP and Williams JE (2009). ‘Modelling the Size and Skill-mix of Hospital Nursing Teams’. Journal of the Operational Research Society 61(5): 768-779. doi: 10.1057/jors.2009.43.
Gartner D and Padman R (2019). ‘Flexible Hospital Wide Elective Patient Scheduling’. Journal of the Operational Research Society, 71 (6): 878-892. doi: 10.1080/01605682.2019.1590509.
Gartner D, Zhang Y and Padman R (2019). ‘Reducing clinical workload in the care prescription process: Optimization of order sets’. IMA Journal of Management Mathematics 30(3): 305-321. doi:10.1093/imaman/dpy018.
Edenharter GM, Gartner D and Pförringer D (2017). ‘Decision Support for the Capacity Management of Bronchoscopy Devices: Optimizing the Cost-Efficient Mix of Reusable and Single-Use Devices Through Mathematical Modelling’. Anesthesia & Analgesia, 124(6):1963– 1967. doi: 10.1213/ANE.0000000000001729.
Gartner D and Padman R (2017). ‘E-HOSPITAL – A Digital Workbench for Hospital Operations and Services Planning Using Information Technology and Algebraic Languages.’ Studies in Health Technology and Informatics 245: 84-88. PMID: 29295057.