Primary Care Patient Scheduling under Uncertainty

Project reference: MN74

Application deadline: 10th April 2023

How to apply

Primary Care General Practice (GP) services in England are under pressure as never before: an ageing population, the COVID pandemic, and increasing numbers of patients with complex multi morbidities mean that services are facing significant pressures. NHS England are expecting primary care services to do more for less whilst ensuring the delivery of personalised care and ensuring the best outcomes for patients. GPs collect large amounts of patient appointments data. However, this data is not currently used in a systematic and structured manner for planning purposes. As a result, appointment times are often either under- or over-estimated, resources are misallocated and uncertainty around cancellations is not properly managed, leading to suboptimal planning, poor prioritisation, and long waiting times.

The overall goal of this project is to improve GP appointment scheduling across all of NHS England by helping GPs to make data-driven planning decisions. In addition to the obvious societal impact, the models, algorithms, and case studies will be published in top operation research journals, such as: Management Science, European Journal of Operational Research and Journal of Operations Management.

Detailed project description:

The aim of this research is to devise GP appointment planning policies for dealing with waiting lists and uncertainty of events The project will develop mathematical models and algorithms to evaluate policies and produce optimal scheduling in terms of priority, sequencing, length of appointment and practitioner/nurse. In particular, the main decisions include determining the optimal number of GPs, nurses and required equipment to attend patients within approved waiting time standards. The complicating element of this problem is uncertainty in visit duration and number/types of visits. Existing works in the literature (Kuiper & Lee 2022; Marynissen & Demeulemeester, 2019) either lack incorporating key factors such as uncertainty of data or are not able to solve real size problems to optimality. Moreover, the focus of the literature is mainly on operating room scheduling and significantly less attention has been paid to primary care.

Optimal allocation of staff and resources is one of key factors contributing towards improving health inequality particularly Geography inequality. To this end, an optimisation model will be developed to find the optimal level of resources which may include GPs, nurses, rooms, and equipment.

Research questions

1. What are the key components that have major impact on planning for primary care?

2. What are uncertain parameters and how are their characteristics I.e., what are major factors impacting uncertain parameters. And how to deal with uncertainty?

3. How do these components interact with each other? How can they be mathematically modelled?

4. How can the problem be mathematically formulated as a whole?

5. Can it be efficiently reformulated within simulation-optimisation framework?

6. What is the most efficient solution method to solve the resulting problem?


Kuiper A. and Lee, R. (2022) Appointment Scheduling for Multiple Servers, Management Science, 68(10) 7422–7440.
Marynissen, J. and Demeulemeester, E. (2019) Literature review on multi-appointment scheduling problems in hospitals, European Journal of Operational Research, 272(2) 407-419