Mathematical modelling for the scheduling of outpatient telemedicine appointments

Marshall, Charlotte 2025. Mathematical modelling for the scheduling of outpatient telemedicine appointments. PhD Thesis, Cardiff University. Item availability restricted.

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Abstract

With telemedicine coming to the forefront during the COVID-19 pandemic, flexi bility in terms of methods of care delivery has emerged. This thesis investigates the optimisation of the scheduling of outpatient healthcare appointments via three different methods of delivery: traditional face-to face, video conferencing platforms, and telephone. The problem is first introduced, inspired by the collaboration with TEC Cymru, a team within NHS Wales which introduced and supported the use of video confer encing during the COVID-19 pandemic. Motivation and background information is explored, including the related literature in the field of scheduling telemedicine appointments and, more generally, the scheduling of outpatient appointments. The chosen approach is then identified, explaining why it is applicable to this problem and how it can be applied. A discrete-time deterministic optimisation model is proposed with the aim to max imise both patient and clinician preferences for delivery mode. This formulation assigns appointments to timeslots within a time horizon, with the problem becom ing large when a large number of timeslots are required. This becomes especially relevant when large time horizons are considered, or when appointment durations differ significantly. To address this challenge, a flow-based deterministic formula tion is proposed, where appointments are instead assigned an ordering, eliminating the need for timeslots. Instances are generated to test and compare these two for mulations, identifying which is more applicable and efficient for different sizes of problem. Real-world clinics are likely to be subject to different sources of uncertainty and so a discrete-event simulation model is proposed to verify and validate schedules created by models within this thesis. This allows for the testing of schedules generated by the optimisation models within this thesis for robustness against uncertainty. Test instances informed by clinical practice are generated, with results indicating the need to consider uncertainty to improve key performance indicators such as patient waiting time, clinician overtime, and clinician idle time. ii To address this, a newsvendor model is first introduced to estimate the number of dummy appointments to schedule emergency walk-in patients. These dummy appointment slots are left empty to ensure clinicians are available to emergency walk-in patients during this time. The resulting schedules from this newsvendor model extension are then compared to the deterministic model using the discrete event simulation model. Results show that the newsvendor extension improves key performance indicators when the emergency walk-in patients are the only source of uncertainty considered in the simulation model. When other sources of uncertainty are included within the simulation model, the impact of the newsvendor model extension to the performance of the schedule is limited, indicating the need for more sources of uncertainty to be considered when scheduling patients. Appointment duration and no-shows were identified as factors which could sig nificantly impact a schedule’s performance. This motivated the development of a two-stage stochastic programming model which considers these uncertainties. Three iterations of this stochastic model are developed, each with one more key perfor mance indicator minimised within the second-stage. The first stage of this model aims to maximise patient and clinician preferences for delivery mode, while the second stage minimises key performance indicators. Finally, all iterations of the model, deterministic and stochastic are compared using the simulation, testing how well each schedule performs and assessing how practical these models are for use within an NHS clinic. The mathematical modelling pre sented in this thesis provides decision makers within healthcare and other fields an efficient tool to schedule appointments and meetings while maximising preferences for delivery method

Item Type:	Thesis (PhD)
Date Type:	Completion
Status:	Unpublished
Schools:	Schools > Mathematics
Uncontrolled Keywords:	1. Scheduling 2. Telemedicine 3. Healthcare Appointments 4. Optimisation 5. Stochastic Programming 6. Operational Research
Date of First Compliant Deposit:	17 April 2026
Last Modified:	17 Apr 2026 11:07
URI:	https://orca.cardiff.ac.uk/id/eprint/186444

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