Timeslot allocation for waiting list control

Timeslot allocation for waiting list control: Tactical planning of orthopaedic surgeons at the Sint Maartenskliniek

van der Vlugt, Yanna (TU Delft Electrical Engineering, Mathematics and Computer Science)

van Essen, J.T. (mentor)

Delft University of Technology

Applied Mathematics

2021-10-26

Patients visiting a hospital for elective surgery often have multiple consultations with a surgeon before undergoing surgery. Hospitals discern between different types of consultations, and make a schedule allocating timeslots of outpatient department sessions to these different consultation types several weeks in advance. Changing the proportion of consultation types affects the patient waiting lists for both consultations and surgery. However, the precise consequences of such interventions are uncertain, as not all patients follow the same treatment pathway. Furthermore, as these planning decisions are made far in advance, they are based on an uncertain prediction of future waiting lists. The goal is to use these interventions to control waiting lists, in order to reduce waiting times for patients and ensure that all available time capacity in the outpatient department and operating room is used. This problem is referred to as the timeslot allocation problem. In this thesis, we study the performance of various solution methods in achieving this goal.

The problem is modelled as a Markov decision process (MDP). As the state space is very large, the problem does not admit an exact solution. Therefore, least-squares policy iteration is used to find an approximate solution. We also formulate an (integer) linear program which is used to solve a deterministic variant of the MDP, and investigate some simple decision rules.

This thesis features a case study at the Sint Maartenskliniek, a hospital focusing on orthopaedic care in Nijmegen, the Netherlands. Data from the hospital is used to make a simulation with which solution methods can be tested and compared. We find that all methods improve on the static roster method used by the hospital, with the linear program leading to the best results. Furthermore, planning less far ahead allows for a better prediction of the state for which to plan, and so also leads to better performance. In the case of SMK, we recommend fixing 60\% of the timeslots using a static roster method 12 weeks in advance, and using the integer linear program to schedule the remaining 40\% of appointments 6 weeks in advance.

Optimization
Least squares policy iteration
Reinforcement learning
Healthcare planning
Linear programming
Markov Decision Process

http://resolver.tudelft.nl/uuid:e2571b9b-59fb-4419-addb-ec911247f3d0

Student theses

master thesis

© 2021 Yanna van der Vlugt