Constructing operating theatre schedules using partitioned graph colouring techniques

ABSTRACT

In hospitals, scheduled operations can often be cancelled in large numbers due to the unavailability of beds for post-operation recovery. Operating theatre scheduling is known to be an $\mathcal{N}\mathcal{P}$-hard optimisation problem. Previous studies have shown that the correct scheduling of surgical procedures can have a positive impact on the availability of beds in hospital wards, thereby allowing a reduction in number of elective operation cancellations. This study proposes an exact technique based on the partitioned graph colouring problem for constructing optimal master surgery schedules, with the goal of minimising the number of cancellations. The resultant schedules are then simulated in order to measure how well they cope with the stochastic nature of patient arrivals. Our results show that the utilisation of post-operative beds can be increased, whilst the number of cancellations can be decreased, which may ultimately lead to greater patient throughput and reduced waiting times. A scenario-based model has also been employed to integrate the stochastic-nature associated with the bed requirements into the optimisation process. The results indicate that the proposed model can lead to more robust solutions.

KEYWORDS:

• OR in health services
• optimisation
• scheduling
• graph colouring
• integer programming

Acknowledgments

The authors would like to thank Andrew Nelson at the case study hospital for providing information and data related to this problem.

Disclosure statement

No potential conflict of interest was reported by the authors.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The authors would like to give thanks to Health and Care Research Wales, who funded this research under grant number [1136].