A robust LP-based approach for a dynamic surgical case scheduling problem with sterilisation constraints

Abstract

The purpose of this article is to investigate a practical scheduling problem in which a group of elective surgical cases are scheduled over time, while considering their unpredictable durations and potential delays in the sterilisation of surgical instruments. The primary objectives were to schedule the maximum number of surgeries and decrease overtime for the surgical staff, as well as limit the number of instruments requiring emergency sterilisation. The study was conducted in collaboration with the University Hospital of Angers in France, which also contributed historical data for the experiments. We propose two robust mixed integer linear programming models, which are then solved iteratively through a rolling horizon approach, in which the objective functions are taken into account in lexicographic order. Experiments on randomly generated instances indicated which of the two approaches had better performance. Comparison of the results for a real-world scenario involving actual planning at the hospital indicated a greater than 69% decrease in overtime, and a minimum of 92% fewer stressful situations in the sterilising unit.

Keywords:

• Operations research
• elective surgeries scheduling
• mixed-integer linear programming
• rolling horizon approach
• robust scheduling
• relax-and-fix heuristic

Acknowledgments

We thank L. Hubert, A.V. Lebelle, and A. Robelet from the CHU for submitting this challenging problem to us, and kindly providing us with a real instance. This research was partially founded by Angers Loire Metropole and Institut Mines-Telecom Atlantique.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Owing to the nature of the research and ethical reasons, supporting data are not available.

Additional information

Notes on contributors

H. Al Hasan

Hasan Al Hasan is an associate professor at Université Catholique de l'Ouest (France). He is a member of the research laboratory LARIS and received his Ph.D. from Université d'Angers (France). His main research interests are the applications of operations research methods in health care and industry optimisation problems.

C. Guéret

Christelle Gueéret holds a Full Professor position at Université d'Angers (France) and is member of the research laboratory LARIS. She received her Ph.D. in Operations Research from the Universiteé de Technologie de Compieégne (France). Her research interests focus on the optimisation of logistic and production systems, in particular, on scheduling and vehicle routeing problems, mainly in the area of health, energy and environment.

D. Lemoine

David Lemoine is a Full Professor at IMT-Atlantique (France) and a member of the Laboratory of Digital Sciences of Nantes (LS2N-UMR CNRS 6004). His research activities focus mainly on production optimisation problems, more particularly on tactical planning optimisation and decision synchronisation in manufacturing, such as consideration of maintenance policies in constraint-based Master Production Scheduling (MPS) formulation problems.

D. Rivreau

David Rivreau is Dean of Faculty of Sciences and full professor at Université Catholique de l'Ouest (France). He is a member of the research laboratory LARIS and received his Ph.D. from Univestité de Technologie de Compiègne (France). His research interests mainly focus on exact methods for scheduling problems with applications in industry and healthcare.