Emergency Departments (EDs) must operate in environments characterized by uncertainty and resource constraints. One of their critical challenges is dual-resource scheduling, that is, synchronizing two resources at the same time on a task. For example, taking a blood sample from a child patient requires two nurses, one to take the sample and another to prevent the patient from moving. Addressing this challenge requires structured approaches capable of ensuring both synchronization and prioritization based on patient urgency. This study explores two distinct optimization models for dual-resource scheduling in EDs, namely, a Mixed Integer Linear Programming (MILP) and a Constraint Programming (CP). The MILP model leverages a linear formulation to globally optimize scheduling and resource synchronization, while the CP model exploits constraint satisfaction techniques to handle task dependencies and resource constraints. We test both models on the same case study. Their comparison highlights key differences in computational complexity, variable representation and constraint formulation. The results demonstrate that neither model consistently outperforms the other, but rather, their effectiveness depends on instance size and problem-specific characteristics.

International audience

The Emergency Department (ED) is a principal sector in the hospital that has to make crucial decisions effectively under uncertainties to ensure that the patients receive good quality care. Improving decision-making in ED, especially the resource scheduling decision, becomes one research interest. A promising approach to improve decision-making is by utilising Digital Twin (DT). This context of decision-making in DT is both (i) an opportunity given by the DT which provides data close to real-time and (ii) constrained by the DT which forces to make decisions dynamically rather than statically. That is, our research contributes to the decision layer of DT. More precisely, we propose a decentralised organisation to enhance the resource scheduling decision-making process in ED. This is a multi-agent system with a local dynamic resource scheduling based on a Mixed Integer Linear Programming (MILP) model. This proposition is compared to two other organisations, which are a centralised organisation that optimises the dynamic scheduling MILP globally, and the FIFO sequencing currently performed in the paediatric ED of the University Hospital Centre in Saint-Étienne, France. The results show that the proposed decentralised organisation provides good results quickly and seems promising for improving resource scheduling decision-making in ED with DT support. Note to Practitioners—This research provides an initial study on the approach to improve the decision-making process in the Emergency Department (ED) of the hospital by using Digital Twin (DT). We focus more on improving resource scheduling decisions, which is a part of the decision layer of DT. We propose a decentralised organisation based on a multi-agent approach for solving the resource scheduling problem. Each resource agent, i.e. nurse, can run a local dynamic resource scheduling based on a Mixed Integer Linear Programming (MILP) model. Through our proposition with a centralised model and current practice in ED based on the triage-based First in First Out (FIFO) rule, we can see that our decentralised organisation is a favourable decision organisation in the context of decision improvement with DT, as it is capable of providing favourable results in a short time. This research will be further extended by including different resources and tasks in ED to make the model closer to reality in ED.

Clustering is an unsupervised machine learning method giving insights on data without early knowledge. Classes of data are return by assembling similar elements together. Giving the increasing of the available data, this method is now applied in a lot of fields with various data types. Here, we propose to explore the case of time series clustering. Indeed, time series are one of the most classic data type, and are present in various fields such as medical or finance. This kind of data can be pre-processed by of dimension reduction methods, such as the recent UMAP algorithm. In this paper, a benchmark of time series clustering is created, comparing the results with and without UMAP as a pre-processing step. UMAP is used to enhance clustering results. For completeness, three different clustering algorithms and two different geometric representation for the time series (Classic Euclidean geometry, and Riemannian geometry on the Stiefel Manifold) are applied. The results are compared with and without UMAP as a pre-processing step on the databases available at UCR Time Series Classification Archive www.cs.ucr.edu/~eamonn/time_series_data/.