Thierry Garaix

Background In this study, we implemented an indoor positioning system to track the activities of healthcare professionals during their shifts in an emergency department, aiming to gain a better understanding of the emergency care production process. Methods An ultrawideband-based tracking system was used in an experiment at the emergency department of Le Corbusier Hospital in Firminy, France. Over a 46-day period, healthcare professionals, including assistant nurses, nurses, doctors, and managers, wore a sensor to record their location within the emergency department. We analyzed a substantial amount of quasi-real-time data to objectively assess physicians’ time allocation and movement patterns and their correlation with the emergency department’s occupancy. Additionally, we developed a user recognition algorithm (i.e., random forest classifier) capable of detecting the job category of the participant wearing the sensor. Results The proportion of time spent on care-related activities ranges from 26% to 39% for doctors. In contrast, this share reaches approximately half of the time for triage nurses and intensive care unit nurses. The burden of non-care-related activities appears to be largely induced by the time spent on administrative duties and transit. For doctors, the share of non-care-related activities is found to be correlated with the occupancy level. The hourly distance walked by nurses (except triage nurses) is found to increase with occupancy, while for doctors, the walking distance remains invariant to patient load. The random forest classifier predicts job categories with 96% accuracy. Conclusions Indoor tracking systems offer additional perspectives for enhancing the understanding of emergency department systems. The technology tested in this study demonstrates its potential to quantify physicians’ time allocation and movements.

We propose a solution method for online vehicle routing, which integrates a machine learning routine to improve tours’ quality. Our optimization model is based on the Bertsimas et al. (2019) re-optimization approach. Two separate routines are developed. The first one uses a neural network to produce realistic pick-up times for the customers to serve. The second one relies on Q-learning in addition to random walks for the construction of the backbone graph corresponding to the instance problem of each time step. The second routine gives improved results compared to the original approach.

We develop an asymptotic approximation and bounds for the traveling salesman problem with time slots, i.e. when the time windows of points to visit are a partition of a given time horizon. Although this problem is relevant in several delivery applications, operational research researchers did not pay close attention to it, contrary to the extensively studied general formulation with time windows. Exploiting the specificity of this problem allows to solve more efficiently instances which may be hard to solve by specifically designed algorithms for the traveling salesman problem with time windows. The asymptotic analysis of the traveling salesman problem with time slots is a step toward developing new approximations for the general problem with time windows.We discuss this case. We equally provide a formulation of the asymptotic approximation under a worst-case demand distribution of the points to visit, based on the principle of the maximum entropy. Computational results are given for the benchmarks of the literature for which the time slots are randomly generated.

The legal driver rules in the European U nion defines a general framework with restrictions in driving time or working time between breaks and rest periods. These constraints must be addressed for an evaluation of any vehicle trip that met the regulation rules. For many real-world applications, the final trips have to satisfy these rules. The set of EU rules is the most complex design of trips and extension to other rules should be easy following the model we propose here. Compared to previous contributions we provide a new mixed integer linear program, which includes all the weekly rules to schedule when the sequence of visits is fixed. We also provide a new benchmark with detailed optimal solutions. Based on a set of numerical experiments, we discuss the relevance of different simplifications in the model used in the literature.