A stochastic optimization model for shift scheduling in emergency departments.

Excessive waiting time in Emergency Departments (ED) can be both a cause of frustration and more importantly, a health concern for patients. Waiting time arises when the demand for work goes beyond the facility's service capacity. ED service capacity mainly depends on human resources and on beds available for patients. In this paper, we focus on human resources organization in an ED and seek to best balance between service quality and working conditions. More specifically, we address the personnel scheduling problem in order to optimize the shift distribution among employees and minimize the total expected patients' waiting time. The problem is also characterized by a multi-stage re-entrant service process. With an appropriate approximation of patients' waiting times, we first propose a stochastic mixed-integer programming model that is solved by a sample average approximation (SAA) approach. The resulting personnel schedules are then evaluated using a discrete-event simulation model. Numerical experiments are then performed with data from a French hospital to compare different personnel scheduling strategies.

Meningioma sampling: how much is enough for the accurate grading of atypical meningiomas?

Meningioma grading relies on several pathological criteria (brain invasion, mitotic count, sheeting, small cell foci, necrosis, macronucleoli and hypercellularity) and histopathological subtypes. Regardless of histopathological subtype, the presence of these pathological parameters can be focally present and not present on each slide of a meningioma. We performed (1) a retrospective work comparing the frequency of parameters used for meningioma grading between two periods with different sampling techniques, and (2) we calculated the probability of presence of each criterion on resected meningiomas entirely processed included and examined. First, we compared two time periods: between 2002-2008 where meningiomas were not all entirely sampled, and between 2012-2018 where all meningiomas were entirely sampled. The frequency of tumour grades was not significantly different between the two periods (p=0.17). Mitosis ≥4/1.6mm2, small cell foci, macronucleoli and hypercellularity were more frequently found when meningiomas were entirely sampled (p<0.05). Second, we focused on 59 grade 2 meningiomas entirely sampled to highlight the distribution of histopathological parameters used for meningioma grading. We have shown that a correct grading of more than 95% of meningiomas can be achieved when at least six slides are examined. Our work suggests that meningioma sampling might be an issue and the sampling system must be specified in research works on grading.