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A study on the impact of prioritising emergency department arrivals on the patient waiting time

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Abstract

In the past decade, the crowding of the emergency department has gained considerable attention of researchers as the number of medical service providers is typically insufficient to fulfil the demand for emergency care. In this paper, we solve the stochastic emergency department workforce planning problem and consider the planning of nurses and physicians simultaneously for a real-life case study in Belgium. We study the patient arrival pattern of the emergency department in depth and consider different patient acuity classes by disaggregating the arrival pattern. We determine the personnel staffing requirements and the design of the shifts based on the patient arrival rates per acuity class such that the resource staffing cost and the weighted patient waiting time are minimised. In order to solve this multi-objective optimisation problem, we construct a Pareto set of optimal solutions via the 𝜖-constraints method. For a particular staffing composition, the proposed model minimises the patient waiting time subject to upper bounds on the staffing size using the Sample Average Approximation Method. In our computational experiments, we discern the impact of prioritising the emergency department arrivals. Triaging results in lower patient waiting times for higher priority acuity classes and to a higher waiting time for the lowest priority class, which does not require immediate care. Moreover, we perform a sensitivity analysis to verify the impact of the arrival and service pattern characteristics, the prioritisation weights between different acuity classes and the incorporated shift flexibility in the model.

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Notes

  1. The One-Way ANOVA and Bonferroni Post-Hoc tests are applied to conduct this analysis. The assumptions of these tests are fulfilled after executing the Shapiro-Wilk test to check the normal distribution and the Levene’s test for the equality of the variances.

  2. The non-parametric Mann-Whitney U test is applied since the number of daily patients arrivals in a month is limited and thereby the normal distribution is not always approximated.

  3. The One-Way ANOVA and Bonferroni tests are applied since the six assumptions are valid

  4. The Mann-Whitney U statistical test and a Bonferroni Post-Hoc test is applied.

  5. These wage costs are mean annual salaries per hour based on a study of the Bureau of Labor Statistics, US (2016)

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Acknowledgements

We are grateful to the emergency department of the Ghent University Hospital for the permission, useful information and real-life data sets to carry out the case study.

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Authors and Affiliations

  1. Faculty of Economics and Business Administration, Ghent University, Tweekerkenstraat, 2 - 9000, Gent, Belgium

    Ellen Van Bockstal & Broos Maenhout

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  1. Ellen Van Bockstal
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  2. Broos Maenhout
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Correspondence to Broos Maenhout.

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Van Bockstal, E., Maenhout, B. A study on the impact of prioritising emergency department arrivals on the patient waiting time. Health Care Manag Sci 22, 589–614 (2019). https://doi.org/10.1007/s10729-018-9447-5

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