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Modeling the arrival process to an Emergency Department (ED) is the firststep of all studies dealing with the patient flow within the ED. Many of themfocus on the increasing phenomenon of ED overcrowding, which is afflictinghospitals all over the world. Since Discrete Event Simulation models are oftenadopted with the aim to assess solutions for reducing the impact of thisproblem, proper nonstationary processes are taken into account to reproducetime-dependent arrivals. Accordingly, an accurate estimation of the unknownarrival rate is required to guarantee the reliability of the results. In thiswork, an integer nonlinear black-box optimization problem is solved todetermine the best piecewise constant approximation of the time-varying arrivalrate function, by finding the optimal partition of the 24 hours into a suitablenumber of non equally spaced intervals. The black-box constraints of theoptimization problem make the feasible solutions satisfy proper statisticalhypotheses; these ensure the validity of the nonhomogeneous Poisson assumptionabout the arrival process, commonly adopted in the literature, and preventmixing overdispersed data for model estimation. The cost function includes afit error term for the solution accuracy and a penalty term to select anadequate degree of regularity of the optimal solution. To show theeffectiveness of this methodology, real data from one of the largest Italianhospital EDs are used.

Determining the optimal piecewise constant approximation for the Nonhomogeneous Poisson Process rate of Emergency Department patient arrivals