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Developing emergency department physician shift schedules optimized to meet patient demand

Published online by Cambridge University Press:  11 February 2015

David W. Savage ,
Douglas G. Woolford ,
Bruce Weaver  and
David Wood
David W. Savage*
Affiliation:
Northern Ontario School of Medicine, Lakehead University, Thunder Bay, ON
Douglas G. Woolford
Affiliation:
Department of Mathematics, Wilfrid Laurier University, Waterloo, ON
Bruce Weaver
Affiliation:
Northern Ontario School of Medicine, Lakehead University, Thunder Bay, ON
David Wood
Affiliation:
Northern Ontario School of Medicine, Lakehead University, Thunder Bay, ON Emergency Department, Thunder Bay Regional Health Sciences Centre, Thunder Bay, ON
*
Correspondence to: Dr. David Savage, Northern Ontario School of Medicine, Lakehead University, 955 Oliver Road, Thunder Bay, ON P7B 5E1; [email protected].

Abstract

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Objectives: 1) To assess temporal patterns in historical patient arrival rates in an emergency department (ED) to determine the appropriate number of shift schedules in an acute care area and a fast-track clinic and 2) to determine whether physician scheduling can be improved by aligning physician productivity with patient arrivals using an optimization planning model.

Methods: Historical data were statistically analyzed to determine whether the number of patients arriving at the ED varied by weekday, weekend, or holiday weekend. Poisson-based generalized additive models were used to develop models of patient arrival rate throughout the day. A mathematical programming model was used to produce an optimal ED shift schedule for the estimated patient arrival rates. We compared the current physician schedule to three other scheduling scenarios: 1) a revised schedule produced by the planning model, 2) the revised schedule with an additional acute care physician, and 3) the revised schedule with an additional fast-track clinic physician.

Results: Statistical modelling found that patient arrival rates were different for acute care versus fast-track clinics; the patterns in arrivals followed essentially the same daily pattern in the acute care area; and arrival patterns differed on weekdays versus weekends in the fast-track clinic. The planning model reduced the unmet patient demand (i.e., the average number of patients arriving at the ED beyond the average physician productivity) by 19%, 39%, and 69% for the three scenarios examined.

Conclusions: The planning model improved the shift schedules by aligning physician productivity with patient arrivals at the ED.

Résumé

Objectifs: L'étude avait pour objectifs de: 1) évaluer dans le temps, d'après des données historiques, l'affluence des patients dans un service des urgences (SU) afin de déterminer l'horaire de roulement des médecins dans une zone de soins impératifs et dans un service de traitement rapide et 2) déterminer s'il serait possible d'améliorer l'horaire des médecins en adaptant leur productivité à l'affluence des patients selon un modèle d'optimisation de la planification.

Méthode: Des données historiques ont fait l'objet d'une analyse statistique afin de déterminer si le nombre de patients arrivant au SU variait selon les jours de la semaine, les fins de semaine, ou les fins de semaine de congé. Nous avons utilisé des modèles additifs généralisés, reposant sur le processus de Poisson, pour élaborer des modèles d'affluence des patients tout le long de la journée. Un modèle mathématique de programmation a servi à élaborer un horaire de roulement optimal au SU en fonction de l'affluence estimée des patients. II y a eu comparaison de l'horaire actuel de travail des médecins avec trois scénarios de roulement: 1) un horaire modifié, produit par le modèle de planification; 2) l'horaire modifié, prévoyant l'ajout d'un médecin dans la zone de soins impératifs; et 3) l'horaire modifie, prévoyant l'ajout d'un médecin au service de traitement rapide.

Resultats: L'analyse a revele que l'affluence des patients variait selon qu'il s'agissait des soins imperatifs ou du traitement rapide; l'affluence etait a peu pres stable, tous les jours, dans la zone de soins imperatifs, tandis que l'affluence variait selon les jours de la semaine ou les fins de semaine au service de traitement rapide. Le modele de planification a permis de reduire le nombre de demandes non satisfaites (c'est-a-dire le nombre moyen d'arrivees au SU, superieur a la productivity moyenne des medecins) de 19%, de 39%, et de 69% dans les trois scenarios etudies.

Conclusion: Le modele de planification a permis d'ameliorer les horaires de roulement en adaptant la productivity des medecins a l'arrivee des patients au SU.

Keywords

mathematical programmingpatient arrivalspatient demandphysician scheduling
Type
Original Research
Information
Canadian Journal of Emergency Medicine , Volume 17 , Issue 1 , January 2015 , pp. 3 - 12
Copyright
Copyright © Canadian Association of Emergency Physicians 2014 

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