Controlling excessive waiting times in emergency departments: an extension of the ISA algorithm.

In an emergency department (ED), the demand for service is not constant over time. This cannot be accounted for by means of waiting lists or appointment systems, so capacity decisions are the most important tool to influence patient waiting times. Additional complexities result from the relatively small system size that characterizes an ED (i.e. a small number of physicians or nurses) and the presence of customer impatience. Assuming a single-stage multiserver M(t)/G/s(t) + G queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman and others (2008) as a method to set staffing levels throughout the day. The main advantage of our extension is that it enables the use of performance measures based on the probability of experiencing an excessive waiting time, instead of the common focus on delay probability as a performance metric.Emergency department; Personnel planning; Time-varying arrival rate;

Personnel planning in service systems with nonstationary demand.

1. Introduction 2. Staffing and scheduling with nonstationary demand for service: state of the art 3. Computing the probability of excessive waiting in M(t)/G/s(t) + G queues with an exhaustive service policy 4. Controlling excessive waiting times in small service systems with time-varying demand: an extension of the ISA algorithm 5. A branch-and-bound algorithm for shift scheduling with nonstationary demand 6. Epiloguenrpages: 184status: publishe

Setting staffing levels in an emergency department: opportunities and limitations of stationary queuing models

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A branch-and-bound algorithm for shift scheduling with stochastic nonstationary demand

Many shift scheduling algorithms presume that the staffing levels, required to ensure a target customer service, are known in advance. Determining these staffing requirements is often not straightforward, particularly in systems where the arrival rate fluctuates over the day. We present a branch-and-bound approach to estimate optimal shift schedules in systems with nonstationary stochastic demand and service level constraints. The algorithm is intended for personnel planning in service systems with limited opening hours (such as small call centers, banks, and retail stores). Our computational experiments show that the algorithm is efficient in avoiding regions of the solution space that cannot contain the optimum; moreover, it requires only a limited number of evaluations to encounter the estimated optimum. The quality of the starting solution is not a decisive factor for the algorithm's performance. Finally, by benchmarking our algorithm against two state-of-the-art algorithms, we show that our algorithm is very competitive, as it succeeds in finding a high-quality solution fast (i.e., with a limited number of simulations required in the search phase).publisher: Elsevier articletitle: A branch-and-bound algorithm for shift scheduling with stochastic nonstationary demand journaltitle: Computers & Operations Research articlelink: http://dx.doi.org/10.1016/j.cor.2015.06.016 content_type: article copyright: Copyright © 2015 Elsevier Ltd. All rights reserved.status: publishe

Setting staffing levels in systems with time-varying demand: the context of an emergency department

Many service systems are characterized by time-varying demand for service. For instance in an emergency department, patient arrival rates are usually not constant throughout the day. This arrival process is stochastic, but nonetheless predictable to some extent (a daily pattern can often be distinguished). However, this feature can severely complicate the process of determining appropriate staffing levels throughout the day. In this paper, an overview of available methods for setting staffing levels under timevarying demand for service is given, with the applicability and appropriateness in the specific context of an emergency department as the main point of interest. An important goal of an emergency department is to strive for patient waiting times that are sufficiently low for all patients, independent of the arrival time, and therefore we particularly emphasize the importance of using performance measures related to waiting times.status: publishe

Staffing and scheduling under nonstationary demand for service: a literature review

Many service systems display nonstationary demand: the number of customers fluctuates over time according to a stochastic - though to some extent predictable - pattern. To safeguard the performance of such systems, adequate personnel capacity planning (i.e., determining appropriate staffing levels and/or shift schedules) is often crucial. This article provides a state-of-the-art literature review on staffing and scheduling approaches that account for nonstationary demand. Among references published during 1991-2013, it is possible to categorize relevant contributions according to system assumptions, performance evaluation characteristics, optimization approaches and real-life application contexts. Based on their findings, the authors develop recommendations for further research.publisher: Elsevier articletitle: Staffing and scheduling under nonstationary demand for service: A literature review journaltitle: Omega articlelink: http://dx.doi.org/10.1016/j.omega.2015.04.002 content_type: article copyright: Copyright © 2015 Elsevier Ltd. All rights reserved.status: publishe

Controlling excessive waiting times in emergency departments: an extension of the ISA algorithm

In an emergency department (ED), the demand for service is not constant over time. This cannot be accounted for by means of waiting lists or appointment systems, so capacity decisions are the most important tool to influence patient waiting times. Additional complexities result from the relatively small system size that characterizes an ED (i.e. a small number of physicians or nurses) and the presence of customer impatience. Assuming a single-stage multiserver M(t)/G/s(t) + G queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman and others (2008) as a method to set staffing levels throughout the day. The main advantage of our extension is that it enables the use of performance measures based on the probability of experiencing an excessive waiting time, instead of the common focus on delay probability as a performance metric.status: publishe

Controlling excessive waiting times in small service systems with time-varying demand: an extension of the ISA algorithm

In many service systems, the arrival pattern is not constant throughout the day. This raises the question how staffing decisions should be adapted in view of controlling customer's waiting times. Assuming a single-stage queueing system with general abandonment and service times and time-varying demand for service, we suggest a method inspired by the simulation-based Iterative Staffing Algorithm (ISA) proposed by Feldman et al. (2008). The main advantage of our extension is that it enables to control the probability of experiencing an excessive waiting time, in particular in small systems. © 2012 Elsevier B.V.status: publishe

A decision support system for capacity planning in emergency departments

In this article, we present a decision support system (DSS) for improving patient flow in emergency departments (EDs). The core of the system is a discrete-event simulation (DES) model that aims to support capacity planning in the ED, in view of controlling patients’ length of stay (LOS). Conceptually, it regards the patient LOS as the result of different queueing systems, the behavior of which is influenced by different types of capacities. Taking inputs from ED patient record data, the DSS allows to analyze the impact of different capacity changes on patient flow, and to detect efficient capacity combinations using data envelopment analysis (DEA). We report on the insights obtained from a case study in a large regional hospital in Belgium.status: publishe

A Markov model for measuring service levels in nonstationary G(t)/G(t)/s(t)+G(t) queues

We present a Markov model to approximate the queueing behavior at the G(t)/G(t)/s(t)+G(t) queue with exhaustive discipline and abandonments. The performance measures of interest are: (1) the average number of customers in queue, (2) the variance of the number of customers in queue, (3) the average number of abandonments and (4) the virtual waiting time distribution of a customer when arriving at an arbitrary moment in time. We use acyclic phase-type distributions to approximate the general interarrival, service and abandonment time distributions. An efficient, iterative algorithm allows the accurate analysis of small- to medium-sized problem instances. The validity and accuracy of the model are assessed using a simulation study.nrpages: 29status: publishe