Applying simulation and DEA to improve performance of emergency department in a Jordanian hospital

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Highlights

  • The performance of emergency department in a Jordanian hospital is improved using simulation and data envelopment analysis.

  • A cellular service system is proposed and utilized for developing ten nurses’ assignment configurations.

  • Simulation runs are conducted for one month period each run with 10 replicates to evaluate performance of each configuration.

  • Aggressive formulation in data envelopment analysis is used to identify the best scenario.

  • The average waiting time is reduced from 195 to 183 min, increasing the number of patients served from 8853 to 8934 patients.

Abstract

The Emergency Department (ED) is considered the most critical department in Jordanian hospitals. Crowdedness and long waiting times of patients in the ED are the most common harmonies problems that hospitals are suffering from. Thus, this study aims at reducing the average waiting time of the patient in the ED, improving the nurses’ utilization, and increasing the number of served patients. A cellular service system is proposed and utilized for developing ten nurse assignment configurations. Simulation is run for a one month period (672 h) each with 10 replicates to evaluate the performance measures for each configuration. The best scenario is then determined using aggressive formulation in Data Envelopment Analysis (DEA). The results showed that the best scenario depends on work load sharing assignments, which results in reducing patient’s average waiting time from 195 to 183 min, increasing the number of patients served from 8853to 8934 patients, and improving the nurses’ utilization from 52% to 62%. In conclusion, nurses’ flexibility in cellular service systems shall provide a great assistance to decision makers in hospitals when improving the performance of ED.

Introduction

Healthcare is a complex configuration that provides primary, secondary and tertiary care. Increases in the cost of healthcare services plays a role in giving an importance and much discussion worldwide and obligates healthcare providers to improve the quality management, efficiency, and economics of their organizations [16]. Hospitals are considered an important tangible sector of the healthcare organizations. In hospitals, Emergency Department (ED) is one of the most crowded departments that bears greater pressure loads in comparing with other components of the health care system. Long waiting times is a common problem for all entities of the health care system. Optimization of patients’ flow and bottleneck elimination in the ED could provide a solution that decreases cost and enhances the quality of care [20].

Simulation is adopted to imitate the current state of any process [4]. Simulation studies within healthcare have been used for a long time to solve bottlenecks related to healthcare in general. Different alternatives depending on the staffing levels and internal processes were studied using simulation model to improve the ED performance and reduce patients waiting time and turn around minimized the patients waiting time by adding appropriate numbers of designated doctors and medical instruments. For example, Ruohonen et al. [19] demonstrated a triage-team method, which makes the operation of the ED effective. Results showed that if the operation is as effective as the staff has estimated, there will be a 26% reduction of the average throughput time. Meng and Spedding [18] used simulation to predict the arrival time of patients and reduce waiting times. Laskowski and Mukhi [17] described an agent based model of an emergency department and its utility for evaluating workflow and assessing patients’ diversion policies. Chockalingam et al. [12] used petri-nets to model patient and resource flow in a hospital system and obtained a stochastic differential equation which models the hospitals proximity to entering a divert state. Weng et al. [21] adopted system simulation to optimize allocation of resources in ED. The overall performance in ED was increased by 8% by new human resources allocation. Cabrera et al. [8] presented an Agent-Based modeling and simulation to design a decision support system (DSS) for the operation of healthcare ED. Optimization is performed to find the configuration of ED staff configuration of doctors, triage nurses, and admission personnel that simultaneously minimizes patients waiting time and maximizes patients throughput.

Data Envelopment Analysis (DEA) is an efficient optimization procedure that is proposed for improving a product/process performance with multiple responses. DEA is a linear programming methodology to measure the efficiency of multiple decision-making units (DMUs) when the production process presents a structure of multiple inputs and outputs [14]. DEA is a fractional mathematical programming technique for measuring the relative efficiency of homogeneous decision making units (DMUs) with multiple inputs and multiple outputs using a single performance measure called “relative efficiency”, which is the sum of the weighted outputs divided by the sum of the weighted inputs. The most popular DEA technique is the CCR model developed by Charnes et al. [10]. Assuming there are n DMUs each with m inputs and s outputs to be evaluated, the CCR model measures the DMU’s relative efficiency once by comparing it to a group of the other DMUs that have the same set of inputs and outputs. Hence, n optimizations are needed. Let the DMU to be individually evaluated on any trial be designated as DMUo; o = 1,  , n. The relative efficiency, Eo, of DMUo with inputs of xio (i = 1,   , m) and outputs of yro (r = 1,  , s) is evaluated by input-oriented CCR model expressed as [11]:Eo=Maxθ=r=1suroyrosubject toi=1mvioxio=1r=1suroyrji=1mvixijj=1,,nu1o,u2o,,uso0v1o,v2o,,vmo0where uro and vio are the virtual weights for the rth output and ith input, respectively, of DMUo and θ is a scalar. The objective function is to maximize the sum of weighted outputs of DMUo. The first constraint is that the sum of weighted inputs is equal to one. The second constraint is that the relative efficiency of each of the n DMUs should be less or equal to one. The DMUo is then identified as CCR-efficient if Eo equals one. Otherwise, DMUo is identified as CCR-inefficient. Weng et al. [22] used simulation and DEA to determine optimal healthcare efficiency allocations. The efficiency was evaluated using the input-oriented CCR model. Three response variables were studies, including doctors, number of nurses and number of beds. The optimal resources were obtained via optimal efficiency and benchmarking. However, Baker and Talluri [7] showed that the CCR model provides misleading efficiency scores by allowing for complete weight flexibility and thus results in identifying a DMU with an unrealistic weighing scheme to be efficient. In addition, when the efficiency scores for some DMUs are equal to one, the CCR model fails to discriminate among efficient DMUs. The aggressive formulation technique can be used to avoid CCR drawbacks [13], [6], [1], [2]. The aggressive formulation technique obtains a weighing scheme of DMUo that would be optimal in CCR model but has as a secondary objective, minimization of the cross-efficiencies of the other DMUs [5], [3]. This model calculates the optimal input and output weights, vio and uro, respectively, of DMUo as follows:Minr=1suro·joyrjsubject toi=1mvio·joxij=1r=1suroyrj-i=1mvioxij0,jor=1suroyro-Eo·i=1mvioxio=0uio,vio0where the Eo is the relative efficiency for DMUo using its own weighing scheme, which is calculated by solving CCR model. In the above model (2), the decision variables are vio and uro. Let Eoj be the cross-efficiency of DMUj calculated according to the optimal weights of DMUo, which are obtained using the CCR model. The Eoj is calculated asEoj=r=1suroyrji=1mvioxijjo

Let the mean cross-efficiency of DMUj be denoted as ej, which is estimated asej=ojEoj/(n-1)j=1,,nOnce the Eoj and ej values are obtained, a matrix called the “cross-efficiencies matrix” is constructed and used for comparing performance of n DMUs. Finally, the cross-efficiencies matrix is established and used for analyzing the performance of the n DMUs. The aggressive formulation technique will be utilized for determining the optimal scenario of nurses’ assignment inside ED.

Cellular Manufacturing (CM) is a model for workplace design. In CM the equipments and workstations are synchronized in an efficient sequence that allows a continuous and smooth movement of inventories and materials to produce products from start to finish in a single process flow, by minimizing transport or waiting time, or any delay for that matter [15], [9]. However, the concept of CM is rarely used in healthcare. This research aims at reducing patients’ average waiting time, increasing the number of patients served, and improving the nurses’ utilization in ED in a Jordanian hospital utilizing CM, or hereafter called cellular service system (CSS). In this research, nurses are considered as operators and the departments are treated as machines. Then, simulation will be used to evaluate each nurse assignment configuration, which is treated as a decision making unit (DMU). Finally, the DMU that improves performance is identified using data envelopment (DEA) techniques. The remaining of this paper is outlined in the following sequence. Section 2 outlines the methodology. Section 3 adopts simulation at current nurse assignment configuration. Section 4 proposes cellular service system in ED. Section 5 carries out improvement analysis. Finally, conclusions are made in Section 6.

Section snippets

Methodology

The ED is a life treating department as well as the most crowded department among the hospital’s departments. This study concentrates on measuring the average waiting time for the patients inside the ED. Moreover, utilization of doctors and nurses is also measured to find out the optimal number of nurses and/or doctors. These two factors affect the number of patients being served inside the ED. Since minimizing waiting time of patients as well as maximizing the utilization of nurses and number

Simulation of ED at current nurse assignment configuration

Fig. 2 maps a patient’s self-arrival process. First of all, the patients go to the reception for the registration and admittance procedures. Then, they move to the triaging area. After that, the patient moves to the required room according to his sickness case. The main ED includes the following rooms:

  • The reception area is the place where patients fill the treatment sheet.

  • Isolation (IS) room controls infected patients from infecting others. IS contains two beds.

  • Patients with chest, stomach,

Proposed cellular service system in ED

The goal of CSS is utilizing nurse flexibility in order to increase the utilization of nursing staff and reduce average time for patients in the ED. CSS is typically designed for dual resource constraint systems, where the number of workers is less than the total number of workstations in the system. Two types of nurse flexibility are considered:

  • 1.

    Inter-room nurse flexibility: refers to the transfer of nurses between ED rooms.

  • 2.

    Intra-room flexibility: relates to nurse transfers between beds within

Research results and discussion

The summary of the obtained results using simulation for performance measures for each scenario are shown in Table 11, where it is noted that:

  • At six nurses, the smallest average time in system is 71.05, which corresponds to scenario one. This scenario reduces the average time by 64% of that at current scenario. However, at this scenario the nurses’ utilization and number of served patients are reduced by 0.98% and 556%, respectively. Further, when seven nurses are assigned the lowest average

Conclusions

This paper implemented successfully simulation and aggressive formulation technique in DEA techniques to improve the performance of the ED in a Jordanian hospital. Four responses are of main interest, including number of nurses, average waiting time in system, nurses’ utilization, and number of served patients. Ten scenarios for nurse assignment configurations are proposed utilizing the concept of nurses’ flexibility in cellular service system. Simulation is run for one month period (672 h) each

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