A simulation optimization approach for integrated resource allocation in an emergency department,pharmacy,and lab

Abstract

In this paper, we presented a simulation optimization approach toward optimizing resource allocation in Firoozgar Emergency Department, Tehran, Iran. Most of the departments have interactions in healthcare systems. Therefore, modeling one isolated department such as the emergency department is not acceptable. Since laboratories, radiology departments, and pharmacies have high interactions with emergency departments, clinical pathway was used as a key for the integrated simulation of the emergency department in this paper. Simulation model was validated using real data. In emergency departments, there are various patients with different priorities. Thus, there should be different response variables, i.e. a multi-response optimization problem. Here, a new approach using the design of experiments, data envelopment analysis, multi-layer perceptron artificial neural network, and radial basis function was presented for optimizing the resource allocation problem. Since resources in healthcare are costly and limited, budget and resource constraints were applied in the model. The framework presented in this study is applicable to any healthcare department.

Keywords

Emergency department resource allocation clinical pathway discrete event simulation data envelopment analysis artificial neural network

1. Introduction

Healthcare systems and managers face different challenges such as high costs, high demands for service, and limited budget and healthcare resources [1]. However, there is higher pressure on emergency departments (EDs), because the patient arrival rate into EDs is stochastic; their health status is critical or may become critical most of the time; and they need a fast examination [2]. Consequently, it is necessary to reduce the patients’ waiting time by considering resource constraints. Healthcare managers need to decrease patients’ waiting time (considering patients’ priorities), increase staff utilization, and patient’s satisfaction. They also need to evaluate the impact of staff level changes on the performance of the department; in other words, they require a tool for what-if analysis. Joustra et al. [3] reduced the access times of an endoscopy department using discrete event simulation (DES) and linear programming. They showed that it is possible to improve the department’s performance without requiring additional resources.

Researchers have used different methods, e.g. DES, mathematical programming, and queue theory to improve the performance of a single department. Nevertheless, some other have pointed out the importance of integrated evaluations, because there are interactions between departments, and modeling a single department without considering interactions will not be accurate [4]. Although there are many tools for planning, since healthcare systems are complicated and most of the parameters are stochastic, simulation is an acceptable tool [5].

There are several tools for evaluating, improving, and optimizing numerous types of processes, and computer simulation is one them. The use of simulation in healthcare systems is not new. Researchers, especially non-academic healthcare practitioners, have been using simulation as a decision support technique for almost four decades.

Kirtland et al. [6] simulated an emergency department in order to minimize the patients’ length of stay. Lowery [7] presented an introduction to simulation in healthcare and discussed challenging issues associated with conducting simulation in healthcare as well as the importance of simulation usage in healthcare. Rau et al. [8] employed DES as an effective tool for strategic capacity planning for an outpatient therapy clinic. They showed that average waiting time for new patients would decreased if they were given priority over returning patients. Jun et al. [9] presented a survey on the application of DES in healthcare and explained the successes and failures in some cases. Benneyan [10] discussed the use of simulation analysis for studying and improving healthcare systems through a case study concerning pediatric waiting times and illustrated the typical steps involved in a simulation study. Eldabi et al. [11] revealed that simulation may not be considered as a technique for deriving solutions to certain problems. In fact, via a case study in a cancer clinic, they concluded that simulation is a tool for understanding the problem and improving systematic debate between the problem owners. Sepúlveda et al. [12] incorporated Arena simulation package to evaluate the impact of alternative floor layouts in a cancer treatment center and, at the end, increased patient throughput by 30% with the same resources. Sanchez et al. [13] provided statements outlining several key factors for success in healthcare simulation projects. Weng and Houshmand [14] presented a system analysis of a clinic by considering variable expenses and patient revenues using Arena computer simulation package.

The ED is one the most important parts of healthcare systems. Since patients’ health status in EDs is critical or may become critical most of the time, the response time of EDs is highly important. Many researchers used simulation to minimize patient flow time or waiting time in EDs. Saunders et al.’s [15] computer simulation is a potentially useful tool that can help predict the results of changes in an ED system without actually altering it, and may have implications for planning, optimizing resources, and improving the efficiency and quality of care. Robert et al. [16] compared the performance of DES and artificial neural network (ANN) for estimating the mean and variance of patients’ waiting time in an EDs.

Table 1
Characteristic comparison chart

Study	Mathematical modeling	DES	Integrated modeling	Case study	Meta heuristics	DEA	ANN	MRO
Zeinali et al. [32]		$\surd$		$\surd$	$\surd$		$\surd$
Zeng et al. [21]		$\surd$		$\surd$
Eskandari et al. [23]		$\surd$		$\surd$
Konrad et al. [24]		$\surd$		$\surd$
Weng et al. [26]		$\surd$		$\surd$
Abo-Hamad and Arisha [28]		$\surd$		$\surd$
Ahmed et al. [51]		$\surd$		$\surd$	$\surd$
Hulshof [4]	$\surd$		$\surd$	$\surd$	$\surd$
Robert et al. [16]		$\surd$		$\surd$	$\surd$		$\surd$
This study		$\surd$	$\surd$	$\surd$		$\surd$	$\surd$	$\surd$

DES: Discrete Event Simulation; DEA: Data envelopment analysis; ANN: Artificial neural network; MRO: Multi response optimization.

Draeger [17] utilized simulation to evaluate the process performance and preview the effects of nurse staffing and patient flow changes on an ED system. Rossetti et al. [18] tested alternative ED attending physician staffing schedules and analyzed the corresponding impacts on patient throughput and resource utilization in an ED using computer simulation. Samaha et al. [19] presented a computer simulation model of the operations in an ED in order to reduce the length of stay. They concluded that the main problem was process-related not resource-dependent. Yeh and Lin [20] used computer simulation and genetic algorithm in order to make appropriate adjustments to the nurses’ schedules and reduce patients’ queue time in an ED. They first incorporated simulation for modeling the problem. After gathering simulation results, they used genetic algorithm to find a near-optimal nurse schedule based on minimizing the patients’ queue time. Zeng et al. [21] presented a simulation model to estimate the optimal number of resources and equipment in order to minimize patients’ waiting time. Taboada et al. [22] introduced an agent-based decision support system for a hospital ED. Eskandari et al. [23] proposed a new framework which integrated the simulation model of patients’ flow process with the group analytical hierarchy process (AHP) and the technique for order preference by similarity to ideal solution (TOPSIS) decision models in order to evaluate and rank scenarios based upon desired performance measures. They reduced the average waiting time of non-fast-track patients by 42.3%. Konrad et al. [24] created a DES model and tested 17 scenarios to estimate the likely impact of a split-flow process redesign, including staffing level changes and patient volume changes. The scenarios were compared in terms of door-to-doctor time and length of stay (LOS) for different patient acuity levels. Finally, the best scenario for the ED was determined. Ghanes et al. [25] utilized DES in order to optimize the resource staffing levels of an ED in France. They minimized average LOS by integrating the staffing budget constraint and a constraint securing that the most severe incidents will see a doctor within a specified time limit. Weng et al. [26] adopted computer simulation to find the optimal allocation of resources in an ED to smoothen the flow of ED. Cabrera et al. [27] presented an agent-based modeling simulation to design a decision support system (DSS) and used exhaustive search (ES) optimization to find out the optimal ED staff configuration. Abo-Hamad and Arisha [28] proposed a new simulation-based decision support framework. They incorporated simulation to examine the impact of potential alternatives and balanced score card (BSC) to support continual and sustainable improvement in an ED. Since there are interactions between departments in the healthcare system, most of the researchers in this field acknowledged that modeling one department without considering interactions and relations between departments is not acceptable, and there is a need for integrated modeling of the healthcare system.

Hulshof [4] presented some challenges in integrated decision making in health care. Ghanes et al. [29] proposed a simulation-based optimization algorithm to minimize average LOS in an ED under a budget constraint. Wang and Lee [30] introduced a multi-objective simulation optimization model for a resource allocation problem in an ED. Keshtkar and Moradi [31] used DES software Arena to compare four different scenarios in an ED in order to reduce the patients’ waiting time. Besides quantitative criteria, they considered some qualitative criteria in their model. Zeinali et al. [32] utilized a simulation-based meta-modeling approach to optimize an ED resource level. They compared their model results with OptQuest ${}^{\text{TM}}$ results and reduced the patients’ waiting time by 48%.

Table 1 presents the characteristics of this study and compares it with studies which merely considered capacity planning in only one department without taking into account other departments’ interactions. In this study, we considered multiple departments, other departments’ interactions, and multi-response variables which transformed the problem into multi-response optimization (MRO).

The rest of this paper is organized as follows: Section 2 presents the method employed in this study including simulation phase and MRO phase. Section 3 discusses the results and explains the performance of the approach used in this study. Finally, Section 4 concludes the paper.

2. Method

In this paper, a new approach was presented to optimize resource allocation in an ED. Figure 1 presents the structure of this study.

2.1 Simulation

EDs are complicated systems and uncertainty is one of their major characteristics. Using DES in order to test the results of changes to resource levels is accepted and reported in the literature. In this paper, we employed DES for modeling the problem. Because integrated modeling was among the objectives of this study, clinical pathway method was adopted in order to consider multi-departments. The data required for simulation were gathered from an ED in Tehran, Iran. Some of the collected data such as the input rate of patients and processing times of each section were earned by historical data, and some other data were gathered by expert judgment method from department experts. The problem was simulated in Rockwell Automation’s Arena ${}^{\text{TM}}$ version 14. After developing the simulation-based model which represented the current situation of the case problem, we had to verify and validate the model. The verification of the model was performed by department experts. To this end, we collected real data according to two variables (30 samples of waiting time of patients in triage and laboratory) and then compared them with simulation results using t-test. The validation result for the simulation-based model is presented in Table 2.

Table 2
T-test results for simulation base model validation

Factor	Real data	Simulation result (min)	t-test result
Wait time in triage	Sample size $=$ 30, Sample mean $=$ 5.5, Standard deviation $=$ 3.5829	4.5405	p-value $=$ 0.138 Confidence level $=$ 0.95
Wait time in laboratory	Sample size $=$ 30, Sample mean $=$ 13.1, Standard deviation $=$ 6.0034	11.2059	P-value $=$ 0.112 Confidence level $=$ 0.95

Figure 1.

Process flow chart of this study.

Integrated decision making in healthcare has been introduced by some researchers in the past decade. After determining several challenges in integrated decision making in healthcare, Hulshof [4] presented a new approach toward integrated decision making based on clinical pathways. In the healthcare system, departments have interactions with one another and it is important to consider these interactions in modeling. The most important interaction between departments in healthcare is patients. Patients are an entity in health care system; they move from one department to another to receive service. Figure 2 presents the schematic view of departments and their interactions in the considered ED.

Table 3

Response variables and controllable factors

Controllable factors	Response variable (minutes)
Number of nurses ( $X1$ )	Mean wait time of patients stage 1 and 2 ( $Y1$ )
Number of triage nurses ( $X2$ )	Mean wait time of patients stage 3 and 4 ( $Y2$ )
Number of doctors ( $X3$ )	Patients mean wait time for bed ( $Y3$ )
Number of beds ( $X4$ )	Mean wait time in drug store queue ( $Y4$ )
Number of pharmacy employees ( $X5$ )	Mean wait time in triage queue ( $Y5$ )

Figure 2.

Patients flow through departments under study.

Controllable factors and response variables are the key parameters of the model, determined based on expert judgment and the objectives of the problem. Controllable factors represent resource levels and response variables represent the objectives of the model [34]. Since radiology and laboratory equipment are expensive and do not fit the department’s budget constraint, no additional resource allocation is possible. Response variables and controllable factors are shown in Table 3.

2.2 Multi-response optimization

Since we considered multi-response variables in our model, we require an MRO method to optimize the problem. Finding the optimal combination of controllable factors in multi-objective problems to obtain appropriate response variables is one of the common problems in healthcare. The differential and often opposite direction of response variables is a usual problem in the simultaneous optimization of multi-responses [35]. Consequently, optimizing one response may cause non-optimal values of others. In order to obtain the optimal points of the problem, it is essential to find a proper method for MRO. Most of the studies on MRO consist of three main steps to find the optimal treatment. In the first step, a model is built for describing the relation between controllable factors and responses. In the second step, an aggregation approach of responses is applied. In the third step, an optimization method is used for optimizing the single response which was obtained from the last step. Some authors have compared response surface and regression models with ANN in model building, and verified the superior performance of ANN in their results [36, 37, 38, 39, 40].

A number of researchers studied the use of ANN and data envelopment analysis (DEA). to model the relationships between controllable factors and response variables and to obtain the optimal value for controllable factors, respectively. Liao and Chen [41] incorporated ANN to estimate the signal-to-noise (SN) ratio of responses for all treatments. Afterwards, efficient treatments were determined by Charnes, Cooper, and Rhodes (CCR) DEA model [42]. Gutierrez and Lozano used a similar approach in order to find the most efficient decision making unit (DMU) among efficient DMUs. Bashiri et al. [35] proposed the neuro-data envelopment analysis approach to find the most efficient treatment in the MRO problem when controllable factors were the smaller-the-better (STB) type.

Table 4
Controllable factors of this study

Controllable factors	Levels
Number of nurses	3	5	7	–	–	–
Number of triage nurses	1	2	3	–	–	–
Number of doctors	1	2	3	–	–	–
Number of beds	2	2	2	–	–	–
Number of pharmacy employees	1	2	3	–	–	–

In this study various controllable factors and response variables existed (Table 2). It was our goal to obtain the best combination of controllable factors in order to obtain optimal response variables. We attempted to minimize response variables using minimum resources (controllable factors), so that both controllable factors and response variables would be the STB type. In this study, we applied the approach proposed by Bashiri et al. [35]. The first design of experiments was employed to develop various experimental scenarios. Then, using simulation model, each scenario was experimented and response variables were extracted. After that, we used ANNs in order to estimate all possible combinations of controllable factors’ levels. At the end, data envelopment analysis was utilized to determine the most efficient scenario.

2.2.1 Experimentation phase

In this phase, we determined the controllable factors’ levels based on the problem. Afterwards, Taguchi method was used to design experimental scenarios. After that, we estimated the responses of all possible scenarios. Eventually, the most efficient combination of controllable factors was determined.

2.2.1.1. Determining the levels of considered controllable factors

The levels of considered controllable factors are presented in Table 4. These levels were determined based on case problem, expert judgment, and limitations (e.g. financial and scarcity limitations for the controllable factors that represented resources).

2.2.1.2. Design of experimental scenarios using Taguchi method

Design of experiments (DOE) is a systematic method to determine the relationship between factors affecting a process and the output of that process. Taguchi method is a broadly accepted method of DOE which has been proven to produce high-quality products at a low cost. For this study, we first determined the controllable factors and their levels by considering case situation and expert judgment. Then, experimental scenarios were developed using the Minitab Statistical Software. The designed experimental scenarios are presented in Table 5.

Table 5
Designed scenarios by Taguchi method

DMU	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
1	3	1	1	21	1
2	3	1	1	21	2
3	3	1	1	21	3
4	3	2	2	23	1
5	3	2	2	23	2
6	3	2	2	23	3
7	3	3	3	25	1
8	3	3	3	25	2
9	3	3	3	25	3
10	5	1	2	25	1
11	5	1	2	25	2
12	5	1	2	25	3
13	5	2	3	21	1
14	5	2	3	21	2
15	5	2	3	21	3
16	5	3	1	23	1
17	5	3	1	23	2
18	5	3	1	23	3
19	7	1	3	23	1
20	7	1	3	23	2
21	7	1	3	23	3
22	7	2	1	25	1
23	7	2	1	25	2
24	7	2	1	25	3
25	7	3	2	21	1
26	7	3	2	21	2
27	7	3	2	21	3

2.2.1.3. Simulating designed experimental scenarios

After developing scenarios using DOE Taguchi method, the simulation-based model was updated based on each scenario. Then, by running the simulation model for each scenario, the related response variables were extracted and gathered.

2.2.2 Estimating all possible scenarios by combining controllable factors’ levels

In order to expand the results of experimental scenarios into all possible combinations of controllable factors, we need an estimation tool. There are many estimation tools such as linear regression, quadratic regression, exponential regression, and ANNs (i.e. MLP and RBF) that try to find some patterns in the data at hand. Using the discovered patterns, it is possible to estimate the new scenarios’ response variables. In order to find the best estimation model for this study, we compared the mean absolute percentage errors (MAPE) of various models.

The data are divided into three subsets: training, validation and testing sets. The training set is used for computing the gradient and updating network weights and biases. As the network begins to over-fit the data, the error on the validation set typically begins to rise. After the specified number of iterations (which can be defined by the researcher) and the increase in validation error, the training is stopped and the weights and biases of the epoch, with minimum validation errors, are returned as the final ANN structure [46].

In this study, 70% of the data were randomly selected for training the network, while 25% and 5% of the data were randomly selected for testing and validating, respectively. The MAPE of testing and validation sets was considered as the ANN’s performance criteria in the estimation of responses. The MAPE is regarded as one of the standard statistical performance measures, shown in Eq. (1) [47].

$\displaystyle\textit{MAPE}=\frac{1}{M}\sum_{i=1}^{M}\left|{\frac{y_{1}-\tilde{% y}_{i}}{y_{i}}}\right|$ (1)

where $y_{i}$ is the target, $\tilde{y}_{i}$ is the neural network’s output (estimated data), and $M$ is the number of testing and validation sets.

2.2.3 Evaluating the efficiency of all scenarios using DEA

Data envelopment analysis (DEA) was adopted to evaluate the relative efficiency of a group of decision making units (DMUs), while there were several inputs and outputs for each DMU. The efficiency computed in this problem equaled the ratio of the weighted sum of outputs to the weighted sum of inputs. Therefore, to maximize the DMUs’ efficiency, inputs had to be minimized while the outputs were fixed (input-oriented model), or outputs had to be maximize while the inputs were fixed (output-oriented model). In healthcare environments, the optimization of objectives (outputs) is much more important than the use of minimum resources (inputs). As a result, we incorporated the DEA output-oriented model in this study. The DEA model used in this study was the CCR output-oriented model proposed by [42]. Assume that there are $n$ DMUs and each of them has $m$ inputs and $s$ outputs. Thus, the efficiency of the $j$ th DMU will be computed by Eq. (2.2.3):

$\displaystyle\text{Max}z=\sum_{r=1}^{s}U_{r}Y_{r0}$ $\displaystyle\text{s.t.}\sum_{r=1}^{s}U_{r}Y_{rj}-\sum_{i=1}^{m}V_{i}X_{ij}% \leqslant 0\quad j=1,\ldots,n\sum_{i=1}^{m}V_{i}X_{i0}=1U_{r},V_{i}\geqslant 0$ (2)

in which $U_{r}$ denotes the weight of output $r$ , $V_{i}$ represents the weight of input $i$ , $Y_{rj}$ equals the value of output $r$ from DMU $j$ , $X_{ij}$ shows the value of input $i$ from DMU $j$ , and DMU ${}_{0}$ is the DMU under study.

In this study, each scenario was considered as a DMU, each controllable factor was regarded as an input variable, and each response variable was considered as an output variable.

Before using DEA, it is important to understand that input variables should be the STB type and output variables should be the larger-the-better (LTB) type. However, we must note that this condition does not necessarily hold in all problems. Thus, before using DEA, it is essential to check if controllable factors are the STB type and response variables are the LTB type. Based on the properties of controllable factors and response variables, we can assure whether they are the STB or LTB type. In this study, response variables were the STB type. For example, patients’ mean waiting time for bed was one of the variables that we wanted to minimize. Consequently, before using DEA, we had to transform response variables into the LTB type using Eq. (3):

$\displaystyle Z_{ij}=\frac{\@setsize{\scriptsize}{8pt}{\viipt}{\@viipt}\max\{Y% _{ij},j=1,2,\ldots,n\}-Y_{ij}}{\begin{subarray}{c}\max\{Y_{ij},j=1,2,\ldots,n% \}\\ -\min\{Y_{ij},j=1,2,\ldots,n\}\end{subarray}}$ (3)

where $Z_{ij}$ is the normalized value of output $j$ . Now, $y_{ij}$ denotes the response values of this problem. At the end of this step, an efficiency value was computed for each scenario (treatment) showing how well the ratio of the sum of outputs to sum of inputs was maximized for each treatment.

Table 6

Architectures of the 10 ANN-RBF models and their associated relative error (MAPE)

RBF ANN	Spread	Maximum number	Output1 MAPE	Output2 MAPE	Output3 MAPE	Output4 MAPE	Output5 MAPE
no.		of neurons
1	2	20	0.161	0.179	0.152	0.153	0.142
2	4	25	0.127	0.173	0.141	0.159	0.149
3	0.5	30	0.183	0.194	0.163	0.171	0.227
4	2	15	0.221	0.184	0.173	0.158	0.195
5	4	12	0.187	0.147	0.169	0.162	0.174
6	3	20	0.249	0.137	0.153	0.138	0.153
7	5	10	0.321	0.169	0.195	0.173	0.168
8	5	20	0.263	0.173	0.187	0.174	0.147
9	4	20	0.142	0.147	0.189	0.130	0.138
10	3	15	0.189	0.142	0.163	0.146	0.157

Table 7

Architectures of 11different ANN-MLP models and their associated relative error (MAPE)

MLP	Training	Number	TF of	Number of	Number of	TF of	Output 1	Output 2	Output 3	Output 4	Output 5
ANN	function	of HLs	the HLs	neurons in	neurons in	the OL	MAPE	MAPE	MAPE	MAPE	MAPE
no.				first HL	the second HL
1	LM	1	logsig	4		purelin	0.182	0.186	0.181	0.199	0.173
2	BFG	2	logsig	4	3	purelin	0.173	0.173	0.212	0.201	0.162
3	BFG	1	tansig	8		purelin	0.154	0.162	0.175	0.186	0.152
4	LM	2	tansig	8	3	purelin	0.152	0.185	0.223	0.175	0.193
5	SCG	2	logsig	8	6	purelin	0.198	0.219	0.274	0.263	0.186
6	CGB	1	logsig	12		purelin	0.122	0.175	0.231	0.146	0.195
7	SCG	2	logsig	12	3	purelin	0.175	0.144	0.135	0.237	0.218
8	LM	2	tansig	12	6	purelin	0.162	0.175	0.204	0.193	0.173
9	BFG	2	tansig	12	9	purelin	0.149	0.162	0.258	0.189	0.163
10	SCG	1	tansig	16		purelin	0.162	0.183	0.224	0.211	0.183
11	CGB	2	tansig	16	3	purelin	0.158	0.168	0.167	0.176	0.193
12	BFG	2	logsig	16	6	purelin	0.189	0.172	0.169	0.185	0.241
13	LM	2	logsig	16	9	purelin	0.213	0.195	0.184	0.215	0.237

Note: TF: Transfer function; HL: Hidden layer; OL: Output layer; LM: Levenberg-Marquardt back propagation; BFG: BFGS Quasi-Newton; CGB: Conjugate Gradient with Powell/Beale Restarts, SCG: Scaled Conjugate Gradient.

2.2.4 Determining the optimal resource allocation

Efficiency takes a value between 0 and 1, and sometimes more than one DMU can become efficient. In this paper, we used Maximin weight model to determine the most efficient DMU among efficient DMUs. The Maximin weight model was presented by Wang et al. for ranking DEA efficient units [48]. We utilized this model for all efficient DMUs. The model is presented in Eq. (2.2.4):

$\displaystyle\text{Max}w$ $\displaystyle\text{s.t.}\sum_{i=1}^{m}v_{i}=1\sum_{r=1}^{s}u_{r}\hat{y}_{r0}-% \sum_{i=1}^{m}v_{i}\hat{x}_{i0}=0\sum_{r=1}^{s}u_{r}\hat{y}_{rj}-\sum_{i=1}^{m% }v_{i}\hat{x}_{ij}\leqslant 0,j=1,\ldots,nu_{r}\geqslant w,r=1,\ldots,sv_{i}% \geqslant w,i=1,\ldots,m$ (4)

in which $w$ is the Maximin weight that can keep DMU ${}_{0}$ efficient, and $\hat{x}_{ij}$ is the normalized input obtained by Eq. (5):

$\displaystyle\hat{x}_{ij}=\frac{x_{ij}}{\sum_{j=1}^{n}x_{ij}},i=1,\ldots,m;j=1% ,\ldots,n$ (5)

3. Computational results and discussion

In this section, we applied the steps presented in Section 2 on the problem under study. The required data were collected from Firoozgar ED in Tehran, Iran. The simulation-based model was created in Arena ${}^{\text{TM}}$ DES package. Other steps were applied respectively and the related results are presented below.

3.1 Simulating the designed scenarios and obtaining response variables for each scenario

As mentioned before, Taguchi method was incorporated to design the experimental scenarios (Table 4). Afterwards, we used simulation modeling to obtain the related response variables of each scenario. Since stochastic data were employed in simulation modeling, results were not constant. Thus, each scenario was simulated five times. The response variables of experimental scenarios are presented in Table 13 in Appendix.

Table 8
MAPE values of optimum estimation networks and regression methods

Estimation model	Output1 MAPE	Output2 MAPE	Output3 MAPE	Output4 MAPE	Output5 MAPE
ANN-MLP	0.122	0.144	0.135	0.146	0.152
ANN-RBF	0.127	0.137	0.141	0.130	0.138
Linear regression	0.346	0.307	0.232	0.333	0.328
Quadratic regression	0.194	0.249	0.243	0.215	0.203
Exponential regression	0.257	0.226	0.184	0.286	0.194

Table 9

Response variables of all possible scenarios

	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee

1	4	2	2	22	3	3.14900	0.27603	0.79426	0.00000	0.03813	1.0000
2	3	1	3	23	2	0.06251	0.27115	0.99626	0.00000	0.00030	0.9672
3	5	2	2	25	2	1.75351	0.27119	0.14309	0.00645	0.00056	0.6893
4	3	1	1	24	1	2.33024	0.00000	1.10682	0.00827	0.05060	0.9213
5	4	2	2	24	1	1.39253	0.10569	0.34794	0.01278	0.00559	0.9428
⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮	⋮
670	3	3	1	21	2	0.00000	0.07965	0.20315	0.00495	0.05944	1.0000
671	4	2	3	25	2	0.00000	0.07730	0.37794	0.01065	0.00000	0.8119
672	5	2	2	22	1	2.99393	0.31721	0.00000	0.00954	0.01339	0.7653
673	5	2	1	25	2	0.00000	0.00000	0.17237	0.01019	0.05735	0.8772
674	6	1	2	22	2	0.82059	0.03979	0.00000	0.00540	0.00847	1.0000
675	6	1	2	23	2	0.83194	0.01734	0.00000	0.00537	0.00865	0.7046

3.2 Estimating all possible scenarios

As the performance of ANNs strongly depends on their effective parameters and structure [49], we had to determine the best structure first and then extract the related MAPE of each structure for comparison. In this study, we considered MLP, ANN, and radial basis function (RBF) as estimation models for the problem.

RBF is an estimator function which can also be interpreted as an ANN. Spread and maximum number of neurons are the most important factors influencing the network’s performance. Table 6 shows the MAPE of different RBF architectures for each response variable (output) of the problem.

An MLP is a feed-forward ANN model that maps sets of input data onto a set of appropriate outputs. It consists of multiple layers of nodes in a directed graph, with each layer fully connected to the next one. Except for the input nodes, each node is a neuron (or processing element) with a nonlinear activation function. MLP utilizes a supervised learning technique called back-propagation for training the network. MLP is a modification of the standard linear perceptron and can distinguish data which are not linearly separable. Different architectures of ANN-MLP models and their related MAPE are presented in Table 7. In order to demonstrate the application of ANNs for this study, we also used conventional regression models for the problem. Results of MAPE and the comparison between all models used for the problem are given in Table 8.

Using optimal estimation functions for each output of the problem, it was possible to estimate all possible scenarios’ response variables. The response variables of all possible scenarios are depicted in Table 9. To enhance the accuracy of the results, some new levels between the initial factor levels (i.e. 22 and 24 beds and 4 and 6 nurses) could be defined. Therefore, the number of treatments that had to be estimated by ANN equaled 5 $\times$ 3 $\times$ 3 $\times$ 5 $\times$ 3 $=$ 675.

3.3 Evaluating the efficiency of all scenarios using DEA and determining the optimal resource allocation

After evaluating the efficiency of all scenarios using ANN, it was time to use DEA-CCR output-oriented model in order to calculate the efficiency of all scenarios. The results for the efficiency of all 675 scenarios are given in Table 14 in Appendix. Sixty-seven scenarios were efficient (i.e. had an efficiency equal to 1). In order to find the most efficient scenario among the efficient ones, we employed Wang model which was explained in Section 2.

After computing $w$ using Maximin weight model for each efficient DMU, the DMU with the largest value of $w$ was the most efficient one. Maximin weight model results are shown in Table 10.

Table 10
Maximin weight model results for efficient DMUs

DMU	$w$	DMU	$w$	DMU	$w$	DMU	$W$
1	1.0084	88	1.0652	321	1.0341	532	1.0389
7	1.0334	92	1.1094	345	0.9201	535	0.9992
11	1.0608	99	0.8478	378	0.9691	561	1.0432
14	0.9287	124	1.1093	395	0.9478	567	1.0203
17	1.0102	165	0.9992	403	0.8894	570	1.0102
18	1.0930	189	1.0432	404	1.0762	582	1.1063
21	0.9868	190	1.0203	426	1.0573	601	0.8996
24	1.0389	191	1.0102	427	1.0313	624	1.0678
27	0.9835	204	1.1008	440	1.0264	641	1.0432
32	1.0289	226	0.8365	461	1.0608	643	1.0011
39	0.9405	238	1.0841	481	0.9287	658	1.0334
41	0.9956	248	1.0432	493	1.0102	659	1.0608
48	1.0662	249	1.0841	514	0.9287	661	1.0843
63	1.1139	266	1.0573	517	1.0102	665	1.0432
68	1.0183	292	1.0011	523	1.1107	670	1.0841
69	0.9998	293	1.0334	526	0.9868	674	1.0573
81	0.9819	294	1.0608	530	1.0389	–	–

Based on the results, DMU Number 63 among efficient DMUs (which is Number 14 among efficient DMUs) was the best scenario for this ED. Table 11 demonstrates the best resource allocation level for the ED.

Table 11

Most efficient scenario for the emergency department resource level

Resource	Level
Number of nurses	4
Number of triage nurses	2
Number of doctors	2
Number of beds	25
Number of pharmacy employees	2

Response variables in optimal point are presented in Table 12.

Table 12

Response variables for optimal point

Response variable	Value (minutes)
Mean wait time of patients stage 1 and 2	59.48
Mean wait time of patients stage 3 and 4	12.38
Patients mean wait time for bed	0.013
Mean wait time in drug store queue	0.28
Mean wait time in triage queue	3.75

By comparing these results with the ED’s current condition, it appears that if the ED adds 3 more beds and 1 more pharmacy employee, it is possible to decrease patients’ waiting time for bed by 32%, reduce mean waiting time in triage queue by about 16%, and decrease mean waiting time in the drugstore by 64%. This additional resource allocation in within the department’s budget constraint.

4. Conclusion

In this paper, we optimized resource allocation in an ED using simulation-multi-response optimization. First, we integrated the simulation of the problem modeled in Arena by considering clinical pathway method for integration. Next, using the design of experiments method, Taguchi, different scenarios were developed for experimentation. After gathering experimental scenarios, the simulation model was updated based on each scenario and run. After gathering the required results (response variables), the response variables of other possible scenarios were estimated by ANN. Finally, using data envelopment analysis, the most efficient DMU was determined. After running the simulation model of the current ED and the most efficient DMU determined in this paper, we concluded that the new resource level decreases patients’ waiting time for bed by 32%, reduces mean waiting time in triage queue by about 16%, and decreases mean waiting time in the drugstore by 64%. Since we assumed that all equipment and staff are present and ready to work all day, future studies can take into account equipment breakdown and staff absence.

Footnotes

Acknowledgments

Authors thank Dr Poorshirazi, the head of Firoozgar Emergency Department for his medical and information support.

Appendix

Table 13

Response variables of experimental scenarios

Scenario	Iteration	Y ${}_{1}$	Y ${}_{2}$	Y ${}_{3}$	Y ${}_{4}$	Y ${}_{5}$
1	1	5.25790	0.31640	1.08620	0.01061	0.05821
	2	5.45831	0.36574	1.04584	0.02759	0.06784
	3	5.02938	0.32857	1.14739	0.01348	0.04858
	4	5.67384	0.39894	1.10848	0.00985	0.53848
	5	4.98753	0.29847	1.09859	0.01139	0.6184
2	1	4.87530	0.36420	1.05940	0.00014	0.04938
	2	4.28384	0.39858	1.06893	0.00019	0.06839
	3	4.98473	0.29853	1.04857	0.00009	0.05473
	4	3.98753	0.40853	1.03958	0.00019	0.04874
	5	4.45858	0.38758	1.05423	0.00013	0.04573
3	1	5.13940	0.32540	1.00530	0.00000	0.07432
	2	5.58382	0.38574	1.01384	0.00000	0.05438
	3	5.23849	0.29847	1.00857	0.00000	0.06857
	4	4.98574	0.38674	1.03859	0.00000	0.05738
	5	4.87664	0.34382	1.12384	0.00000	0.06583
4	1	0.07135	0.05689	0.76730	0.01852	0.00548
	2	0.09847	0.07583	0.67583	0.02737	0.00637
	3	0.05868	0.06747	0.87482	0.01838	0.00599
	4	0.08474	0.07473	0.75832	0.02384	0.00843
	5	0.13845	0.05647	0.84741	0.01576	0.00736
5	1	0.06733	0.04414	0.81730	0.00679	0.00468
	2	0.08482	0.05673	0.67484	0.00874	0.00757
	3	0.07382	0.06372	0.86527	0.00737	0.00674
	4	0.09388	0.04573	0.82949	0.00475	0.00567
	5	0.08747	0.05732	0.73848	0.00674	0.00563
6	1	0.07844	0.05312	0.72440	0.00000	0.00704
	2	0.08473	0.06748	0.84853	0.00000	0.00938
	3	0.06784	0.04758	0.67843	0.00000	0.00783
	4	0.09748	0.05768	0.73848	0.00001	0.00586
	5	0.08732	0.08394	0.98374	0.00000	0.00768
7	1	0.08094	0.03973	1.14310	0.02149	0.00154
	2	0.09382	0.04658	1.21738	0.03473	0.00327
	3	0.13849	0.03758	1.17683	0.02475	0.00237
	4	0.11938	0.05385	1.38573	0.02894	0.00278
	5	0.09485	0.04758	1.74735	0.03827	0.00173
8	1	0.08338	0.03563	1.09483	0.00783	0.00104
	2	0.09483	0.04657	1.12748	0.00984	0.00272
	3	0.09374	0.04658	1.12849	0.00874	0.00184
	4	0.08239	0.03645	1.09385	0.00657	0.00374
	5	0.07583	0.05839	1.12738	0.00783	0.00137
9	1	0.09347	0.03634	1.16394	0.00000	0.00184
	2	0.08938	0.04757	1.12841	0.00000	0.00284
	3	0.08937	0.03475	1.09385	0.00000	0.00194
	4	0.10273	0.04895	1.12748	0.00000	0.00238
	5	1.28384	0.05372	1.14858	0.00000	0.00174
10	1	0.04743	0.06107	0.11870	0.01467	0.00564
	2	0.06372	0.07382	0.10938	0.01765	0.00764
	3	0.04573	0.05673	0.09848	0.01235	0.00638
	4	0.06738	0.06473	0.14678	0.01986	0.00459
	5	0.05678	0.08978	0.13786	0.01367	0.00764
11	1	0.06432	0.05746	0.15420	0.00345	0.00646
	2	0.07864	0.07834	0.18734	0.00289	0.00873
	3	0.06578	0.05647	0.13847	0.00475	0.00475
	4	0.04586	0.04589	0.16574	0.00346	0.00578
	5	0.07864	0.05893	0.14837	0.00318	0.00679

Table 13, continued
Scenario	Iteration	Y ${}_{1}$	Y ${}_{2}$	Y ${}_{3}$	Y ${}_{4}$	Y ${}_{5}$
12	1	0.04574	0.05685	0.13550	0.00001	0.00523
	2	0.06478	0.06748	0.15834	0.00002	0.00674
	3	0.06738	0.05382	0.17484	0.00001	0.00586
	4	0.05783	0.04986	0.14583	0.00002	0.00674
	5	0.07637	0.06839	0.15837	0.00001	0.00475
13	1	2.04120	0.36560	0.10860	0.01534	0.00114
	2	2.18384	0.34724	0.12483	0.01748	0.00283
	3	2.37483	0.28947	0.14748	0.01388	0.00183
	4	2.36532	0.27894	0.19474	0.01573	0.00283
	5	2.00384	0.37483	0.10938	0.01485	0.03844
14	1	2.45432	0.42152	0.12902	0.00464	0.00214
	2	2.89731	0.47853	0.14758	0.00573	0.00283
	3	2.27842	0.38958	0.13858	0.00475	0.00382
	4	2.47854	0.35783	0.11938	0.00683	0.00294
	5	2.89737	0.49884	0.15738	0.00394	0.00208
15	1	2.32160	0.34210	0.12142	0.00000	0.00159
	2	2.18384	0.38728	0.13738	0.00000	0.00284
	3	2.28310	0.28947	0.10938	0.00000	0.00184
	4	2.01838	0.27493	0.15728	0.00000	0.00285
	5	2.47573	16.58	0.14853	0.00000	0.00287
16	1	0.00305	0.00040	0.11394	0.01428	0.05813
	2	0.00472	0.00035	0.13457	0.01674	0.07345
	3	0.00389	0.00043	0.10976	0.01367	0.06452
	4	0.00412	0.00041	0.10975	0.01785	0.09124
	5	0.00336	0.00035	0.13462	0.01236	0.04565
17	1	0.00463	0.00053	0.10435	0.00623	0.06244
	2	0.00567	0.00075	0.12426	0.00736	0.05783
	3	0.00347	0.00047	0.11745	0.00578	0.04782
	4	0.00784	0.00056	0.12840	0.00578	0.07837
	5	0.00567	0.00068	0.11983	0.00475	0.06793
18	1	0.00503	0.00042	0.11259	0.00000	0.06138
	2	0.00674	0.00063	0.13762	0.00000	0.07863
	3	0.00457	0.00047	0.14637	0.00000	0.06489
	4	0.00487	0.00086	0.12835	0.00000	0.05376
	5	0.00593	0.00046	0.10985	0.00000	0.08637
19	1	0.01598	0.00289	0.00934	0.01059	0.00114
	2	0.01783	0.00387	0.00863	0.01283	0.00128
	3	0.01479	0.00278	0.00784	0.01492	0.00118
	4	0.01873	0.00190	0.00893	0.01238	0.00148
	5	0.01578	0.00289	0.00683	0.01183	0.00139
20	1	0.01753	0.00349	0.01033	0.00035	0.00185
	2	0.01892	0.00478	0.01284	0.00038	0.00218
	3	0.01673	0.00572	0.01372	0.00042	0.00273
	4	0.01783	0.00478	0.01283	0.00039	0.00179
	5	0.01578	0.00893	0.01384	0.00042	0.00278
21	1	0.01577	0.00321	0.01234	0.00000	0.00153
	2	0.01783	0.00378	0.01424	0.00000	0.00167
	3	0.01893	0.00428	0.02893	0.00000	0.00187
	4	0.01539	0.00389	0.01783	0.00000	0.00147
	5	0.01483	0.00289	0.02184	0.00000	0.00178
22	1	0.03548	0.07149	0.01424	0.01295	0.04986
	2	0.03873	0.08723	0.01658	0.01473	0.05783
	3	0.02894	0.06274	0.01378	0.01378	0.04984
	4	0.03893	0.09734	0.01478	0.01783	0.05382
	5	0.03894	0.05783	0.01674	0.01347	0.06293
23	1	0.03224	0.06143	0.01104	0.00735	0.05294
	2	0.04382	0.07845	0.01287	0.00839	0.07364
	3	0.03893	0.08364	0.01562	0.00683	0.08743
	4	0.04284	0.06573	0.01293	0.00918	0.06753
	5	0.05782	0.08743	0.01487	0.00473	0.07384

Table 13, continued
Scenario	Iteration	Y ${}_{1}$	Y ${}_{2}$	Y ${}_{3}$	Y ${}_{4}$	Y ${}_{5}$
24	1	0.02985	0.06534	0.01313	0.00025	0.05596
	2	0.03783	0.07384	0.01572	0.00042	0.06373
	3	0.02845	0.05673	0.01482	0.00038	0.05892
	4	0.03874	0.06783	0.01294	0.00382	0.04883
	5	0.04108	0.08384	0.01783	0.00028	0.05838
25	1	2.94280	0.34250	0.01248	0.00000	0.00789
	2	2.84835	0.41783	0.01472	0.00000	0.00893
	3	3.48520	0.32894	0.01683	0.00000	0.00793
	4	3.28341	0.38938	0.01398	0.00000	0.00983
	5	2.78342	0.48291	0.01109	0.00000	0.00783
26	1	3.54320	0.36750	0.01482	0.00000	0.00784
	2	3.89273	0.39828	0.01793	0.00000	0.00789
	3	2.98355	0.31993	0.01893	0.00000	0.00938
	4	3.20841	0.38941	0.01488	0.00000	0.00683
	5	3.39021	0.29842	0.01873	0.00000	0.00589
27	1	3.87320	0.29840	0.01094	0.00000	0.00817
	2	3.78394	0.37482	0.01382	0.00000	0.00784
	3	3.28938	0.21884	0.01284	0.00000	0.00783
	4	2.98384	0.27893	0.01572	0.00000	0.00578
	5	3.78831	0.31894	0.01372	0.00000	0.00793

Table 14

Efficiency of all scenarios calculated by DEA-CCR output oriented

	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
1	4	2	2	22	3	3.14900	0.27603	0.79426	0.00000	0.03813	1.0000
2	3	1	3	23	2	0.06251	0.27115	0.99626	0.00000	0.00030	0.9672
3	5	2	2	25	2	1.75351	0.27119	0.14309	0.00645	0.00056	0.6893
4	3	1	1	24	1	2.33024	0.00000	1.10682	0.00827	0.05060	0.9213
5	4	2	2	24	1	1.39253	0.10569	0.34794	0.01278	0.00559	0.9428
6	5	2	2	21	2	3.19671	0.36040	0.00000	0.00594	0.01528	0.6683
7	4	1	3	21	2	0.00000	0.28898	0.88121	0.00000	0.00000	1.0000
8	6	3	3	22	1	1.22829	0.13748	0.00000	0.01736	0.00000	0.9793
9	6	3	2	21	1	2.84073	0.28397	0.00000	0.01168	0.01542	0.9039
10	4	1	1	22	2	4.11921	0.25537	0.31809	0.00631	0.04726	0.9341
11	6	2	1	24	2	0.00000	0.04923	0.07669	0.00993	0.05223	1.0000
12	5	3	3	22	1	0.73262	0.07861	0.00000	0.01742	0.00000	0.5607
13	3	2	1	21	1	2.02553	0.24378	0.03059	0.00994	0.04465	0.7197
14	3	2	3	21	1	0.00000	0.25672	0.67432	0.00571	0.00000	1.0000
15	3	3	2	22	3	0.00000	0.05004	1.19814	0.00126	0.06427	0.8403
16	7	3	1	25	1	0.00000	0.00000	0.10692	0.00840	0.05759	0.7938
17	5	2	3	23	1	0.00000	0.08799	0.01892	0.01508	0.00000	0.7992
18	3	3	3	24	3	0.57577	0.10696	1.07396	0.00368	0.00936	1.0000
19	4	3	2	22	3	0.92463	0.15128	0.36749	0.00374	0.03213	0.8938
20	4	3	2	24	2	0.00000	0.03345	0.31985	0.00809	0.02884	0.8694
21	5	1	2	25	1	0.42479	0.09001	0.08629	0.00818	0.00280	1.0000
22	6	3	3	24	2	1.69234	0.18060	0.02664	0.01182	0.00000	0.9130
23	7	1	3	21	2	0.12845	0.03727	0.02608	0.00515	0.00250	0.8711
24	3	3	2	23	2	0.00000	0.00780	0.58959	0.00652	0.03424	1.0000
25	7	3	2	22	1	2.85456	0.26041	0.00000	0.01287	0.01672	0.8759
26	6	3	3	21	3	3.19422	0.36041	0.00000	0.00525	0.00691	0.7528
27	6	1	3	23	1	0.00000	0.00000	0.32661	0.00881	0.00000	1.0000
28	7	3	3	24	3	3.06812	0.29065	0.04832	0.00488	0.00570	0.8742
29	4	3	1	25	3	0.00000	0.00000	0.21176	0.00384	0.06411	0.7485
30	3	2	2	21	1	1.15227	0.27478	0.60824	0.00727	0.01238	0.8572
31	4	1	1	24	1	2.80086	0.07009	0.29563	0.00933	0.04212	0.8002
32	6	3	2	25	1	2.58630	0.08745	0.05356	0.01722	0.02455	1.0000
33	4	2	1	22	2	0.00000	0.09732	0.12117	0.00923	0.05373	0.9909

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
34	5	1	3	22	3	0.18114	0.15195	0.82538	0.00128	0.00160	0.9040
35	3	2	1	25	3	0.83671	0.00000	1.33244	0.00000	0.08789	0.9354
36	3	2	1	22	2	0.53858	0.14244	0.63453	0.00621	0.06096	0.9024
37	7	2	1	22	3	1.18080	0.09144	0.02183	0.00249	0.05625	0.9665
38	7	3	1	24	2	0.18233	0.04499	0.08961	0.00630	0.05332	0.4223
39	5	3	2	21	2	2.85094	0.32124	0.00000	0.00702	0.01254	1.0000
40	7	1	3	24	2	0.00000	0.00000	0.09720	0.00539	0.00050	0.7987
41	7	1	3	24	1	0.00000	0.00000	0.10284	0.00834	0.00108	1.0000
42	7	1	2	25	2	0.89885	0.00000	0.00000	0.00567	0.00968	0.9523
43	3	3	3	25	1	0.00000	0.03619	0.83544	0.01264	0.00000	0.8034
44	4	1	2	25	2	0.06278	0.04803	0.67147	0.00119	0.01922	0.8060
45	7	2	1	21	3	1.62876	0.11444	0.00064	0.00195	0.05515	0.9666
46	3	3	2	23	1	1.10893	0.05849	0.30640	0.01441	0.02099	0.9880
47	5	2	3	25	3	0.62368	0.18065	0.25438	0.00585	0.00000	0.7727
48	6	1	3	24	2	0.00000	0.00000	0.31264	0.00527	0.00000	1.0000
49	6	3	1	23	3	0.16613	0.04461	0.10707	0.00395	0.05010	0.8470
50	6	1	1	25	1	2.81247	0.12135	0.00000	0.00544	0.03189	0.7624
51	3	3	1	25	3	0.00000	0.00000	0.47052	0.00191	0.06568	0.8079
52	6	3	3	22	2	2.54357	0.30593	0.00000	0.00886	0.00000	0.8175
53	6	3	1	25	2	0.00000	0.00000	0.11728	0.00573	0.06032	0.8181
54	5	2	2	21	3	3.75947	0.31879	0.13651	0.00363	0.03280	0.7797
55	4	3	2	25	3	0.00000	0.00000	0.73756	0.00131	0.03921	0.9943
56	5	1	1	22	2	3.38695	0.19969	0.00000	0.00834	0.03733	0.9346
57	5	3	3	23	1	0.23123	0.04134	0.00000	0.01768	0.00000	0.8010
58	7	3	3	21	3	3.30991	0.34966	0.00000	0.00462	0.01096	0.8431
59	5	1	2	21	1	1.54764	0.20562	0.09533	0.00669	0.01358	0.9954
60	4	2	1	23	1	2.05982	0.12524	0.00626	0.01261	0.04642	0.8633
61	3	2	3	23	1	0.00000	0.04299	0.70339	0.01128	0.00000	0.9541
62	4	3	1	24	2	0.00000	0.00000	0.13259	0.00490	0.06175	0.9016
63	4	2	2	25	2	0.99130	0.2063	0.000216	0.00201	0.06251	1.0000
64	3	2	3	21	3	2.09638	0.32657	1.12744	0.00000	0.01577	0.9667
65	6	2	2	23	2	3.09492	0.34130	0.00000	0.00640	0.00974	0.6703
66	4	3	1	23	1	0.83246	0.03035	0.08317	0.01208	0.05104	1.0000
67	4	2	3	23	3	1.28546	0.27398	0.69646	0.00063	0.00671	0.9156
68	4	1	2	21	3	2.30972	0.21751	0.59148	0.00133	0.02553	1.0000
69	7	1	3	22	3	0.13728	0.03211	0.02951	0.00423	0.00076	1.0000
70	6	2	3	25	2	0.30766	0.17720	0.02213	0.01089	0.00000	0.8852
71	7	2	3	25	3	0.60237	0.08063	0.00000	0.00611	0.00066	0.9481
72	3	3	3	21	2	0.76947	0.15357	0.87479	0.00676	0.00000	0.9261
73	3	1	2	24	3	1.86320	0.22343	1.12511	0.00000	0.03481	0.9283
74	5	3	1	25	1	0.12965	0.00000	0.12507	0.00981	0.05667	0.8864
75	6	1	3	23	2	0.00000	0.00526	0.23265	0.00496	0.00000	0.8421
76	4	2	3	21	2	1.08836	0.44094	0.39982	0.00026	0.00000	0.8647
77	3	1	2	21	2	2.38891	0.32218	1.24029	0.00000	0.02755	0.7821
78	4	1	2	22	2	1.73788	0.22333	0.69132	0.00031	0.02261	0.8777
79	4	2	3	21	1	0.24530	0.24453	0.07159	0.01011	0.00000	0.9343
80	7	1	3	23	3	0.04514	0.00733	0.01289	0.00440	0.00029	0.9486
81	7	2	1	24	1	0.80182	0.13636	0.00000	0.00854	0.04496	1.0000
82	4	3	3	23	3	1.46969	0.23410	0.55770	0.00451	0.00050	0.7985
83	3	2	1	22	1	1.68652	0.17586	0.04645	0.01083	0.04603	0.9938
84	4	1	3	25	1	0.00000	0.00000	0.49022	0.01271	0.00000	0.5712
85	4	2	3	22	1	0.00000	0.10545	0.14643	0.01326	0.00000	0.7853
86	7	3	2	21	1	2.90716	0.30405	0.00000	0.01138	0.01552	0.6679
87	6	2	3	24	3	0.61056	0.15649	0.00000	0.00682	0.00000	0.5038
88	5	3	2	21	3	4.07405	0.33633	0.00475	0.00380	0.01218	1.0000
89	4	2	2	22	1	2.59518	0.23964	0.09603	0.01032	0.01504	0.7506
90	4	3	1	24	3	0.00000	0.00000	0.17302	0.00413	0.06430	0.6573
91	4	3	2	21	1	2.24619	0.11439	0.00000	0.01457	0.03169	0.9023
92	5	2	3	25	1	0.00000	0.02116	0.13113	0.01611	0.00000	1.0000

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
93	5	2	1	22	3	1.95359	0.07927	0.11998	0.00320	0.06328	0.5104
94	7	3	1	22	3	0.41312	0.10378	0.11391	0.00241	0.03628	0.7487
95	5	3	1	24	1	0.00000	0.00000	0.12700	0.01030	0.05595	0.6635
96	5	3	3	22	2	2.06202	0.23468	0.01680	0.00985	0.00000	0.6770
97	7	3	2	24	1	2.75541	0.13321	0.02021	0.01585	0.02327	0.8250
98	4	1	3	23	2	0.00000	0.17056	0.75383	0.00142	0.00000	0.7382
99	5	3	2	24	3	0.17265	0.09992	0.26459	0.00276	0.02435	1.0000
100	5	2	1	23	1	1.98487	0.12669	0.00000	0.01265	0.04609	0.9821
101	7	3	2	21	3	3.03965	0.23083	0.07336	0.00242	0.01902	0.6745
102	6	2	3	22	2	2.03329	0.27587	0.00000	0.00615	0.00000	0.7973
103	4	3	1	22	3	0.02276	0.00215	0.15531	0.00420	0.06475	0.9027
104	5	3	2	23	3	1.71731	0.17579	0.17595	0.00339	0.01939	0.8013
105	6	3	1	24	1	0.00000	0.00000	0.12654	0.00894	0.05828	0.7919
106	3	1	1	22	3	4.77621	0.29832	1.48507	0.00000	0.06753	0.8775
107	4	2	1	22	1	2.31335	0.16229	0.00000	0.01212	0.04639	0.7247
108	5	1	1	24	2	3.39164	0.09810	0.00000	0.00850	0.04167	0.7204
109	6	3	2	23	3	2.21017	0.18580	0.12196	0.00260	0.02068	0.9829
110	5	1	2	23	2	1.06391	0.07727	0.08952	0.00414	0.01223	0.7188
111	5	3	2	24	1	2.37600	0.08480	0.03523	0.01693	0.02575	0.7843
112	6	1	2	25	2	0.68276	0.00000	0.00000	0.00555	0.00900	0.7859
113	5	1	3	22	1	0.00000	0.00000	0.52533	0.00871	0.00000	0.7072
114	7	2	3	21	1	0.84985	0.17621	0.00000	0.01154	0.00000	0.6437
115	4	1	2	24	1	0.46611	0.04644	0.34405	0.00778	0.01424	0.8965
116	6	2	2	24	1	2.73013	0.30092	0.00000	0.01054	0.00845	0.8054
117	6	3	2	23	2	3.03102	0.25442	0.02883	0.00677	0.01512	0.7186
118	4	1	3	21	3	1.06685	0.20840	1.09384	0.00000	0.01224	0.8671
119	3	1	2	24	1	0.50156	0.00000	1.19010	0.00651	0.03444	0.3648
120	4	1	1	23	1	3.12505	0.12321	0.20538	0.00921	0.04162	0.5342
121	6	2	2	24	2	3.00816	0.33261	0.01809	0.00666	0.00694	0.7552
122	3	1	1	25	2	0.23479	0.00000	1.51962	0.00247	0.06163	0.7749
123	7	3	1	25	2	0.07684	0.03108	0.09457	0.00685	0.05493	0.7770
124	7	3	3	22	3	3.34728	0.34198	0.00000	0.00470	0.00878	1.0000
125	4	2	3	22	2	0.72762	0.34608	0.34934	0.00341	0.00000	0.7289
126	6	3	1	23	2	0.04627	0.01452	0.11336	0.00522	0.05733	0.7627
127	4	2	3	24	3	0.99025	0.22461	0.65201	0.00185	0.00702	0.9505
128	3	1	3	25	1	0.00000	0.00000	0.67543	0.01103	0.00000	0.7302
129	7	3	3	25	1	0.47188	0.05600	0.00000	0.02090	0.00000	0.8613
130	3	3	3	24	2	0.25092	0.04723	0.93572	0.00862	0.00057	0.8530
131	4	1	2	21	1	2.16255	0.25644	0.22077	0.00666	0.02100	0.7702
132	6	1	1	23	1	2.69953	0.16452	0.00000	0.00678	0.02467	0.6536
133	4	2	1	24	3	0.09718	0.00000	0.51137	0.00255	0.07343	0.8268
134	5	1	2	21	3	1.91505	0.14670	0.21757	0.00440	0.01738	0.8235
135	6	2	3	24	1	0.00000	0.09822	0.00000	0.01546	0.00000	0.7963
136	6	2	3	23	3	0.92648	0.17980	0.00000	0.00633	0.00081	0.9531
137	4	1	3	24	3	0.56195	0.11041	0.74712	0.00087	0.01742	0.8809
138	6	1	1	24	3	2.71400	0.00000	0.00000	0.00466	0.04314	0.8537
139	6	3	2	22	3	3.19151	0.24267	0.07207	0.00290	0.01591	0.8874
140	4	3	3	21	2	2.02432	0.25011	0.18424	0.00847	0.00000	0.8208
141	6	1	2	25	1	0.64640	0.10767	0.05482	0.00642	0.00000	0.8649
142	5	1	3	25	2	0.00000	0.00000	0.42246	0.00538	0.00000	0.9530
143	4	3	2	24	1	1.75815	0.06956	0.12677	0.01625	0.02253	0.9412
144	5	1	3	24	1	0.00000	0.00000	0.59967	0.01125	0.00000	0.8206
145	3	3	3	25	2	0.13382	0.04418	0.98832	0.00857	0.00066	0.6257
146	3	3	1	23	1	0.36039	0.02650	0.06619	0.01183	0.05089	0.5748
147	4	2	3	23	1	0.00000	0.04393	0.21350	0.01437	0.00000	0.6330
148	7	2	2	22	2	3.15643	0.30670	0.00000	0.00581	0.01986	0.9761
149	7	3	2	24	2	2.61413	0.15651	0.09932	0.00663	0.03179	0.7978
150	3	1	3	22	1	0.00000	0.27426	0.69019	0.00275	0.00000	0.8226
151	7	3	1	21	2	0.40443	0.10280	0.06615	0.00442	0.04535	0.8475

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
152	4	1	3	24	1	0.00000	0.00000	0.48785	0.01215	0.00000	0.8719
153	7	3	3	24	2	2.43211	0.24569	0.00000	0.01098	0.00000	0.8180
154	6	1	3	22	2	0.00000	0.03786	0.20810	0.00465	0.00000	0.9969
155	5	3	2	22	3	3.15699	0.25981	0.08257	0.00371	0.01490	0.9214
156	7	2	3	22	1	0.62051	0.16033	0.00000	0.01253	0.00000	0.9951
157	3	3	1	24	3	0.00000	0.00000	0.43109	0.00252	0.06702	0.8663
158	7	2	2	24	2	3.28028	0.27720	0.01210	0.00668	0.02236	0.7302
159	7	3	3	23	3	3.33544	0.32633	0.00000	0.00476	0.00682	0.6869
160	6	1	2	21	3	1.34315	0.07448	0.01369	0.00478	0.01250	0.9394
161	5	3	2	24	2	1.47538	0.12678	0.12839	0.00823	0.02234	0.9453
162	3	1	3	22	2	0.12256	0.30968	1.08801	0.00000	0.00000	0.7635
163	7	1	1	24	3	2.48179	0.00000	0.00000	0.00657	0.03521	0.9788
164	7	3	2	24	3	1.21440	0.12317	0.15347	0.00203	0.03021	0.8972
165	7	2	3	24	2	0.96162	0.20411	0.00000	0.00772	0.00000	1.0000
166	3	2	3	22	3	2.13415	0.31138	1.15687	0.00000	0.01874	0.8093
167	7	3	2	25	3	0.91501	0.10756	0.16771	0.00195	0.03144	0.5892
168	4	3	3	21	3	2.33133	0.34039	0.49673	0.00144	0.00605	0.5132
169	3	3	2	23	3	0.00000	0.00000	1.24472	0.00092	0.06141	0.7234
170	7	2	1	22	2	1.60354	0.14159	0.00035	0.00727	0.04607	0.6571
171	6	1	2	21	1	0.93028	0.14186	0.08497	0.00604	0.00743	0.4607
172	7	2	1	22	1	2.16689	0.24395	0.00000	0.00881	0.03553	0.9164
173	7	1	3	22	1	0.07022	0.02039	0.00325	0.00714	0.00325	0.7598
174	6	1	2	24	3	1.15275	0.00000	0.00000	0.00420	0.01310	0.5707
175	3	1	3	21	2	0.05211	0.32509	1.09743	0.00000	0.00000	0.8334
176	6	3	1	22	2	0.11530	0.02816	0.10860	0.00503	0.05448	0.6000
177	7	1	2	24	2	0.78282	0.00000	0.00000	0.00565	0.00839	0.5976
178	4	3	3	22	1	0.24365	0.03034	0.13319	0.01617	0.00000	0.8756
179	4	1	1	23	3	3.73308	0.22183	0.52332	0.00195	0.05329	0.7040
180	6	1	1	23	2	3.02248	0.04731	0.00000	0.00808	0.03551	0.5146
181	5	3	1	21	1	0.60532	0.04500	0.03238	0.01211	0.05047	0.8747
182	3	3	1	24	1	0.00000	0.00590	0.18733	0.01100	0.05245	0.6514
183	4	1	2	22	1	1.66632	0.20443	0.19296	0.00675	0.01718	0.5172
184	6	2	3	24	2	0.89278	0.21952	0.00157	0.00922	0.00000	0.8801
185	6	3	3	22	3	2.99023	0.34122	0.00000	0.00545	0.00357	0.8119
186	5	1	3	24	2	0.00000	0.00000	0.43772	0.00487	0.00000	0.7653
187	4	1	2	24	2	0.35369	0.09214	0.64516	0.00087	0.01855	0.8772
188	4	1	2	25	1	0.05638	0.00000	0.45499	0.00850	0.01522	0.7126
189	7	3	3	23	1	1.04790	0.12173	0.00000	0.01877	0.00000	1.0000
190	4	2	1	21	3	4.63475	0.16667	0.65865	0.00021	0.07909	1.0000
191	4	2	3	24	1	0.00000	0.01669	0.28837	0.01456	0.00000	1.0000
192	7	2	3	21	3	1.13057	0.17523	0.00000	0.00555	0.00758	0.8675
193	4	1	2	25	3	0.00000	0.07586	0.51607	0.00107	0.01990	0.8220
194	7	3	1	21	1	0.00000	0.07307	0.04056	0.00901	0.04922	0.5673
195	5	2	3	22	2	1.62585	0.29968	0.09937	0.00640	0.00000	0.4041
196	5	2	1	22	1	2.46428	0.17984	0.00000	0.01200	0.04450	0.9209
197	6	2	1	22	3	1.38909	0.08645	0.03246	0.00354	0.05807	0.6759
198	4	1	3	22	2	0.00000	0.25386	0.89018	0.00000	0.00000	0.5223
199	5	1	2	22	2	1.43361	0.12339	0.10153	0.00435	0.01459	0.8907
200	5	1	2	22	3	1.68885	0.11766	0.19177	0.00391	0.01750	0.4265
201	4	2	2	25	1	0.63793	0.06417	0.45046	0.01407	0.00041	0.6327
202	6	2	1	23	2	0.49398	0.09274	0.05121	0.00969	0.04880	0.7156
203	4	2	2	25	3	0.00000	0.03528	1.08219	0.00000	0.03953	0.8071
204	5	3	1	22	2	0.00000	0.01148	0.09669	0.00520	0.05776	1.0000
205	4	2	3	25	1	0.00000	0.00181	0.35597	0.01457	0.00000	0.7854
206	3	1	1	23	1	3.22153	0.07633	1.06032	0.00839	0.05177	0.6694
207	3	3	3	24	1	0.00000	0.03406	0.75299	0.01296	0.00000	0.6351
208	3	3	3	22	3	1.18473	0.28272	1.05586	0.00000	0.00583	0.8405
209	6	3	3	23	3	2.65146	0.31092	0.06540	0.00582	0.00060	0.6793
210	4	3	2	25	2	0.00000	0.01404	0.49113	0.00689	0.02880	0.6668

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
211	5	3	3	21	1	1.24565	0.12989	0.00000	0.01643	0.00000	0.9163
212	6	2	2	22	1	2.96025	0.32254	0.00000	0.00921	0.01615	0.8869
213	7	1	3	23	2	0.00000	0.00098	0.02173	0.00526	0.00161	0.6520
214	5	1	2	23	3	1.19173	0.06353	0.11657	0.00335	0.01646	0.8323
215	6	1	3	22	3	0.00000	0.07942	0.35322	0.00334	0.00000	0.8191
216	4	2	1	25	1	0.37095	0.01789	0.16698	0.01297	0.04880	0.7863
217	5	1	2	25	2	0.34811	0.01743	0.28208	0.00378	0.01240	0.9243
218	4	3	2	21	2	2.08258	0.24790	0.00000	0.00834	0.02565	0.8766
219	3	3	2	21	2	0.17053	0.16684	0.28955	0.00744	0.03335	0.9675
220	5	2	3	23	2	0.99973	0.23094	0.11083	0.00843	0.00000	0.9574
221	6	2	3	23	2	1.51793	0.25258	0.00000	0.00756	0.00000	0.7033
222	3	1	1	21	3	5.42046	0.32743	1.22149	0.00035	0.06405	0.6111
223	4	2	2	23	3	1.90148	0.21603	0.88283	0.00000	0.03468	0.9516
224	6	1	2	23	1	0.96237	0.11421	0.05664	0.00563	0.00480	0.8432
225	5	1	1	23	3	3.31337	0.13248	0.00000	0.00453	0.04257	0.6780
226	3	1	1	23	3	3.39640	0.21627	1.66479	0.00000	0.07206	1.0000
227	3	3	3	21	3	1.45576	0.32511	0.98568	0.00000	0.00673	0.5639
228	5	1	3	23	1	0.00000	0.00000	0.56475	0.01030	0.00000	0.6958
229	6	2	2	21	2	3.15905	0.34231	0.00000	0.00583	0.01713	1.0000
230	6	3	2	24	2	2.70574	0.18917	0.09317	0.00679	0.02125	0.8722
231	6	2	1	21	1	2.84845	0.28964	0.00000	0.01010	0.03402	0.8300
232	7	1	1	24	1	2.92481	0.10070	0.00000	0.00297	0.02887	0.8227
233	3	3	1	25	2	0.00000	0.00000	0.45494	0.00275	0.06453	0.8151
234	4	1	1	21	3	4.87725	0.30696	0.41762	0.00299	0.05027	0.7678
235	6	2	1	23	3	0.87797	0.06314	0.05378	0.00372	0.05840	0.8572
236	3	2	2	22	1	0.58172	0.14529	0.70097	0.00921	0.01242	0.9446
237	3	3	1	21	3	1.40267	0.05885	0.61321	0.00132	0.07904	0.9586
238	4	1	1	22	1	3.42050	0.19279	0.17004	0.00918	0.04191	1.0000
239	3	2	1	25	1	0.00000	0.00000	0.45386	0.01078	0.04730	0.8620
240	3	2	1	25	2	0.00000	0.00000	0.89541	0.00454	0.05919	0.6287
241	6	1	3	21	1	0.00000	0.05035	0.23312	0.00692	0.00072	0.9285
242	3	2	2	21	3	4.04988	0.30236	1.42408	0.00000	0.05376	0.9861
243	7	3	2	25	1	2.89627	0.10113	0.04403	0.01631	0.02634	0.7733
244	4	3	2	24	3	0.00000	0.00201	0.67990	0.00192	0.03774	0.9446
245	3	3	2	25	3	0.00000	0.00000	1.33131	0.00039	0.05521	0.8981
246	7	3	1	22	1	0.00000	0.03297	0.07105	0.00869	0.05296	0.6983
247	6	1	1	21	3	3.38715	0.13100	0.00000	0.00597	0.02985	0.6274
248	3	3	2	25	1	0.27342	0.03898	0.60096	0.01379	0.01201	1.0000
249	3	1	2	23	2	1.44441	0.25165	1.36861	0.00000	0.02945	1.0000
250	3	3	3	23	2	0.36712	0.05630	0.90813	0.00856	0.00069	0.7889
251	4	1	1	21	2	4.37058	0.29735	0.35305	0.00600	0.04807	0.7660
252	6	1	3	25	2	0.00000	0.00000	0.38939	0.00564	0.00000	0.4320
253	7	1	3	21	1	0.12521	0.03966	0.00000	0.00688	0.00367	0.9561
254	6	2	2	21	1	3.00472	0.32706	0.00000	0.00874	0.01836	0.7639
255	6	3	2	24	1	2.50626	0.11130	0.02800	0.01685	0.02184	0.8064
256	3	2	1	24	1	0.40366	0.04921	0.29983	0.01122	0.04607	0.9228
257	3	3	1	22	1	0.73871	0.05880	0.00000	0.01191	0.04959	0.6350
258	3	2	3	22	1	0.00000	0.13706	0.72155	0.00860	0.00000	0.5597
259	3	1	3	25	3	0.80787	0.15485	0.67953	0.00034	0.02347	0.9296
260	3	2	1	23	3	2.41238	0.00440	1.46691	0.00086	0.09846	0.6817
261	3	1	3	23	3	1.69582	0.21824	1.00904	0.00000	0.02552	0.4316
262	6	1	3	24	1	0.00000	0.00000	0.44863	0.00988	0.00000	0.9247
263	3	3	1	22	3	0.33289	0.00723	0.50138	0.00235	0.07366	0.8148
264	4	1	1	24	3	1.15182	0.04308	0.62342	0.00195	0.05584	0.4765
265	6	2	2	25	2	2.75902	0.30337	0.06053	0.00696	0.00621	0.8403
266	4	2	2	23	2	1.72711	0.25032	0.33195	0.00405	0.01384	1.0000
267	7	3	1	25	3	0.31080	0.07792	0.10278	0.00323	0.04335	0.7977
268	4	3	1	25	2	0.00000	0.00000	0.15695	0.00469	0.06240	0.8702
269	4	2	2	21	3	3.64838	0.29810	0.64913	0.00000	0.04049	0.7018

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
270	6	1	2	25	3	1.00212	0.00000	0.00000	0.00427	0.01427	0.7118
271	5	3	1	21	3	0.19727	0.03366	0.09138	0.00444	0.05707	0.8132
272	3	3	3	22	1	0.00000	0.03762	0.61966	0.01363	0.00050	0.8990
273	4	2	1	24	2	0.00000	0.00000	0.27373	0.00958	0.05608	0.9031
274	6	1	2	23	3	1.24573	0.00000	0.00000	0.00427	0.01302	0.8415
275	4	1	1	21	1	3.72885	0.26100	0.21612	0.00914	0.04343	0.4758
276	3	3	2	21	1	1.77046	0.09610	0.12039	0.01439	0.02774	0.4369
277	7	3	2	22	2	3.06678	0.25978	0.02474	0.00649	0.01861	0.9289
278	5	1	3	25	3	0.00000	0.00000	0.40428	0.00237	0.00829	0.5984
279	3	3	3	23	3	0.89194	0.19480	1.05739	0.00193	0.00750	0.4068
280	3	3	2	25	2	0.00000	0.00000	0.98540	0.00485	0.03159	0.9074
281	4	3	3	24	1	0.00000	0.01188	0.36517	0.01484	0.00000	0.5573
282	5	3	3	25	3	0.78215	0.16847	0.47546	0.00676	0.00000	0.8749
283	4	3	3	21	1	0.72527	0.06415	0.03478	0.01661	0.00000	0.7196
284	7	1	1	21	1	2.03414	0.14738	0.00000	0.00570	0.01812	0.8432
285	5	2	1	25	3	0.00000	0.00000	0.17478	0.00393	0.06162	0.4604
286	6	1	1	25	3	2.25847	0.00000	0.00000	0.00536	0.04626	0.7881
287	7	1	2	24	1	0.78353	0.08711	0.03790	0.00516	0.00115	0.6486
288	6	3	1	21	1	0.00000	0.02365	0.06838	0.01070	0.05237	0.5760
289	4	3	2	22	2	1.11593	0.14828	0.00000	0.00896	0.02788	0.8796
290	7	2	1	25	3	0.36994	0.06747	0.02991	0.00441	0.05648	0.7111
291	5	3	3	24	3	1.30746	0.21726	0.38629	0.00637	0.00000	0.4357
292	3	3	3	25	3	0.34240	0.06081	1.12983	0.00431	0.01050	1.0000
293	5	3	1	23	2	0.00000	0.00308	0.10723	0.00504	0.05989	1.0000
294	5	3	3	21	3	3.01345	0.35831	0.09838	0.00441	0.00537	1.0000
295	3	2	3	24	3	1.48365	0.23844	1.00740	0.00000	0.01997	0.8340
296	3	1	3	21	3	1.68558	0.22365	1.07031	0.00000	0.02401	0.8008
297	7	2	2	24	1	2.77674	0.29436	0.00000	0.00949	0.01548	0.7826
298	5	1	1	21	2	3.39129	0.23520	0.00000	0.00864	0.03829	0.9167
299	7	3	2	23	2	2.86183	0.20605	0.06847	0.00650	0.02537	0.9642
300	6	1	3	25	1	0.00000	0.00000	0.55152	0.01076	0.00000	0.9837
301	6	3	3	23	1	0.81085	0.09446	0.00000	0.01876	0.00000	0.8400
302	4	3	1	22	2	0.00000	0.01245	0.08651	0.00555	0.05844	0.6070
303	4	3	3	24	3	1.07882	0.17889	0.62294	0.00547	0.00006	0.5771
304	3	2	1	21	3	5.25268	0.16448	1.30095	0.00076	0.09389	0.9409
305	6	1	1	21	1	2.20150	0.19275	0.00000	0.00845	0.02219	0.6840
306	6	1	3	21	2	0.00000	0.09105	0.26781	0.00421	0.00000	0.6419
307	3	2	2	23	3	2.70439	0.21711	1.65714	0.00000	0.05867	0.7423
308	7	2	2	22	3	4.37629	0.24093	0.00000	0.00219	0.02919	0.6373
309	7	3	1	23	3	0.37974	0.09560	0.11182	0.00264	0.03833	0.8031
310	4	2	2	21	2	2.99082	0.36601	0.13583	0.00438	0.01766	0.9766
311	4	1	3	22	1	0.00000	0.12732	0.63635	0.00714	0.00000	0.9491
312	5	1	3	21	2	0.00000	0.20077	0.56292	0.00197	0.00000	0.8108
313	7	3	1	24	3	0.34782	0.08724	0.10776	0.00292	0.04068	0.8267
314	3	1	1	23	2	2.99316	0.16575	1.62368	0.00196	0.05834	0.7650
315	7	1	2	21	1	0.77750	0.11736	0.00000	0.00610	0.00517	0.7721
316	6	3	2	22	2	3.10811	0.30272	0.00000	0.00669	0.01095	0.7530
317	7	2	2	21	1	2.60345	0.30393	0.00000	0.00798	0.01734	0.9577
318	4	3	3	24	2	0.33982	0.04815	0.50695	0.01075	0.00000	0.7704
319	6	1	2	21	2	0.68321	0.08408	0.01828	0.00569	0.00800	0.7993
320	6	3	3	23	2	2.22394	0.25357	0.00000	0.01017	0.00000	0.9805
321	7	2	3	23	2	1.33294	0.21673	0.00000	0.00666	0.00000	1.0000
322	5	2	1	23	3	0.87860	0.02510	0.12932	0.00383	0.06330	0.9074
323	7	2	1	25	1	0.32261	0.09295	0.02311	0.00847	0.04839	0.9598
324	5	1	1	25	1	2.93247	0.13334	0.00000	0.00806	0.03635	0.7681
325	5	1	3	23	3	0.00000	0.07472	0.72903	0.00174	0.00516	0.9842
326	4	3	1	24	1	0.62868	0.01808	0.11677	0.01137	0.05288	0.9231
327	3	1	2	25	1	0.20171	0.00000	1.18178	0.00789	0.03471	0.9535
328	3	2	2	21	2	2.03764	0.33321	1.24511	0.00000	0.03335	0.9204

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
329	5	3	2	22	1	2.48368	0.13838	0.00000	0.01507	0.02633	0.7809
330	6	3	3	25	2	1.03576	0.10952	0.09486	0.01327	0.00000	0.7209
331	5	1	2	24	1	0.87768	0.12168	0.03524	0.00742	0.00537	0.7843
332	3	3	3	22	2	0.47546	0.08495	0.92293	0.00803	0.00036	0.9206
333	6	1	1	22	1	2.42431	0.17885	0.00000	0.00764	0.02285	0.6857
334	3	3	1	25	1	0.00000	0.00000	0.31976	0.00949	0.05518	0.9853
335	7	2	1	23	3	0.89686	0.08082	0.02726	0.00304	0.05679	0.6967
336	5	3	2	23	1	2.41336	0.10251	0.00000	0.01627	0.02658	0.9922
337	7	3	1	23	1	0.00000	0.00747	0.08907	0.00849	0.05532	0.9579
338	7	3	3	21	2	2.79584	0.34127	0.00000	0.00731	0.00428	0.6953
339	6	1	1	25	2	3.14198	0.00000	0.00000	0.00784	0.04569	0.5927
340	3	1	3	21	1	0.00000	0.34488	0.69540	0.00096	0.00000	0.9799
341	4	3	2	25	1	1.38624	0.05939	0.25023	0.01627	0.01798	0.7117
342	3	1	1	22	2	4.17242	0.29411	1.52169	0.00169	0.05566	0.4896
343	4	1	3	24	2	0.00000	0.07805	0.55261	0.00336	0.00000	0.9793
344	5	2	2	23	3	2.59515	0.25392	0.36486	0.00251	0.02395	0.6678
345	6	1	1	23	3	3.03288	0.00000	0.00000	0.00433	0.03846	1.0000
346	3	3	3	23	1	0.00000	0.03290	0.66845	0.01333	0.00000	0.8163
347	6	3	1	22	3	0.25160	0.05840	0.10903	0.00371	0.04668	0.8328
348	5	3	2	25	1	2.33255	0.07601	0.07661	0.01719	0.02462	0.8274
349	3	1	1	25	1	1.69148	0.00000	1.21211	0.00781	0.05043	0.8521
350	4	2	2	21	1	2.95687	0.31240	0.00000	0.00926	0.01867	0.6938
351	6	1	2	22	1	0.98505	0.12093	0.06291	0.00566	0.00630	0.7402
352	7	2	3	23	1	0.39162	0.14734	0.00000	0.01337	0.00000	0.7624
353	6	3	3	24	1	0.36948	0.05663	0.00000	0.01972	0.00000	0.7566
354	5	3	1	25	2	0.00000	0.00000	0.11830	0.00504	0.06198	0.8205
355	5	3	1	24	2	0.00000	0.00000	0.11328	0.00499	0.06120	0.7935
356	3	3	3	21	1	0.00000	0.06173	0.63053	0.01351	0.00062	0.4162
357	4	1	3	22	3	1.11397	0.20065	1.12285	0.00000	0.01478	0.4804
358	6	3	1	25	1	0.00000	0.00000	0.12570	0.00879	0.05858	0.9433
359	3	3	1	24	2	0.00000	0.00000	0.37301	0.00374	0.06351	0.7074
360	5	3	3	23	2	1.39482	0.15335	0.10383	0.01142	0.00000	0.3275
361	6	1	3	22	1	0.00000	0.00000	0.23540	0.00774	0.00000	0.8849
362	3	1	2	22	2	2.02782	0.30684	1.37489	0.00000	0.02780	0.6344
363	6	1	1	22	2	2.67840	0.07940	0.00000	0.00884	0.03073	0.9933
364	5	3	3	25	2	0.21096	0.05181	0.29574	0.01256	0.00000	0.7256
365	3	1	2	23	3	2.35998	0.25336	1.20413	0.00000	0.03502	0.7989
366	5	2	3	21	2	2.15192	0.37094	0.10945	0.00404	0.00000	0.4223
367	5	2	2	24	1	2.38873	0.24249	0.02331	0.01153	0.00402	0.8226
368	5	3	1	24	3	0.00000	0.00015	0.11300	0.00445	0.06193	0.6655
369	7	2	2	24	3	3.95826	0.17681	0.04323	0.00138	0.03591	0.5647
370	3	2	2	22	3	3.62406	0.27980	1.61247	0.00000	0.05628	0.9069
371	4	2	2	23	1	2.07332	0.16501	0.22422	0.01155	0.01070	0.7634
372	4	2	3	21	3	1.77373	0.35258	0.73183	0.00000	0.00350	0.5763
373	3	2	3	24	2	0.00000	0.07611	0.76987	0.00721	0.00000	0.9075
374	6	3	2	25	3	0.47923	0.09787	0.20756	0.00188	0.02753	0.7998
375	5	2	1	21	3	3.58951	0.17138	0.12643	0.00169	0.06279	0.8335
376	6	2	3	22	1	0.81249	0.18317	0.00000	0.01336	0.00000	0.8322
377	5	1	2	21	2	1.61751	0.17200	0.21021	0.00441	0.01589	0.7794
378	7	2	3	22	2	1.59335	0.22538	0.00000	0.00589	0.00511	0.8785
379	5	1	1	25	3	0.67105	0.00000	0.13231	0.00444	0.05185	0.9165
380	4	2	2	24	3	0.34860	0.12097	0.98341	0.00000	0.03495	0.9105
381	5	2	2	23	1	2.78229	0.29112	0.00000	0.01035	0.00898	0.9711
382	7	1	2	23	1	0.76802	0.09075	0.02585	0.00526	0.00248	0.7727
383	7	2	1	25	2	0.34663	0.07118	0.02990	0.00842	0.05190	0.6335
384	5	3	1	25	3	0.00000	0.00000	0.12408	0.00439	0.06251	0.7613
385	4	3	1	23	2	0.00000	0.00075	0.11111	0.00517	0.06051	0.9022
386	3	2	1	21	2	2.10527	0.23331	0.60359	0.00549	0.06025	0.5642
387	6	2	3	25	1	0.00000	0.05554	0.01652	0.01628	0.00000	0.5650

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
388	6	2	1	21	2	2.21221	0.22617	0.00000	0.00904	0.03720	0.8159
389	4	1	1	25	1	2.29040	0.01735	0.42300	0.00944	0.04325	0.6918
390	6	3	3	25	1	0.00000	0.02714	0.00000	0.02003	0.00000	0.8909
391	5	2	2	23	2	2.81703	0.34085	0.02883	0.00603	0.00419	0.7977
392	6	2	1	22	1	2.51824	0.24498	0.00000	0.01063	0.03750	0.8712
393	5	1	1	24	1	3.17574	0.17260	0.00000	0.00815	0.03421	0.6747
394	7	1	2	21	2	0.52704	0.05606	0.00000	0.00638	0.00617	0.8274
395	5	1	3	23	2	0.00000	0.04700	0.48984	0.00415	0.00000	1.0000
396	7	2	1	21	2	2.18758	0.18632	0.00000	0.00698	0.04180	0.8433
397	4	1	2	22	3	2.00820	0.21036	0.72694	0.00034	0.02550	0.7779
398	4	1	1	23	2	3.50832	0.16356	0.31034	0.00662	0.04570	0.9368
399	5	2	2	22	3	3.33447	0.30017	0.23171	0.00303	0.02739	0.6590
400	6	1	3	21	3	0.00000	0.14233	0.37771	0.00280	0.00000	0.7343
401	3	2	3	23	2	0.00000	0.21748	0.77311	0.00362	0.00000	0.8303
402	3	1	2	24	2	0.54676	0.14106	1.22663	0.00000	0.03143	0.7865
403	6	2	2	21	3	3.82785	0.31470	0.00000	0.00446	0.02871	1.0000
404	7	1	1	24	2	2.90750	0.00000	0.00000	0.00558	0.03885	1.0000
405	3	3	1	21	1	1.13625	0.11495	0.00000	0.01132	0.04747	0.7853
406	4	2	3	25	3	0.72457	0.18577	0.67429	0.00234	0.00747	0.9745
407	7	1	1	23	1	2.78254	0.12548	0.00000	0.00396	0.02431	0.9948
408	7	1	1	22	3	3.04709	0.00000	0.00000	0.00510	0.03199	0.8927
409	5	3	2	21	1	2.60170	0.19432	0.00000	0.01331	0.02483	0.9612
410	5	3	3	25	1	0.00000	0.00307	0.18009	0.01662	0.00000	0.7817
411	6	2	2	22	2	3.12121	0.34152	0.00000	0.00612	0.01349	0.6634
412	7	3	3	23	2	2.62268	0.29587	0.00000	0.00942	0.00000	0.6998
413	6	1	1	24	2	3.24640	0.01641	0.00000	0.00776	0.04090	0.8748
414	3	1	2	22	3	2.54879	0.26118	1.18352	0.00000	0.03465	0.9244
415	4	3	2	22	1	2.14636	0.08805	0.00000	0.01551	0.02992	0.9509
416	3	1	3	23	1	0.00000	0.14119	0.64879	0.00646	0.00000	0.7368
417	6	1	2	24	2	0.78108	0.00377	0.00000	0.00545	0.00879	0.8769
418	6	1	1	21	2	2.41012	0.12509	0.00000	0.00993	0.02789	0.9675
419	6	2	3	21	3	1.55741	0.24690	0.00000	0.00504	0.00728	0.7641
420	5	2	1	24	1	1.07765	0.06655	0.05776	0.01301	0.04824	0.6674
421	7	1	3	25	3	0.00000	0.00000	0.14776	0.00448	0.00000	0.7450
422	3	3	1	23	2	0.00000	0.00000	0.29783	0.00458	0.06255	0.8876
423	4	2	1	24	1	1.50853	0.07999	0.08719	0.01296	0.04682	0.6288
424	3	1	2	22	1	2.13590	0.21400	1.33449	0.00280	0.03432	0.8552
425	4	3	2	23	1	2.01282	0.07754	0.02692	0.01602	0.02675	0.9855
426	7	2	2	22	1	2.66608	0.30480	0.00000	0.00837	0.01695	1.0000
427	7	3	3	25	2	2.14260	0.17812	0.03945	0.01271	0.00000	1.0000
428	3	2	2	25	1	0.00000	0.01929	0.88140	0.01256	0.00358	0.8263
429	6	2	3	25	3	0.36993	0.13868	0.00000	0.00723	0.00000	0.7986
430	6	1	3	24	3	0.00000	0.00000	0.28260	0.00380	0.00000	0.8133
431	7	2	1	24	2	0.72150	0.08852	0.02400	0.00799	0.05073	0.6794
432	3	2	2	24	1	0.00000	0.04037	0.80604	0.01148	0.00575	0.8520
433	3	2	2	25	2	0.00000	0.00000	1.41454	0.00036	0.04452	0.9342
434	5	1	2	24	3	0.65681	0.01606	0.12324	0.00288	0.01535	0.9643
435	3	1	3	22	3	1.72437	0.22356	1.05428	0.00000	0.02489	0.9303
436	3	2	1	24	2	0.00000	0.00000	0.81676	0.00551	0.05959	0.6891
437	3	3	2	24	2	0.00000	0.00000	0.79839	0.00553	0.03275	0.5265
438	6	3	1	21	3	0.40542	0.07866	0.10390	0.00346	0.04299	0.6876
439	5	2	3	24	1	0.00000	0.04642	0.06972	0.01583	0.00000	0.8490
440	6	3	1	23	1	0.00000	0.00000	0.12206	0.00933	0.05733	1.0000
441	5	1	2	22	1	1.52866	0.17425	0.02217	0.00656	0.01122	0.4203
442	7	1	2	23	3	1.39289	0.00000	0.00000	0.00462	0.01268	0.8853
443	4	1	2	23	3	1.45852	0.18098	0.70956	0.00018	0.02478	0.7371
444	5	3	3	23	3	1.90471	0.26540	0.28705	0.00583	0.00000	0.6873
445	6	2	3	22	3	1.27338	0.21239	0.00000	0.00577	0.00431	0.7078
446	7	2	3	25	1	0.00000	0.10353	0.00000	0.01491	0.00000	0.6580

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
447	4	1	2	23	2	0.93822	0.15950	0.65867	0.00052	0.01982	0.5019
448	6	2	2	25	1	2.47665	0.26851	0.00000	0.01154	0.00377	0.8531
449	7	1	1	23	2	2.91973	0.00000	0.00000	0.00638	0.03392	0.7116
450	3	2	3	24	1	0.00000	0.00979	0.72141	0.01224	0.00000	0.4956
451	3	2	2	23	1	0.14854	0.07193	0.74541	0.01046	0.00938	0.8553
452	5	2	2	25	1	1.77172	0.16772	0.08565	0.01319	0.00000	0.7097
453	4	3	2	21	3	2.99135	0.27920	0.17774	0.00402	0.02850	0.7679
454	6	3	2	21	2	3.07379	0.33298	0.00000	0.00657	0.00879	0.8850
455	3	3	2	24	3	0.00000	0.00000	1.27692	0.00058	0.05704	0.8462
456	4	3	2	23	3	0.00000	0.04714	0.55344	0.00291	0.03560	0.7511
457	6	3	1	21	2	0.22542	0.05098	0.09664	0.00486	0.05018	0.8281
458	3	1	1	24	2	1.38207	0.00000	1.57904	0.00242	0.06012	0.7603
459	4	1	1	22	3	4.81197	0.29334	0.48387	0.00244	0.05230	0.8605
460	3	3	2	22	1	1.51978	0.07195	0.17388	0.01471	0.02500	0.9342
461	5	1	1	23	1	3.19451	0.19912	0.00000	0.00851	0.03296	1.0000
462	7	1	1	23	3	2.74869	0.00000	0.00000	0.00573	0.03409	0.9494
463	4	3	1	21	3	0.36462	0.02832	0.18066	0.00370	0.06577	0.6706
464	4	2	1	25	2	0.00000	0.00000	0.33042	0.00908	0.05697	0.7454
465	7	3	2	25	2	2.45919	0.12071	0.11621	0.00700	0.03643	0.8855
466	5	3	2	23	2	2.24829	0.20373	0.01734	0.00807	0.01812	0.8997
467	7	3	3	21	1	1.60725	0.19626	0.00000	0.01570	0.00000	0.5010
468	4	3	3	25	1	0.00000	0.01300	0.46753	0.01441	0.00000	0.3910
469	3	2	2	23	2	0.00000	0.10678	1.44287	0.00000	0.04107	0.8328
470	7	2	3	25	2	0.50347	0.18301	0.00000	0.00909	0.00000	0.8189
471	7	2	3	23	3	0.94339	0.11628	0.00000	0.00550	0.00429	0.9596
472	6	3	1	24	2	0.00000	0.00540	0.11564	0.00545	0.05918	0.7183
473	4	2	1	22	3	2.64795	0.06069	0.60702	0.00158	0.07936	0.6955
474	4	2	1	23	2	0.00000	0.00964	0.20369	0.00970	0.05512	0.6306
475	3	2	2	25	3	0.00000	0.00000	1.55272	0.00000	0.06085	0.8028
476	3	3	1	22	2	0.00000	0.01397	0.23962	0.00509	0.06135	0.7652
477	3	2	3	21	2	0.42831	0.42850	0.80667	0.00000	0.00000	0.8614
478	5	3	2	22	2	2.64245	0.27166	0.00000	0.00751	0.01481	0.7571
479	6	3	2	23	1	2.57322	0.16302	0.00000	0.01555	0.01925	0.8204
480	5	1	2	23	1	1.27971	0.14770	0.01213	0.00684	0.00844	0.8013
481	5	3	3	21	2	2.58547	0.31609	0.00000	0.00836	0.00000	1.0000
482	6	3	3	21	2	2.72432	0.33806	0.00000	0.00793	0.00159	0.8871
483	6	2	1	24	3	0.52058	0.05047	0.06590	0.00390	0.05794	0.8144
484	7	2	2	25	1	2.78758	0.27184	0.00000	0.01035	0.01486	0.8814
485	6	2	1	22	2	1.34174	0.15240	0.01044	0.00944	0.04365	0.9140
486	7	1	1	25	2	2.61212	0.00000	0.00000	0.00508	0.04276	0.8147
487	5	1	2	25	3	0.22876	0.00000	0.18163	0.00269	0.01591	0.9082
488	4	1	1	25	2	2.01064	0.00000	0.56472	0.00767	0.05228	0.9672
489	3	1	3	24	3	1.45852	0.19759	0.89284	0.00000	0.02558	0.6893
490	3	2	1	22	3	3.85656	0.08778	1.42371	0.00087	0.09791	0.8732
491	4	2	1	21	2	1.33148	0.20349	0.06809	0.00808	0.05151	0.7634
492	5	2	1	25	1	0.00000	0.00411	0.12197	0.01289	0.05112	0.6683
493	4	2	3	23	2	0.38220	0.21689	0.30907	0.00728	0.00000	1.0000
494	4	1	2	24	3	0.58340	0.12742	0.57637	0.00066	0.02203	0.9793
495	7	1	3	21	3	0.03562	0.08550	0.13486	0.00380	0.00000	0.9342
496	5	3	1	23	1	0.01858	0.00329	0.11774	0.01102	0.05445	0.8788
497	6	1	3	25	3	0.00000	0.00000	0.31007	0.00367	0.00101	0.7730
498	4	3	3	22	2	1.27319	0.13484	0.30073	0.01024	0.00000	0.5607
499	5	2	2	22	2	3.02529	0.35106	0.00000	0.00594	0.00945	0.7197
500	6	3	1	22	1	0.00000	0.00000	0.10655	0.00998	0.05546	0.9009
501	6	2	3	23	1	0.35950	0.14440	0.00000	0.01444	0.00000	0.8403
502	7	1	1	21	2	2.28513	0.02850	0.00000	0.00840	0.02437	0.7938
503	7	3	2	23	1	2.77165	0.19467	0.00000	0.01455	0.01959	0.7992
504	5	3	1	23	3	0.01452	0.00535	0.10739	0.00448	0.06093	0.8832
505	4	3	3	22	3	1.91445	0.29579	0.53006	0.00284	0.00255	0.8782

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
506	7	2	3	22	3	1.04723	0.14001	0.00000	0.00547	0.00623	0.8694
507	7	2	1	23	1	1.45407	0.18936	0.00000	0.00869	0.04050	0.9969
508	7	1	2	21	3	1.13841	0.03774	0.00000	0.00491	0.01037	0.9130
509	4	3	3	25	2	0.11637	0.03375	0.59768	0.01047	0.00000	0.8711
510	6	2	1	21	3	2.33726	0.13796	0.00000	0.00315	0.05694	0.9121
511	4	3	2	23	2	0.01374	0.07525	0.14776	0.00890	0.02889	0.8759
512	5	3	3	22	3	2.50853	0.31660	0.18211	0.00505	0.00137	0.7528
513	7	1	2	23	2	0.68265	0.00424	0.00000	0.00572	0.00738	0.7890
514	5	1	1	22	1	3.14348	0.22524	0.00000	0.00913	0.03248	1.0000
515	7	2	3	24	1	0.13040	0.13063	0.00000	0.01413	0.00000	0.7485
516	4	3	3	23	1	0.00000	0.01607	0.25179	0.01545	0.00000	0.8572
517	7	2	1	24	3	0.65044	0.07406	0.02862	0.00366	0.05686	1.0000
518	7	3	3	24	1	0.75001	0.08612	0.00000	0.02000	0.00000	0.8002
519	3	2	2	22	2	1.07739	0.24851	1.46433	0.00000	0.03756	0.9909
520	3	1	2	23	1	1.18139	0.07167	1.27882	0.00480	0.03474	0.9040
521	5	2	1	21	2	1.81161	0.22141	0.00000	0.00933	0.04249	0.9354
522	5	2	3	22	3	1.47987	0.29267	0.19244	0.00376	0.00048	0.9265
523	7	1	2	25	1	0.81419	0.08629	0.03849	0.00522	0.00009	1.0000
524	7	1	1	21	3	3.35106	0.00000	0.00000	0.00507	0.02871	0.4223
525	7	2	2	23	3	4.45277	0.21588	0.00000	0.00172	0.03267	0.6790
526	6	1	2	24	1	0.85867	0.11210	0.05328	0.00589	0.00273	1.0000
527	5	3	3	24	1	0.00000	0.01676	0.07671	0.01727	0.00000	0.8089
528	5	1	1	23	2	3.40282	0.15273	0.00000	0.00816	0.03839	0.9523
529	5	1	3	25	1	0.00000	0.00000	0.62175	0.01190	0.00000	0.8034
530	5	2	3	22	1	0.51619	0.15104	0.00000	0.01375	0.00000	1.0000
531	7	3	1	22	2	0.33601	0.07952	0.07710	0.00506	0.04868	0.9666
532	7	3	1	23	2	0.26661	0.06087	0.08413	0.00569	0.05128	1.0000
533	4	1	3	21	1	0.00000	0.24599	0.65153	0.00380	0.00000	0.7727
534	7	1	3	23	1	0.00000	0.00644	0.03596	0.00765	0.00242	0.8475
535	5	3	1	22	3	0.05747	0.01403	0.10312	0.00450	0.05936	1.0000
536	3	2	3	23	3	1.99228	0.28406	1.11718	0.00000	0.02076	0.7624
537	3	2	3	25	1	0.00000	0.00000	0.76818	0.01263	0.00000	0.8079
538	3	1	1	25	3	0.00000	0.00000	1.61313	0.00000	0.08046	0.8175
539	4	2	2	22	2	2.53424	0.32044	0.21872	0.00415	0.01500	0.8181
540	6	2	3	21	1	1.23070	0.21599	0.00000	0.01215	0.00000	0.7797
541	4	1	2	21	2	2.36912	0.26189	0.61476	0.00074	0.02428	0.9943
542	3	2	1	23	1	1.16337	0.10998	0.15124	0.01130	0.04607	0.9346
543	7	2	3	21	2	1.76930	0.23379	0.00000	0.00534	0.00937	0.8010
544	6	2	2	22	3	3.69995	0.29177	0.00000	0.00450	0.02635	0.8232
545	4	2	1	23	3	0.83017	0.00000	0.52445	0.00266	0.07612	0.9954
546	6	3	3	25	3	1.04263	0.19205	0.29568	0.00686	0.00000	0.9023
547	4	2	3	22	3	1.53591	0.32215	0.76222	0.00000	0.00499	0.9541
548	7	2	3	24	3	0.79452	0.09903	0.00000	0.00572	0.00223	0.8930
549	6	2	2	23	3	3.46950	0.26029	0.03372	0.00451	0.02524	0.9212
550	6	3	1	24	3	0.10750	0.03337	0.10465	0.00414	0.05315	0.9667
551	6	2	1	23	1	1.71983	0.17272	0.00000	0.01120	0.04209	0.6703
552	5	1	1	25	2	3.10039	0.02092	0.00000	0.00927	0.04614	0.8216
553	6	2	2	23	1	2.87963	0.31563	0.00000	0.00979	0.01284	0.9156
554	5	1	2	24	2	0.66433	0.04346	0.16965	0.00395	0.01148	0.7623
555	7	3	2	21	2	3.13616	0.30367	0.00000	0.00648	0.01337	0.9757
556	7	2	2	23	1	2.72729	0.30290	0.00000	0.00886	0.01628	0.8852
557	3	1	1	21	2	4.70253	0.34205	1.30791	0.00225	0.05371	0.9481
558	6	3	2	22	1	2.71940	0.22944	0.00000	0.01362	0.01695	0.9261
559	4	1	3	23	3	0.98948	0.17196	1.02954	0.00000	0.01688	0.8989
560	7	1	3	25	1	0.00000	0.00000	0.20887	0.00920	0.00000	0.8864
561	4	2	2	24	2	0.62337	0.17137	0.47695	0.00385	0.01530	1.0000
562	7	3	3	22	1	1.34187	0.15981	0.00000	0.01728	0.00000	0.8647
563	6	1	1	22	3	3.25075	0.04071	0.00000	0.00471	0.03331	0.7821
564	6	2	1	25	3	0.15728	0.03937	0.07910	0.00416	0.05666	0.8777

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
565	3	1	3	25	2	0.00000	0.09189	0.67850	0.00274	0.00530	0.9343
566	3	1	3	24	2	0.00000	0.18926	0.80738	0.00017	0.00358	0.9486
567	7	2	2	25	3	2.84150	0.12515	0.09218	0.00125	0.03848	1.0000
568	3	3	1	23	3	0.00000	0.00000	0.42906	0.00280	0.06915	0.8329
569	6	2	1	24	1	0.53817	0.08967	0.03355	0.01145	0.04721	0.9938
570	6	3	2	24	3	1.24182	0.13590	0.16657	0.00226	0.02493	1.0000
571	4	1	1	24	2	2.83063	0.04332	0.41728	0.00722	0.04765	0.7834
572	7	3	3	22	2	2.73142	0.32534	0.00000	0.00821	0.00205	0.6679
573	4	1	3	23	1	0.00000	0.01081	0.55313	0.01058	0.00000	0.5038
574	4	3	1	21	1	1.18484	0.07911	0.00000	0.01217	0.04839	0.7865
575	7	3	2	23	3	1.63386	0.14647	0.13705	0.00211	0.02771	0.7506
576	6	3	3	21	1	1.59191	0.18254	0.00000	0.01572	0.00000	0.6573
577	5	2	3	21	1	1.24037	0.23419	0.00000	0.01198	0.00000	0.9023
578	3	1	1	21	1	5.00611	0.28185	1.15811	0.00745	0.05620	0.6879
579	4	3	3	23	2	0.71386	0.07637	0.40357	0.01084	0.00000	0.5104
580	4	1	1	25	3	0.00000	0.00000	0.74563	0.00164	0.06064	0.6878
581	4	2	3	24	2	0.00000	0.13003	0.32350	0.00958	0.00000	0.6635
582	5	2	2	24	3	1.33704	0.17429	0.52629	0.00200	0.02565	1.0000
583	5	2	1	24	2	0.00000	0.00000	0.14514	0.01019	0.05558	0.8250
584	5	1	3	21	3	0.22874	0.18447	0.74464	0.00151	0.00000	0.7382
585	5	3	1	21	2	0.07530	0.02782	0.07695	0.00551	0.05445	0.7124
586	3	1	2	21	1	2.69800	0.29800	1.18397	0.00192	0.03187	0.9821
587	3	3	2	24	1	0.64782	0.04665	0.46562	0.01400	0.01654	0.6745
588	7	1	3	24	3	0.00000	0.00000	0.06642	0.00447	0.00000	0.7973
589	3	2	3	25	3	0.88675	0.18023	0.95544	0.00000	0.01804	0.9027
590	7	2	1	23	2	1.12452	0.11049	0.01551	0.00761	0.04892	0.8013
591	4	3	1	22	1	1.01939	0.04945	0.02632	0.01237	0.04961	0.7919
592	3	3	2	21	3	0.72175	0.13568	0.99914	0.00170	0.06046	0.8775
593	7	1	2	25	3	1.57116	0.00000	0.00000	0.00500	0.01624	0.7247
594	4	2	1	25	3	0.00000	0.00000	0.57165	0.00171	0.07223	0.7204
595	3	2	1	24	3	1.32911	0.00000	1.41698	0.00000	0.09322	0.9829
596	6	2	1	25	2	0.00000	0.01580	0.09415	0.01024	0.05437	0.7188
597	5	2	3	25	2	0.02938	0.13432	0.15081	0.01132	0.00000	0.7843
598	7	1	3	25	2	0.00000	0.00000	0.20392	0.00561	0.00000	0.7859
599	7	1	1	25	3	2.23487	0.00000	0.00000	0.00742	0.03577	0.7072
600	4	2	1	21	1	2.49066	0.20985	0.00000	0.01141	0.04518	0.6437
601	3	2	2	24	2	0.00000	0.00000	1.39422	0.00011	0.04303	1.0000
602	7	3	1	21	3	0.46174	0.11364	0.11191	0.00219	0.03445	0.8054
603	3	1	1	22	1	4.33955	0.20302	1.12816	0.00789	0.05455	0.7186
604	5	1	3	22	2	0.00000	0.13083	0.56136	0.00300	0.00000	0.8671
605	4	3	1	21	2	0.00000	0.03994	0.05974	0.00595	0.05546	0.3648
606	6	1	3	23	3	0.00000	0.01703	0.29262	0.00373	0.00000	0.5342
607	6	3	2	21	3	3.93992	0.30103	0.01891	0.00313	0.01189	0.7552
608	4	3	1	25	1	0.44374	0.01115	0.13119	0.01052	0.05461	0.7749
609	5	3	1	22	1	0.25705	0.01875	0.08872	0.01173	0.05244	0.7770
610	5	2	3	21	3	1.92789	0.33301	0.18209	0.00249	0.00265	0.7959
611	4	3	1	23	3	0.00000	0.00000	0.15486	0.00426	0.06444	0.7289
612	7	2	2	21	3	4.03250	0.25948	0.00000	0.00269	0.02599	0.7627
613	3	1	1	24	3	1.60781	0.06680	1.70464	0.00000	0.07819	0.9505
614	3	1	3	24	1	0.00000	0.01367	0.61766	0.01001	0.00000	0.7302
615	6	2	1	25	1	0.00000	0.02236	0.09061	0.01128	0.05151	0.8613
616	7	2	2	25	2	3.15767	0.23992	0.05539	0.00720	0.02425	0.8530
617	6	2	2	24	3	2.77179	0.20795	0.09187	0.00435	0.02644	0.7702
618	3	2	2	24	3	1.14014	0.10247	1.59011	0.00000	0.05956	0.6536
619	6	1	1	24	1	2.90409	0.14669	0.00000	0.00598	0.02780	0.8268
620	6	3	3	24	3	2.00092	0.25968	0.18450	0.00634	0.00000	0.8235
621	5	3	2	25	2	0.40734	0.06838	0.21791	0.00755	0.02667	0.7963
622	7	1	1	22	1	2.41337	0.14003	0.00000	0.00495	0.02057	0.9531
623	3	2	1	23	2	0.00000	0.01722	0.70204	0.00645	0.06057	0.8809

Table 14, continued
	Inputs (controllable factors)					Outputs (response variables)
Scenario	Bed	Nurse	Doctor	Triage	Pharmacy	1	2	3	4	5	Efficiency
				nurse	employee
624	5	2	1	24	3	0.28038	0.00000	0.14342	0.00399	0.06283	1.0000
625	7	3	3	25	3	2.23646	0.22445	0.15172	0.00510	0.00640	0.8238
626	5	2	2	24	2	2.45002	0.31826	0.08056	0.00618	0.00094	0.8208
627	5	2	1	23	2	0.00000	0.04079	0.10192	0.01023	0.05242	0.8649
628	7	3	1	24	1	0.00000	0.00000	0.10015	0.00839	0.05676	0.9530
629	7	1	2	22	3	1.27840	0.00000	0.00000	0.00464	0.01162	0.9412
630	4	1	2	23	1	1.03176	0.12258	0.23809	0.00716	0.01449	0.8206
631	3	1	2	25	3	0.88085	0.16438	0.97460	0.00000	0.03255	0.6257
632	7	2	2	23	2	3.25230	0.29809	0.00000	0.00622	0.02077	0.5748
633	3	2	3	22	2	0.08437	0.36177	0.81071	0.00000	0.00000	0.6330
634	7	1	2	22	2	0.60569	0.02232	0.00000	0.00592	0.00666	0.9761
635	5	3	3	24	2	0.72399	0.09146	0.19348	0.01239	0.00000	0.7978
636	6	3	2	25	2	2.12148	0.12543	0.14530	0.00670	0.02768	0.8226
637	4	3	3	25	3	0.74302	0.12863	0.72145	0.00584	0.00086	0.8475
638	7	3	2	22	3	2.25312	0.18195	0.11195	0.00224	0.02383	0.8719
639	3	1	2	21	3	2.70332	0.26142	1.10497	0.00000	0.03474	0.8180
640	6	1	2	22	3	1.32725	0.01921	0.00000	0.00451	0.01329	0.9969
641	6	3	1	25	3	0.06010	0.02363	0.10427	0.00428	0.05571	1.0000
642	5	3	2	25	3	0.00000	0.05247	0.32801	0.00210	0.02792	0.9951
643	5	1	3	21	1	0.00000	0.10433	0.51289	0.00677	0.00000	1.0000
644	7	1	2	22	1	0.77073	0.10024	0.00217	0.00556	0.00388	0.7302
645	5	2	3	24	2	0.45199	0.17761	0.12952	0.01003	0.00000	0.6869
646	7	1	1	25	1	2.66128	0.06782	0.00000	0.00224	0.03350	0.9394
647	4	1	3	25	3	0.10524	0.04912	0.46598	0.00160	0.01582	0.9233
648	5	1	1	22	3	3.93887	0.21700	0.00000	0.00499	0.04103	0.7635
649	5	2	3	23	3	1.11161	0.24262	0.18522	0.00508	0.00000	0.9788
650	6	2	2	25	3	1.13169	0.12393	0.16841	0.00395	0.03039	0.8972
651	5	2	2	21	1	3.11707	0.33444	0.00000	0.00897	0.01683	0.8330
652	5	2	1	22	2	0.50170	0.12022	0.02821	0.01002	0.04780	0.8653
653	5	2	1	21	1	2.72657	0.22852	0.00000	0.01127	0.04277	0.5892
654	3	1	2	25	2	0.00000	0.03097	1.14778	0.00000	0.03379	0.5132
655	3	2	3	25	2	0.00000	0.01118	0.83222	0.00842	0.00000	0.7653
656	7	2	1	21	1	2.66880	0.28533	0.00000	0.00882	0.03106	0.6571
657	5	2	3	24	3	0.82530	0.20426	0.21160	0.00570	0.00000	0.4607
658	7	1	3	22	2	0.13710	0.01252	0.00000	0.00517	0.00236	1.0000
659	5	2	2	25	3	0.00000	0.07518	0.67305	0.00149	0.03131	1.0000
660	7	1	1	22	2	2.65355	0.00000	0.00000	0.00739	0.02867	0.5707
661	7	2	2	21	2	3.06164	0.30958	0.00000	0.00541	0.01962	1.0000
662	5	1	1	21	1	3.10530	0.25354	0.00000	0.00991	0.03287	0.6000
663	3	3	2	22	2	0.00000	0.06064	0.42278	0.00734	0.03494	0.5976
664	7	1	2	24	3	1.51268	0.00000	0.00000	0.00472	0.01420	0.8756
665	5	1	3	24	3	0.00000	0.00236	0.51891	0.00222	0.00697	1.0000
666	6	2	3	21	2	2.38610	0.29737	0.00000	0.00504	0.00689	0.5146
667	5	1	1	21	3	4.09809	0.25034	0.00000	0.00535	0.04015	0.8747
668	4	1	3	25	2	0.00000	0.02300	0.46543	0.00446	0.00126	0.6514
669	5	1	1	24	3	2.18947	0.01586	0.03341	0.00445	0.04687	0.5172
670	3	3	1	21	2	0.00000	0.07965	0.20315	0.00495	0.05944	1.0000
671	4	2	3	25	2	0.00000	0.07730	0.37794	0.01065	0.00000	0.8119
672	5	2	2	22	1	2.99393	0.31721	0.00000	0.00954	0.01339	0.7653
673	5	2	1	25	2	0.00000	0.00000	0.17237	0.01019	0.05735	0.8772
674	6	1	2	22	2	0.82059	0.03979	0.00000	0.00540	0.00847	1.0000
675	6	1	2	23	2	0.83194	0.01734	0.00000	0.00537	0.00865	0.7046

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DMU	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
1	3	1	1	21	1
2	3	1	1	21	2
3	3	1	1	21	3
4	3	2	2	23	1
5	3	2	2	23	2
6	3	2	2	23	3
7	3	3	3	25	1
8	3	3	3	25	2
9	3	3	3	25	3
10	5	1	2	25	1
11	5	1	2	25	2
12	5	1	2	25	3
13	5	2	3	21	1
14	5	2	3	21	2
15	5	2	3	21	3
16	5	3	1	23	1
17	5	3	1	23	2
18	5	3	1	23	3
19	7	1	3	23	1
20	7	1	3	23	2
21	7	1	3	23	3
22	7	2	1	25	1
23	7	2	1	25	2
24	7	2	1	25	3
25	7	3	2	21	1
26	7	3	2	21	2
27	7	3	2	21	3

DMU	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
1	3	1	1	21	1
2	3	1	1	21	2
3	3	1	1	21	3
4	3	2	2	23	1
5	3	2	2	23	2
6	3	2	2	23	3
7	3	3	3	25	1
8	3	3	3	25	2
9	3	3	3	25	3
10	5	1	2	25	1
11	5	1	2	25	2
12	5	1	2	25	3
13	5	2	3	21	1
14	5	2	3	21	2
15	5	2	3	21	3
16	5	3	1	23	1
17	5	3	1	23	2
18	5	3	1	23	3
19	7	1	3	23	1
20	7	1	3	23	2
21	7	1	3	23	3
22	7	2	1	25	1
23	7	2	1	25	2
24	7	2	1	25	3
25	7	3	2	21	1
26	7	3	2	21	2
27	7	3	2	21	3

A simulation optimization approach for integrated resource allocation in an emergency department,pharmacy,and lab

Abstract

Keywords

1. Introduction

Table 1 Characteristic comparison chart

2.1 Simulation

Table 2 T-test results for simulation base model validation

Table 4 Controllable factors of this study

2.2.1.1. Determining the levels of considered controllable factors

2.2.1.2. Design of experimental scenarios using Taguchi method

Table 5 Designed scenarios by Taguchi method

2.2.1.3. Simulating designed experimental scenarios

3.1 Simulating the designed scenarios and obtaining response variables for each scenario

Table 8 MAPE values of optimum estimation networks and regression methods

3.3 Evaluating the efficiency of all scenarios using DEA and determining the optimal resource allocation

Table 10 Maximin weight model results for efficient DMUs

Footnotes

Acknowledgments

Appendix

References

Table 1
Characteristic comparison chart

Table 2
T-test results for simulation base model validation

Table 4
Controllable factors of this study

Table 5
Designed scenarios by Taguchi method

Table 8
MAPE values of optimum estimation networks and regression methods

Table 10
Maximin weight model results for efficient DMUs

DMU	$X_{1}$	$X_{2}$	$X_{3}$	$X_{4}$	$X_{5}$
1	3	1	1	21	1
2	3	1	1	21	2
3	3	1	1	21	3
4	3	2	2	23	1
5	3	2	2	23	2
6	3	2	2	23	3
7	3	3	3	25	1
8	3	3	3	25	2
9	3	3	3	25	3
10	5	1	2	25	1
11	5	1	2	25	2
12	5	1	2	25	3
13	5	2	3	21	1
14	5	2	3	21	2
15	5	2	3	21	3
16	5	3	1	23	1
17	5	3	1	23	2
18	5	3	1	23	3
19	7	1	3	23	1
20	7	1	3	23	2
21	7	1	3	23	3
22	7	2	1	25	1
23	7	2	1	25	2
24	7	2	1	25	3
25	7	3	2	21	1
26	7	3	2	21	2
27	7	3	2	21	3