Case Study: Simulation Modeling

A Deeper LookIndustrial Engineers traditionally perform detailed facility planning in manufacturing, aviation and other industries. Today, as the healthcare industry looks to provide higher quality and more cost effective care, Industrial and Systems Engineers are playing a more prominent role in this area. One tool that is often used to test new systems without physically changing the current process is simulation. In healthcare facility planning, simulation can be used to determine the impact of different layouts and new workflows before knocking down a single wall, saving valuable time and money.

Recently, an outpatient spinal surgery center decided to extend its services by building satellite facilities in different parts of the country. These new facilities will be smaller than the existing facility and operate using a slightly altered process flow. In order to determine the appropriate space requirements for the new, smaller scale model, a simulation model was built using Arena Simulation software. The model was developed using process time data from the headquarters facility. Two major goals of this project were confirming patients could recover completely in a PACU room, without causing other patients to wait in the operating room, and determining whether the space was large enough to bring in an additional surgeon, potentially leading to the treatment of more patients.

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SIMULATION IN FACILITY DESIGN

Many times, simulation is used for improving workflows and processes that involve ordered steps, such as production lines. A hospital generally follows the same type of processes, but the entities flowing through the system are people instead of parts and it is often much more difficult to reduce variation, especially when surgery is involved. Healthcare personnel typically do not initially trust a simulated system because they believe the system is unable to properly factor human error and human reaction times into the system. Therefore, when using simulation as a tool to recreate a system, it is very important to clearly show how the simulated system is working in relation to the actual one. It is also critical to stress that the simulation is a simplified version of the actual system that takes into account the specific variables that can affect the process being studied. In order to obtain complete client buy-in for a simulation model, all assumptions concerning the actual system that are developed into the model should be discussed at length. Healthcare is a great place for simulation to be used in facility design because it allows for spaces to be planned more efficiently when they are built. Basing the layouts on more efficient practices leads to an easier implementation of more productive workflows, staff movement and patient routing.

Simulation ModelingCHALLENGEAn outpatient spinal surgery center has experienced exponential

growth over the past 10 years. Today, this institution has expanded to

over 450 employees who help perform over 400 surgeries each month.

The growing demand for minimally invasive outpatient surgery led this

surgery center to expand their reach by offering services in additional

locations. Because these new locations will be smaller, they will use

fewer resources. The administration also hopes that the new locations

will have more efficient spaces and processes.

SOLUTIONA simulation study will determine if the newly designed process is

optimal and if the number of rooms is adequate for the volume of

patients the outpatient spinal surgery center hopes to serve.

The results of the simulation study showed that four PACU rooms are

adequate, as long as PRE-OP rooms are used for recovery when there

is a full PACU. Additionally, adding a surgeon negligibly increases time

spent waiting for a PACU room, but decreases the average total waiting

time when the same quantity of patients is seen. Further research

involving optimal patient scheduling, maximum capacity, personnel

utilization, and cost analysis can be done using simulation and other

operations research tools.

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ObjECTIvES FOr ThE SIMULATION STUDY The project architect and the client have defined three objectives for this simulation study:

1. Confirm that full recovery (phase 1 and phase 2) can take place in the PACU with out blocking patients exiting the operating room.

2. Optimize the number of PACUs needed for an outpatient spinal surgery center while minimizing the amount of time a patient must wait for a PACU.

3. Determine if this optimal space program will be adequate if an additional surgeon is added to the team.

The first objective involves determining which resources would be affected if patients are allowed to recover completely in a PACU room. The second objective involves two goals; the first is to determine the optimal number of PACU rooms needed to operate the surgery center using the new patient flow. The second goal requires that the time patients spend waiting in the operating room for a PACU room is reduced to zero, if possible. Any time a patient spends in the operating room that is not related to their surgery is considered non-value added time. The third and final objective is to determine if this optimal space program will be adequate if an additional surgeon is added to the team. Discrete event simulation will be used to investigate potential solutions to each of the aforementioned objectives.

ASSUMpTIONS When a simulation model is developed, it is not meant to replicate every detail of the actual system. The main goal is to incorporate the relevant parts of the system in a simplified model. By removing extra steps and resources, the model can be designed to answer specific questions. This simplification process is one characteristic of simulation modeling that makes it such a powerful tool. As complexity increase, the model becomes more difficult to work with, leading to a greater chance of mistakes and over-development. To prevent unnecessary work, an assumptions document is generated to account for any elements that are intentionally removed from the simulation model. The following selection of assumptions was incorporated into the simulation model:

• The previously described current operating conditions are accurate

• There are strictly three operating rooms

• All areas will be appropriately staffed.

• The maximum number of patients treated in one day is ten

• Patients arrive on time

• All pre-operative activities, including meeting with a PRE-OP nurse, anesthesiologist, and surgeon, using the restroom, and being prepared for surgery, are consolidated into one process

• Additional ancillary services are not pertinent to this study

These assumptions, along with several others, were carefully considered when building the model. This list provided a starting point for validation of the model, once the initial prototype was completed.

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INpUT DATA ANALYSIS Many times, it is difficult to obtain actual data from the healthcare system whose process is being analyzed. The difficulties are typically caused by a lack of available data or wariness about sharing confidential patient information. In this study, the client was able to provide six months of de-identified patient data. After obtaining the data, it needed to be prepared before it could be ap-plied to the simulation model. The raw data contained “start” and “finish” times for five different processes, including PRE-OP, sur-gery, operating room, phase 1 and phase 2. Some records only contained a PRE-OP start time and no other times. These records and others with similar characteristics were removed from the data set because there was not enough information to use them.

Once the data records were prepared, regression analysis tests were used to determine if the data was accurate. It was assumed that there should be high correlation between the amount of time patients spend in the operating room and the amount of time the surgeon takes to perform the operation. It was also assumed that there should be little correlation between the amount of time spent preparing for surgery and the amount of time it takes to perform the operation. Both of these assumptions were correct. The

graph below with an R value of .0052, confirms the second assumption.

rELATION bETwEEN SUrGErY LENGTh OF STAY AND prE-Op LENGTh OF STAY

After determining that the data was accurate, the histogram for each process was fit to an empirical distribution using the Input Analyzer included with the Arena Simulation software package. Before fitting the data, some conclusions could be made about the general shape of the distribution based on the qualities of the data. For instance, the data is a list of process times, therefore, it would be impractical to include distributions that contain numbers less than zero. Additionally, time is continuous, so all discrete distributions could be eliminated. After eliminating a number of distributions, a few candidates remained to decide between. As expected, all of the process times followed a log-normal distribution.

Empirical distribution ovErlaid on

prE-op lEngth of stay data

TIME SpENT IN prE-Op

TIM

E S

pEN

T IN

SU

rG

ErY

PATIEnTS LInEAR REGRESSIOn

2

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SIMULATION LOGIC Many different parts go into a simulation model before it is even built. After learning about the process that is being stud-ied, making the necessary assumptions and gathering all of the data needed to run a proper simulation model, the model needs to be put together. Experienced model builders might call this the easy part, but no matter how seasoned the builder, creating a model still takes time.

A great starting point for building a simulation model is the process flow chart. This chart shows all of the major parts that need to be included in the simulation in a more simplified way. After translating the flow chart into a proper sequence of events in the model, process time distributions are added. Relevant variables are adjusted so the elements of the model correlate with the elements of the actual system.

Throughout the simulation, the Arena Simulation software automatically keeps statistics. Additionally, the modeler uses a specific element to keep track of some statistics manually. All of the data collected from this baseline model was used to ensure the model was appropriately representing the actual system. Verification and validation methods confirmed the accuracy of the model. Once the model was verified and validated, small changes were made so that different scenarios could be tested.

vALIDATION AND vErIFICATION After developing a simulation model using appropriate assump-tions and input data, it was imperative to ensure that the model was performing accurately. Process time distributions and faulty model logic were two potential sources of variation between the actual system and the simulated system. Two different tech-niques, validation and verification, help check the performance level of a simulation model and ensure that it properly rep-resents the actual system.

Techniques presented by Law in Simulation Modeling and Analysis were used to validate and verify the simulation model. Verification techniques used to confirm that the assumptions are suitably applied to the simulation model include creating the simulation in modules with increasing complexity, observing animations of the output, and reviews by an unbiased colleague familiar with simulation modeling. Animation, when used prop-erly, is useful because it show the entities moving through the system in real time. Throughout the creation of this model, rudi-mentary animations were used to track entities and determine why different problems were occurring. The Arena Simulation software also uses a program language- based debugging tool to show where discrepancies in variable names and other logic can be found. This tool was useful for correcting technical imper-fections involving the terminology used in the model.

Law’s validation techniques were also used to confirm the accu-racy of the model. Since a similar system already exists, a model was developed based on the existing system. A paired-t confi-dence test was used to determine, with approximately 99.9% confidence, that there was not a significant difference between data collected from the existing system and output data from the simulation model. In addition to this mathematical validation, the graph below clearly shows that the actual values and simu-lated values are almost exactly the same. Additionally, a written assumptions document was kept, the system was observed, the modeler had conversations with subject-matter experts, such as nurses, physicians and other support staff, and existing theory regarding patient procedure and waiting times was explored. After confirming the design using validation and verification techniques, different options and scenarios could be tested.

ExpECTED SYSTEM vALUES vS. ACTUAL SIMULATED vALUES

prO

CES

S T

IMES

(hO

Ur

S)

prOCESS CATEGOrYExPECTED (TIME STUDy VALUES) ACTUAL (SIMULATIOn VALUES)

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SCENARIOS OPTIONSCurrentoperatingconditions(ValidationModel) Changenothing

1.CompleterecoveryinPACU;nooverflow A.Addasurgeon

2.CompleterecoveryinPACU;overflowdirectlyfromsurgerytoPRE-OP B.AddaPACUroom

3.CompleterecoveryinPACU;overflowfromPACUtodischargechairforphase2recovery C.AddasurgeonandaPACUroom

SCENArIOS AND OpTIONS Three different scenarios were developed along with three options to be tested in each scenario. The data obtained from the client based off of the situation in which patients complete phase 1 recovery in the PACU and then move to a discharge recliner for phase 2 recovery. Therefore, this situation was used as the validation model. The first scenario requires that a patient complete phase 1 and phase 2 recovery in the PACU, with no specified location for overflow. If the PACU is full when a patient is finished with surgery, that patient must wait in the operating room until a PACU room is available. Obviously, this non-value added use of the operating room does not seem like an ideal situation, but the Healthcare Systems Engineer included it to determine whether an overflow plan was actu-ally necessary. The second scenario requires that a patient fully recovers in the PACU and specifies open PRE-OP rooms as the designated overflow location. This scenario requires that patients be moved from the operating room directly to a PRE-OP room if the PACU is full. The third scenario once again requires that a patient complete phase 1 and phase 2 recovery in the PACU and specifies that discharge recliners be used for overflow recovery. In this case, when the PACU reaches capac-ity, a patient who has transitioned into phase 2 recovery may be moved to a discharge recliner to create a vacancy in a PACU room for a patient just exiting the operating room. These three scenarios directly relate to the change in patient flow that the client is considering.

In addition to these three scenarios, three options were also created to test the proposed objectives. Each of these three options was applied separately to the individual scenarios, leading to the creation of twelve different simulation models. The first option simply added one surgeon to the team. The goal of this option was to determine if hiring an additional surgeon decreased waiting times at any of the process steps. The second option added one PACU to the center. Once again, the goal of this option was to determine if the returns for adding

one PACU room could be measured in decreased patient waiting time. The third option combined the first two by adding one surgeon and one PACU room. The goal of this option was to determine if more patients could be treated and if rooms were better utilized.

Each of these scenarios, combined with the three options led to a wide range of results to compare. Some of the results were surprising; others were expected. The analysis of these results led to a better idea of how different resources impact the waiting time of patients at an outpatient surgery center.

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OUTpUT DATA ANALYSIS In each of the simulation models, including the baseline model, 40 replications were simulated to ensure that the modeled system mimicked the actual system. Producing this many repli-cations allowed for a very small half width to be achieved when determining confidence intervals based on the output data.

The first scenario was created to show that it was possible to allow patients to recover completely in the PACU without moving to a discharge recliner upon reaching phase 2 recovery. This scenario was also used to determine if an overflow plan was not needed. The results show that, with approximately 99.9% confidence, scenario 1 is worse than the current operating conditions and an overflow area is essential to the patient flow in this outpatient surgery center. The calculation for the preceding confidence interval can be found in Appendix IV. Adding a surgeon does not improve the results of this scenario; in fact, it worsens them. Increasing the number of PACU rooms helps mitigate the problem of not having an overflow area, but not any more than having the discharge recliners, as was the case in the current operating conditions. The addition of a surgeon and a PACU room only reduces the amount of time a patient spends waiting for a surgeon; it does not help reduce the time spent waiting for a PACU room. It

is clear from this comparison of recovery waiting times that scenario 1 was, in three out of four of the options, worse than the validation model.

The second scenario was the first option that allowed for an overflow of patients. In scenario two, patients were moved to PRE-OP rooms after surgery if the PACU was full, which proved to be a much better solution. The results of this scenario were excellent, with no non-value added time spent in the operating room, leading to the hypothesis that scenario 2 is better than scenario 1, which was proven at approximately 99.9% confidence using a paired-t comparison test. This outcome aligns perfectly with the one of the objectives proposed by the client. When looking at the total waiting time, scenarios 2 and 2B had much longer total waiting times when compared to scenarios 2A and 2C. In fact, it can be stated with approximately 99.9% confidence that there is a statistically significant different between these two scenarios, and that 2A and 2C have the better outcome. In addition, there is no statistically significant difference between the recovery waiting times in each of these scenarios. Scenario 2 provides solid evidence for all three objectives, but scenario 3 must be presented before drawing conclusions.

Recovery OR Surgeon PersoninFront PreOp TotalPTWaitingTime(min)

Validation 0.56 5.66 44.99 42.59 0.18 93.98

Scenario1 9.94 5.44 45.62 40.86 0.39 102.25

Scenario1A 18.78 11.71 27.58 19.71 0.02 77.80

Scenario1B 0.47 5.40 45.73 40.67 0.39 92.66

Scenario1C 5.99 11.79 26.95 19.41 0.02 64.17

Scenario2 0.00 5.43 45.39 40.38 0.39 91.59

Scenario2A 0.07 11.73 27.13 19.17 0.02 58.13

Scenario2B 0.00 5.43 45.39 40.38 0.39 91.59

Scenario2C 0.01 11.75 27.09 18.95 0.02 57.82

Scenario3 6.11 4.90 45.11 42.22 0.29 98.62

Scenario3A 10.45 11.22 24.29 14.31 0.00 60.28

Scenario3B 0.13 5.70 45.49 38.77 0.35 90.44

Scenario3C 1.69 11.40 26.39 18.40 0.02 57.90

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In the third scenario, patients who were in phase 2 recovery could be moved from a PACU room to a discharge recliner if a patient exiting the operating room needed a PACU room.

Two options in this scenario had poor recovery waiting times. Overall, scenario 3 did not provide any added benefit over the other scenarios. There is not a statistically significant difference between the recovery times in option 3C when compared to option 2C, which was proven at approximately 99.9% confidence using a paired-t comparison test. There is also not a statistically significant difference between the total patient waiting time when comparing any of the options in scenario 3 to the parallel options in the other scenarios, as proven by inferring from the results of the previous comparison tests. Additionally, when a surgeon is added to the team, the recovery waiting time in scenario 3 actually increases

significantly; proving that scenario 3 fails to meet all of the objectives provided by the client.

The results presented in this section highlight scenario 2 as the best option, but there are other factors that need to be considered when making recommendations. These additional variables will be recognized in the final section of this report.

CONCLUSION There are a number of variables that go into a decision about a large capital investment such as this, including time and money. While certain conclusions can be made about this study based solely on the numerical outcomes, the results may lead the client to an entirely different solution due to the previously mentioned decision variables. The conclusions are based off of pure data and the project objectives, and are ignorant of monetary or time constraints.

It was determined that the desired future state could be achieved. In this future state, where patients are moved to a PRE-OP room if the PACU is full, four PRE-OP rooms and four PACU rooms will provide adequate space for up to ten patients to be treated. This workflow was referred to as Scenario 2 throughout the study. When adding a single surgeon, Scenario 2 once again proved to be the best solution for minimizing time spent waiting for a recovery room. This minimized waiting time is slightly higher than zero, but the change is not statistically significant. Based strictly on the three objectives presented by

Optimize the number of PACUs needed for an outpatient spinal surgery center

while minimizing the amount of time a patient must wait for a PACU.

Complete recovery in PACU; no overflow

No Changes

Determine if this optimal space program will be adequate if an additional

surgeon is added to the team.

Complete recovery in PACU; overflow directly from surgery to Pre-Op

Add a Surgeon

Confirm there are enough rooms for full recovery (phase 1 and phase 2) to take

place in a single place.

Recover in PACU; overflow from PACU to discharge chair for phase 2 recovery

Add a PACU Bay

Add a Surgeon and a PACU Bay Observation helped us understand the day-to-day operations

of an LSI surgery center. Staff and patient movement were

assessed using spaghetti diagrams (Fig. 1) so we could minimize

any wasteful activities in the future layout. A value stream map

showing the high-level patient experience was also defined

though observation and staff interviews.

Data was extracted from client’s EMR,

cleaned up (approx. 2,400 records) and

tested for accuracy (Fig. 2)

Verification of the model included colleague reviews, building with

increasing complexity, using animations (Fig. 3) and checking

outputs for reasonable results. Model validation included a written

assumptions document, which was confirmed by the client,

observations and conversations with current staff, literature review

and a paired-t confidence test (Fig. 4) to check the relationship

between the existing system and the model output.

In the current state of the surgery center, patients moved from

PACU rooms to discharge recliners once they transitioned

out of phase 1 recovery. The desired future state hopes to

see patients recover completely in PACU rooms with overflow

available in Pre-Op. Patients do not need to be held in the OR

until a PACU becomes available (non-value activity added.)

After confirming accuracy, the simulation model was varied to

address the objectives of the study. Three scenarios were tested to

determine which overflow pattern would work best and four options

were added resulting in 12 different simulation models.

It was determined that the desired future state could

be achieved. An example of a partial floor plan to

accommodate this workflow can be seen in Fig. 5. The

three scenarios were combined with each of the four

options and tested. Four Pre-Op rooms and four PACU

rooms will provide adequate space for up to ten patients to

be treated in this future state with no non-value added use

of the operating room (Fig. 6). Adding one surgeon resulted

in a negligible increase in time spent waiting for a PACU

room, coupled with a reduced overall waiting time (Fig. 7).

(Fig. 1)

Spaghetti diagram showing patient and staff movement.

understand the future

refine the outcome document & deliver

OBSERVATION

DATA ANALYSIS

VALIDATION AND VERIFICATIONOPTIONS

SCENARIOS TESTEDCURRENT AND FUTURE STATE

OBJECTIVES

PROCESS SIMULATIONREDEFINITION OF A CARE MODEL

LASER SPINE INSTITUTE

(Fig. 6)

(Fig. 7)

(Fig. 5)

RESULTS: ThE SIMuLATION wILL bE A uSEFuL AID FOR ThE DECISION MAkINg TEAM. FuTuRE STuDIES INVOLVINg OPTIMAL SChEDuLINg, MAxIMuM CAPACITY, AND PERSONNEL uTILIzATION ARE RECOMMENDED.

Desiring significant growth, Laser Spine Institute, an Outpatient Surgery

Center, needed to reconsider their operational model to fulfill their business

goals. They wanted to enhance the patient and family experience and increase

staff efficiency- two sometimes conflicting goals. The new space will be built

with 3 ORs, Pre-Op unit, PACU, diagnostic imaging, clinic, café, and other

necessary support areas. There are certain guidelines that exist regarding

the number of Pre-Op and PACU rooms needed per operating suite. Array

requested that discrete event simulation be used to determine if there are

other scenarios that might lead to a more efficient and effective use of space.

define the inputs

1

1

A

2

2

B

3

3

C

D

(Fig. 2)

The Pre-Op data follows a lognormal distribution, as found

by the Input Analyzer tool from Arena. Data was tested

assuming there is no correlation between Pre-Op and Surgery

time and there is no high correlation between length of

surgery and time spent in OR. Once the data was known to be

accurate, each set of process time data was fit to theoretical

distribution to be used in the simulation.

(Fig. 4)

We can see in this graph that the expected

values for processing found in the actual data

match very closely with the processing values

produced in the simulation. Also note, that

when developing a simulation, there should not

be a one-to-one correspondence between the

model and the actual system.

(Fig. 3)

(Left Image)

The simulation was built so that patients must stay

in the Pre-Op room until there is a doctor and OR

available for them. Time spent waiting for these

resources was tracked for each patient.

Discrete Event Simulation

provides a virtual environment to track and

visualize patients, equipment and providers

as they move through the steps of care.

Site Visits

were arranged to allow for process map validation

and to give the healthcare systems engineer an

opportunity to speak with front-line employees.

Length of time in Pre-oP DistriBution

LOGN (1.5,0.736)

SIMULATION STUDIES

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the client, Scenario 2A as the recommended optimal solution. This scenario is able to handle a third surgeon and it has eliminated all but an insignificant amount of non-value added use of the operating room at the surgery center, while reducing overall patient waiting time when compared to the current operating conditions.

FUTUrE STUDIES After analyzing these three objectives and determining a potential solution, it became clear that there are a number of opportunities for future study the client could pursue. An extension of the current study involving cost analysis for each of the scenarios presented could be performed. This cost analysis could determine if there would be additional revenue gained from hiring a third surgeon and performing additional surgeries. It could also focus on how much it would cost to build an additional PACU and compare that cost with the potential revenue from performing additional surgeries. Taking the time to study the scheduling of surgery times and case mix could lead to a more productive surgery center with even less idle time for surgeons, nurses and patients. If the scheduling is optimized, the surgery center may be able to perform additional procedures without increasing the patient waiting time at any point in the workflow, thus leading to increased revenue and patient satisfaction. By optimizing the patient schedule, a more specific maximum capacity could also be defined. Additionally, once the patient schedule is optimized, the staff schedule could also be optimized, leading to more effective personnel utilization. The cost analysis previously described could also be performed after the capacity and staff utilization studies are performed to further the understanding of the monetary implications of each of these studies.

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