Intro DES-Capacity

Introduction into Discrete Event Simulation Methodology (DES):

The Use of DES for Capacity Analysis and Planning

Alexander Kolker Data Scientist

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OUTLINE

• Examples: •Capacity of hospital surgical services •Smoothing elective scheduled surgeries

•The concept of simulation and its use in healthcare services with random patient volumes and random service time

•Demonstrating manually a simple discrete event simulation model: step-by-step

•Reviewing components of simulation modeling

•Demonstrating simulation models for capacity analysis and planning in healthcare settings with variable patient volumes

Alexander Kolker. All rights reserved

Alexander Kolker. All rights reserved 3

SIMULATE! • In general, simulation is a process of studying a complex system using its mathematical representation (a model), e.g.

• Flight simulator-the aircraft response to the cockpit input controls • Nuclear plant operators simulators-reactor output response to the various operator inputs • Surgical and physiology procedures simulators on mannequins

•Simulation is a methodology of choice for situations that are too complex, or dangerous, or not suitable for performing actual multiple physical manipulations •Our focus here is simulation of healthcare business operations


Some Typical Business Healthcare Questions to get Answered:

• How many nurses are needed in an inpatient unit in order to provide required patient coverage?

• Is another CT scanner needed to radiology service in order to reduce wait time?

• How many beds are needed to staff at different times of the day or days of the week?

• What additional resources (nurses, beds, etc.), if any, are needed to decrease the rate of ‘left without being seen’ in the ED?


(cont.)

• How many phlebotomists are needed to guarantee acceptable waiting times for blood draw?

• How many beds or staff should be budgeted for?

and so on…..

• Key Point: There is no way to answer any of the above (or similar) business questions without analytic quantitative analysis based on simulation modeling. Everything else would be just guessing.


Basic types of business simulation: • System Dynamics (SD)- operates mostly with macro-level

patient volumes and flows, and large-scale patient categories.

Most appropriate for analyzing the large-scale nationwide healthcare systems, and the implications of the different policies implementation.

• Discrete Event Simulation (DES)- operates mostly with

individual patients and their attributes. Most appropriate for analyzing business operations of separate hospitals and clinics.

• Agent-Based Simulation (ABS)- operates mostly with the

actions and interactions of autonomous entities. Includes emerging rules of behavior that did not exist in the original model design.

Most appropriate for analyzing an effect of emerging individual behavior on the system response as a whole.


(cont.) • All three methodologies can be merged if it is

warranted by the problem to be solved

• However, the most powerful and versatile simulation methodology used for Healthcare business analytics is Discrete Event Simulation


Discrete Event Simulation (DES) Methodology.

What is it, and how does a simple DES model work?

•A discrete event simulation (DES) model of a system/process is a computer model that mimics the dynamic behavior of the system/process as it evolves over time in order to quantitatively analyze its performance, i.e. getting system output as response on the various multiple random inputs.


(cont.) •DES models track patients (documents, work-pieces) moving through the distinct steps of the system (called events) at distinct (discrete) points of time

•Therefore, it is called Discrete Events

•The detailed track is recorded for all processing times and waiting times. Then the system’s output statistics is gathered for the various inputs values.


•The validated and verified model is then used to study response of the system/process to input variables in order to identify the ways for its improvement (scenarios) based on some improvement criteria

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So, how can it help us?

Waiting Line Service System

Customers

arrivals

Let’s look at an example. How can we simulate the random patient arrivals and service system response, e.g. wait time and queue size?

arrivals Queue (Waiting Line) Service Exit Alexander Kolker. All rights reserved


Inter-arrival time,

min

Service time,

min

2.6 1.4

2.2 8.8

1.4 9.1

2.4 1.8

Suppose that we measured the actual time between patient arrivals and the service time


Let’s start at the time, t=0, with no patients in the system. We will be tracking any change (event) that happened in the system. A summary of what is happening in the system looks like this:

Event

#

Time Event that happened in the system

1 2.6 1-st customer arrives. Service starts that should end at

time = 4 (2.6+1.4) 2 4 Service ends. Server waits for patient. 3 4.8

(2.6+2.2) 2-nd patient arrives. Service starts that should end at time

= 13.6 (4.8+8.8). Server idles 0.8 minutes. 4 6.2

(4.8+1.4) 3-rd patient arrives. Joins the queue waiting for service.

5 8.6

(6.2+2.4) 4-th patient arrives. Joins the queue waiting for service.

6 13.6 2-nd patient’s (from event 3) service ends. 3-rd patient

at the head of the queue (1-st in, 1-st out) starts service

that should end at time 22.7 (13.6+9.1). 7 22.7 4-th patient starts service…and so on.


• These simple but tedious logical and numerical event- tracking operations (algorithm) are suitable, of course, only for a computer operations

• However, they illustrate the basic principles of a typical discrete event simulation model, in which discrete events (changes) in the system are tracked when they occur over the time In this particular example, we were tracking events at discrete points in time t=2.6, 4.0, 4.8, 6.2, 8.6, 13.6, 22.7 min What is next?....


• Once the simulation is completed for any length of time, the system’s output statistics is calculated, such as: • the average patient and server waiting time • the number of patients in the queue • the confidence intervals • any other custom process statistics/ information


In this example, only 2 patients out of 4 waited in the queue. Patient 3 waited 13.6-6.2=7.4 min and patient 4 waited 22.7-8.6=14.1 min, so the simple average waiting time for all four patients is (0+0+7.4+14.1)/4=5.4 min. Notice, however, that the first two patients did not wait at all while patient 4 waited 2.6 times longer than the average.


Similarly, the average number of waiting patients (the average queue size) is 0.5 (2 waiting patients out of 4).

Key Points: •DES models are capable of tracking thousands of individual entities arriving randomly or in a complex pattern • Each entity has its own unique attributes, enabling one to simulate the most complex systems with interacting events and component interdependencies.


Typical DES applications include:

•staff and production scheduling •capacity planning •cycle time and cost reduction •throughput capability • resources and activities utilization •bottleneck finding and analysis

• DES is the most powerful tool to perform quantitative ‘what-if’ analysis and play different scenarios of the process behavior as its parameters change with time • This simulation capability allows one to make experiments on the computer, and to test different options before going to the hospital floor for actual implementation.


The basic elements (building blocks) of a simulation model: •Flow chart of the process, i.e. a diagram that depicts logical flow of a process from its inception to its completion •Entities, i.e. items to be processed, e.g. patients, documents, customers, etc. •Activities, i.e. tasks performed on entities, e.g. medical procedures, exams, customer check-in, etc •Resources, i.e. agents used to perform activities and move entities, e.g. service personnel, equipment, nurses, physicians •Entity routings that define directions and logical conditions flow for entities


Typical information (data) usually required to populate the model includes: • Arrival pattern and quantities, e.g. periodic, random, scheduled, daily pattern, etc. • The time that the entities spend in the activities, i.e. service time. This is usually not a fixed time but a statistical distribution. • Capacity of each activity, i.e. the max number of entities that can be processed concurrently in the activity •The maximum size of input and output queues for the activities •Resource assignments: their quantity and scheduled shifts


Example 1: Process Simulation Methodology to Plan for the Facility Renovation of the Surgical Suite at the Children’s Hospital of Wisconsin (CHW)


Step 1: Problem Description: • Children’s Hospital of Wisconsin believes that it has maximized the

capacity of its current operating rooms and special procedure rooms.

• Surgical services are spread in the facility requiring a majority of patients to arrive to one floor for preoperative preparation and then transport to another floor for their surgical procedure.

• As a result, the CHW is in the planning stages for a major facility renovation of its surgical suite to increase capacity, patient, physician and staff satisfaction, and efficiency of surgical services.

• The expansion will also allow for the streamlining of patient flow both in preoperative services and within the operating room areas.


Step 2. Questions to be answered using simulation (DES) • Is the designed number of general and specialized operating

rooms and prep/post operative beds adequate to meet the projected patient flow and volume increases through 2013?

• If the design does not meet the need, how many operating

rooms and/or prep/post operative beds would be needed?

• Ensure that the renovation cost is under control and maintain a high level of quality and satisfaction standards


Step 3. System performance criteria • Patient delay to be admitted to a pre-operative surgical bed should

not exceed 15 minutes. • Delay to enter operating room from a pre-operative surgical bed

should not exceed the following: General OR – 2 hours Urgent OR – 3 hours Cardiovascular OR – 5 hours Neurosurgery OR – 3 hours Orthopedic OR – 2 hours Cardiac Cath Lab – 2 hours

• Percent of patients waiting longer than the acceptable delay to enter operating room from a pre-operative surgical bed should not exceed 5%.

• Delay to enter post anesthesia care beds (PACU) from an operating room should not exceed 5 minutes.


Step 4. Model design: simulation scenarios to be analyzed. • Scenario 1: Baseline operations - all surgical services function as

currently specified between two floors, but move 2 general operating rooms onto 4-th floor to serve otolaryngology (OTO), gastroenterology (GI), and pulmonary (PUL) patients volumes from the 3-rd floor.

• Scenario 2: Move GI, OTO and PUL patient volume from the 4-th floor to a separate service area into the outside Surgical Service Center.

• Scenario 3: Move GI and PUL patient volume into the separate service area. OTO moved to 4-th floor.

Total annual patient volume included in the simulation models is in the range from 15,000 to 18,500 for the annual projected patient volume increase from 2009 to 2013.


Decision variables are: •The number of pre-operative beds and PACU (Post- Anesthesia Care Unit) beds • The number of general and specialized Operating Rooms, as well as special procedure rooms (SPR)

and • Their allocation for surgical services.


3-rd floor 4-th floor

Layout of the simulation model-flow map

Example of Input Data File (total 18,520 records)


Name

Action L

ogic

Week

Weekd

ay

Time

Quantity

Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 8:34 AM 1

Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 10:07 AM 1

Service =NEURO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 10:30 AM 1

Service =GEN Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 12:50 PM 1

Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 1:28 PM 1

Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 3:12 PM 1

Service =OTO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Mon 3:12 PM 1

Service =ORTHO Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:30 AM 1

Service =OTO Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:31 AM 1



Service =CV_Surg Status=InP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:50 AM 1

Service =CATH Status=SS Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 7:52 AM 1


Service =GEN Status=OP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 8:02 AM 1

Service =GEN Status=IA Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 8:05 AM 1

Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Trauma 1 Tue 8:06 AM 1


Service =ORTHO Status=InP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 8:13 AM 1




Service =UROL Status=OP Surgery=not_done PICU=No Surg_Type=Elec 1 Tue 8:55 AM 1

Service =HEMA Status=OP Surgery=not_done PICU=Y Surg_Type=Other 1 Tue 9:05 AM 1




Patient attributes Arrival pattern


SIMULATION OUTPUT

• Based on simulation of these scenarios, it is recommended: • use scenario 3 as the most feasible to meet performance criteria

• re-allocate the number of beds:

-make 10 Prep beds on the 3-rd floor (instead of 8) and -25 prep/post beds on the 4-th floor (instead of 31)

The number of OR:

3-rd floor: -12 ORs (5 general, 2 CV, 1 Neuro, 2 Ortho, 2 Urgent) and 1 Cath Lab 4-th floor: - 2 procedure ORs (SPR) and 2 general ORs (total 4 interchangeable OR)

A Big Picture: Interdependency of Hospital Departments and Hospital-

Wide Patient Flows (Kolker, A., Chapter 2, Patient Flow, 2-nd Ed, Springer, 2013)


Emergency random

Scheduled-smoothed


Example 2: Smoothing of Scheduled Elective Procedures

Step 1: Problem Description

• In most hospitals, random (emergency) surgeries compete for

the same operating rooms (OR) resources with scheduled

(elective) surgeries.

• While the variable number of daily emergency surgeries is

beyond hospital control (natural random variability), there

is a significant variation in the number of daily scheduled

elective surgical cases (artificial non-random variability)


• A daily load leveling of elective cases would reduce the

chances of excessive peak demand for the system’s capacity

(operating rooms and ICU) and, consequently, would reduce

patient waiting time.

• In 2011 The Leapfrog Group Hospital Survey included in the

new section Patient Experience of Care the use of smoothing

elective patient scheduling.

The Leapfrog Bibliography: Smoothing Patient Scheduling


Step 2: Question to be answered using simulation modeling (DES)

What is a quantitative effect of the daily

load leveling (smoothing) of elective

surgeries on wait for surgical and post-

surgical procedures in the presence of the

competing demand for OR resources from

random emergency surgeries?

Step 3. Model design.


It is required to develop two simulation models: (i) baseline model that uses current elective and emergency

admission schedules (mixed patient arrival pattern) to calculate the delay for emergency and scheduled patients;

(ii) model with load-leveled (smoothed) elective schedule and the same emergency admissions to calculate the delay for emergency and scheduled patients. A comparison of the difference in the delay helps to make a conclusion.


It was assumed that 3 interchangeable operating rooms (OR) are available in this case. The emergency surgery duration is in the range from 1.5 to 2.5 hours, with this most likely time of 2.1 hours. Elective surgeries duration is in the range from 1.5 to 3 hours, with the most likely time of 2.4 hours.


Elective, emergency and daily load leveled admissions for the 4-week period

Week Day of week Number of

elective

admissions

Number of

emergency

admissions

Number of daily-

leveled (smoothed)

elective admissions

1 Monday 9 16 6

1 Tuesday 11 14 7

1 Wednesday 8 14 7

1 Thursday 5 20 7

1 Friday 5 15 7

2 Monday 10 18 7

2 Tuesday 13 20 7

2 Wednesday 11 9 7

2 Thursday 8 11 7

2 Friday 3 20 7

3 Monday 5 17 7

3 Tuesday 9 11 7

3 Wednesday 8 15 7

3 Thursday 6 15 7

3 Friday 6 20 7

4 Monday 7 15 7

4 Tuesday 4 13 7

4 Wednesday 3 12 7

4 Thursday 4 11 7

4 Friday 3 20 6

Total 138 306 138

Input Data. CHW, June, 2009


Simulation Output:

• The original un-smoothed elective schedule along with competing emergency cases resulted in the average patient waiting time:

0.74 hours for emergency cases (99% CI is 0.73 – 0.76 hours) and 1.2 hours for elective cases (99% CI is 1.19 - 1.24 hours).

• The smoothed (load-leveled) elective schedule along with the

same competing emergency cases resulted in the average patient waiting time

0.58 hours for emergency (99% CI is 0.57 – 0.6 hours) and 0.82 hours for elective cases (99% CI is 0.8 – 0.84 hours).

• Thus, in this example, elective daily smoothing results in about

21% reduction in waiting time for emergency surgeries and about 32% reduction in waiting time for elective cases.


Take-away:

Elective schedule smoothing (daily load- leveling) is indeed a very powerful approach of reducing patient waiting time and improving efficiency.


• A simple simulation model also allows testing an effect of

the different smoothing schemes.

• For example, if nearly the same daily number of elective

cases is not possible due to some practical limitations, it is

possible to test another less perfect smoothing scheme to

make sure that the end result is still worth the effort of its

implementation (or maybe not) .

• No traditional management methods are capable of

providing such insights for decision-making.

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The Power of Simulation Modeling

• Used for studying behavior of the complex systems/processes with random components

• Provides a framework for experimenting with system behavior without experimenting with the actual system

• Compresses time for new improved system design

• Valuable tool for training decision-makers

Alexander Kolker. All rights reserved

Intro DES-Capacity

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