Download - SHS ASQ 2010 Conference Presentation: Hospital System Patient Flow

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Alexander Kolker, PhD

Outcomes Operations Project Manager

Children’s Hospital and Health System

Milwaukee, Wisconsin

SHS/ASQ 2010 Conference and ExpoFebruary 26, 2010

System Engineering

and Management Science

for Healthcare

Examples and Fundamental Principles

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• Main concept and some definitions.

• Typical hospital system as a set of interdependent subsystems:

• Subsystem 1: Emergency Department (ED).

• Subsystem 2: Intensive Care Unit (ICU).

• Subsystem 3: Operating Rooms (OR)- Surgical Department.

• Subsystem 4: Medical/Surgical Nursing Units (Floor_NU).

• Interdependency of subsystems.

• Main take-away.

• Summary of fundamental management engineering principles.

Outline

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Kolker, A, Queuing Theory and Discreet Events Simulation for Healthcare: from Basic

Processes to Complex Systems with Interdependencies. Chapter 20. In: Handbook of

Research on Discrete Event Simulation: Technologies and Applications, 2009, pp. 443

- 483. IGI Global Publishing, Hershey, PA.

Kolker, A, Process Modeling of Emergency Department Patient Flow: Effect of Patient

Length of Stay on ED Diversion. Journal of Medical Systems, 2008, v. 32, N 5, pp. 389 -

401.

Kolker, A, Process Modeling of ICU Patient Flow: Effect of Daily Load Leveling of Elective

Surgeries on ICU Diversion. Journal of Medical Systems, 2009, v. 33, N 1, pp. 27 - 40.

Kolker, A, Norell, B., O’Connor, M., Hoffman, G., Oldham, K., The Use of Predictive

Simulation Modeling for Surgical Capacity Expansion Analysis

Presented at the 2010 SHS/ASQ joint Conference, Atlanta, GA, February 26, 2010 (poster

session).

Kolker, A, Effective Managerial Decision Making in Healthcare Settings: Examples and

Principles. Quality Management Journal, 2009 (submitted).

This presentation is adapted from

the following System Engineering Publications

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A real impact on efficiency and sustainability of the healthcare

system can be achieved only by using healthcare delivery

engineering which is based on hard science such as: probability

theory, forecasting, calculus, stochastic optimization, computer

simulation, etc.

• Modern medicine has achieved great progress in treating individual

patients. This progress is based mainly on hard science: molecular

genetics, biophysics, biochemistry, design and development of

medical devices and imaging.

• However relatively little resources have been devoted to the proper

functioning of overall healthcare delivery as an integrated system,

in which access to efficient care should be delivered to many

thousands of patients in an economically sustainable way. (Joint report

of National Academy of Engineering and Institute of Medicine, 2005).

Main Concept

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Traditional (Intuitive) Management is based on• Past experience.

• Intuition or educated guess.

• Static pictures or simple linear projections.

Resource input

Syste

m o

utp

ut

Linear projection assumes that the output is directly proportional to the

input, i.e. the more resources (material and human) thrown in, the more

output produced (and vice versa).

What is Management?

Management is controlling and leveraging available resources (material,

financial and human) aimed at achieving the performance objectives.

Some Definitions

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• Management Engineering (ME) is the discipline of

building and using validated mathematical models of

real systems to study their behavior aimed at making

justified business decisions.

• This field is also known as operations research.

Thus, Management Engineering is the application of

mathematical methods to system analysis and

decision-making.

What is Management Engineering?

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The Underlying Premise of ME is

• Decisions should be made that best lead to reaching the goal.

• Valid mathematical models lead to better justified decisions than an

educated guess, past experience, and linear extrapolations (traditional

decision-making).

• A goal that is clearly stated and measurable, so the decision-maker

(manager) always knows if the goal is closer or farther away.

• Identification of available resources that can be leveraged (allocated) in

different ways.

• Development of mathematical models or numeric computer algorithms

to quantitatively test different decisions for the use of resources and

consequences of these decisions (especially unintended

consequences) before finalizing the decisions.

Scientific Management is Based On

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• Subsystems are then reconnected in a way that recaptures

the interdependency between them.

• The entire system is re-analyzed using the output of one

subsystem as the input for another subsystem.

Main Steps for System Engineering Analysis

S t e p 1

S t e p 2

• Large systems are deconstructed into smaller subsystems

using natural breaks in the system.

• Subsystems are modeled, analyzed, and studied separately.

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High-Level Layout of a Typical Hospital System

Key

ED – Emergency Room Floor NU – Med/Surg Units

ICU – Intensive Care Unit OR – Operating Rooms

WR – Waiting Room

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• Simulation and Analysis of the Main Subsystems:

Subsystem 1: Emergency Department (ED).

Subsystem 2: Intensive Care Unit (ICU).

Subsystem 3: Operating Rooms (OR).

Subsystem 4: Floor Nursing Units (NU).

Step 1

• Deconstruction of the entire hospital system into

Main Subsystems.

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ED structure and in-patient unitsThe high-level layout of

the entire hospital system:

Subsystem 1: Typical Emergency Department (ED)

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High Level ED Analysis Goal

• Quantitatively predict the relationship between patient LOS

and ED diversion.

• Identify the upper LOS limit (ULOS) that will result in

significant reduction or elimination ED diversion.

Typical ED Challenges

ED Performance Issues

• ED ambulance diversion is unacceptably high (about 23% of

time sample ED is closed to new patients).

• Among many factors that affect ED diversion, patient Length of

Stay in ED (LOS) is one of the most significant factors.

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Arrival pattern

wk, DOW, time

Mode of transp

Disposition

ED simulation model layout

Simulation

Digital clock

Typical ED Simulation Model Layout

ED pre-filled at the

simulation start

Mode of Transportation

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Modeling Approach

• ED diversion (closure) is declared when ED patient census

reaches ED bed capacity.

• ED stays in diversion until some beds become available after

patients are moved out of ED (discharged home, expired, or

admitted as in-patients).

• Upper LOS limits (simulation parameters) are imposed on the

baseline original LOS distributions: A LOS higher than the

limiting value is not allowed in the simulation run.

Take Away

Baseline LOS distributions should be recalculated as

functions of the upper LOS limits.

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MODELING APPROACH (cont.)Given original distribution density and the limiting value of th e random variable T,

what is the conditional distribution of the restricted random va riable T ?

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LOS, Hrs

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3-Parameter Gamma

Distribution of LOS_ home, Hrs

Imposed LOS limit 6 hrs

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Re-calculated bounded distribution of LOS_ home, Hrs

dTTf

TfLOSTf

LOS

original

originalnew

0

)(

)() ,(

LOST if ,0)( newTf

T, HrsLOT, Hrs

Original unbounded distribution New re-calculated distribution

origTf )(

LOS limit

Given original distribution density and the limiting value of the random variable T, what is the conditional

distribution of the restricted random variable T?

Modeling Approach – continued

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• ED diversion could be negligible (~0.5%) if patients discharged home stay NOT more than 5

hrs and admitted patients stay NOT more than 6 hrs.

• Relaxing of these LOS limits results in low digits % diversion that still could be acceptable

SIMULATION SUMMARY & MODEL VALIDATION

Low single

digits

diversion

~4%24 hrs5 hrs3

Low single

digits

diversion

~ 2%6 hrs6 hrs2

Practically NO

diversion

~ 0.5 %6 hrs

Currently

24% with

LOS more

than 6 hrs;

5 hrs

Currently 17%

with LOS more

than 5 hrs;

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Actual ED

diversion

was 21.5%

23.7%24 hrs24 hrsCurrent, 07

(Baseline)

NotePredicted ED

diversion, %

LOS for

admitted NOT

more than

LOS for discharged

home NOT more thanScenario/option

Take-away:

Simulation Summary and Model Validation

Take Away

• ED diversion could be negligible (~0.5%) if patients discharged home stay not more

than five hours and admitted patients stay not more than six hours.

• Relaxing of these LOS limits results in a low digits percent diversion that still could be

acceptable.

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ULOS_adm, hrs

Mea

n pr

edic

ted

Div

%

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24.0

22.5

21.0

19.5

18.0

16.5

15.0

13.5

12.0

10.5

9.0

7.5

6.0

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3.0

1.5

0.0

5

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ULOS_home, hrs

Simulated Div % as a function of upper LOS limits, hrs

What other combinations of upper limits LOS are possible to get low

single digits % ED diversion ?

Low single digits

% diversion

Performed full factorial DOE with two factors ( ULOS_home and ULOS_adm) at 6 levels each

using simulated % diversion as a response function.

What other combinations of upper LOS limits are possible to get a low single digit percent ED

diversion?

Simulation Summary – continued

Perform full factorial DOE with two factors (ULOS_home and ULOS_adm) at six levels each using

simulated percent diversion as a response function.

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Conclusions for Subsystem 1:

Emergency Department

• ED diversion can be negligible (less than 1%) if hospital-

admitted patients stay in ED not more than six hours.

• Currently 24% of hospital-admitted patients in study

hospital stay longer than this limit, up to 20 hours.

• This long LOS for a large percentage of patients results in

ED closure/diversion.

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Subsystem 2: Typical Intensive Care Unit (ICU)Patients move between the units:

• If no beds in CIC, move to SIC

• If no beds in MIC, move to CIC, else SIC, else NIC

• If no beds in SIC, move CIC

• If no beds in NIC, move to CIC, else SIC

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ICU Performance Issues

• Elective surgeries are usually scheduled for Operating Room block times

without taking into account the competing demand from emergency and

add-on surgeries for ICU resources.

• This practice results in:

Increased ICU diversion due to ‘no ICU beds’.

Increased rate of medical and quality issues due to staff overload and capacity constraints.

Decreased patient throughput and hospital revenue.

High Level ICU Analysis Goal

• Establish a relationship between daily elective surgeries schedule,

emergency and add-on cases and ICU diversion.

• Given the number of the daily scheduled elective surgeries and the number

of unscheduled emergency and add-on admissions, predict ICU diversion

due to lack of available beds.

Typical ICU Challenges

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ICU Census:

Elective surgeries current pattern - No daily cap

Closed due to No ICU beds: 10.5 % of time

3536373839404142434445464748495051

0 168 336 504 672 840 1008 1176 1344 1512 1680 1848 2016 2184 2352 2520 2688 2856 3024

Hrs/ weeks

cn

s

Red zone:

Critical census limit exceeded

wk1 wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 wk10 wk11 wk12 wk13 wk14 wk15 wk16 wk17

Baseline – Existing Number of Elective Cases

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• There is a significant variation in the number of scheduled

elective cases between the same days of the different weeks

(Monday to Monday, Tuesday to Tuesday, and so on).

• Smoothing the number of elective cases over time (daily load

leveling) is a very significant factor which strongly affects ICU

closure time due to ‘no ICU beds.’

• Using Simulation it was demonstrated that daily load leveling of

elective cases to not more than 4 cases per day will result in a

very significant reduction of closure time due to ‘no ICU beds’

(from ~10.5% down to ~1%).


Intensive Care Unit

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Design Challenges

• Is the number of general and specialized operating rooms and

pre/post operative beds adequate to meet the projected patient

flow and volume increases?

• If it is not, how many operating rooms and pre/post operative

beds would be needed?

• Ensure that the renovation cost is under control and maintain a

high level of quality and satisfaction standards for surgical

services.

• Utilize Management Engineering to determine that the number of

operating rooms and pre/post operative beds is not excessive.

Subsystem 3: Typical Operating Rooms (OR)

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The following performance criteria

were used for the simulation model

1. Patient delay to be admitted to a preoperative surgical bed should not

exceed 15 minutes.

2. Delay to enter operating room from a preoperative surgical bed should

not exceed:

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

3. Percent of patients waiting longer than the acceptable delay to enter

operating room from a preoperative surgical bed should not exceed

5%.

4. Delay to enter PACU beds from an operating room should not exceed

5 minutes.

5. Average annual utilization of operating rooms should be in the range

of 60% to 90%.

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Total annual patient volume included in the simulation models is in the range from

15,000 to 17,000.

Decision variables were: The number of pre-operative beds and PACU beds,

number of Operating Rooms and special procedure rooms and their allocation for

surgical services.

The following simulation models

were developed and analyzed

Model 1: Baseline operations - all surgical services function as

currently specified between two floors. Construct two general operating

rooms onto upper level floor to serve otolaryngology, gastroenterology

and pulmonary patient volume from lower level floor.

Model 2: Move gastroenterology and pulmonary patient volume from

upper level to a separate service area.

Model 3: Separate service area for gastroenterology and pulmonary

patient volume that includes 2 to 3 special procedure rooms and 8 to11

pre/post beds and PACU beds.

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Simulation Model Layout (Scenarios 1 – 3)

Operating Rooms: OpR-general; U_OR-urgent; CV_OR-cardiovascular; Cath_OR-catheterization; SPR-special procedure.

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• Model 3 is selected as the best. Twelve Operating Rooms

and four Special Procedure Rooms will be adequate to

handle patient volume up to the year 2013.

• Cath Lab could become an issue by 2013 with more than

10% of patients waiting longer than acceptable limit 2

hours.

• All other performance criteria will be met.


Operating Rooms (OR)

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Census (i) (current period) = census (i-1) (previous period) +

[# admissions (i) – # discharges (i) ]; i = 1, 2, 3, …….

This is a dynamic balance of supply (beds) and demand (admissions).

Patient Length of Stay

(LOS) is in the range from

2 days to 10 days;

The most likely LOS is 5

days.

Subsystem 4: Medical/Surgical

Nursing Units (NU)

Total number of specialized nursing units: 24

Total number of licensed beds: 380

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Census (i) (current period) = census (i-1) (previous period) +

[# admissions (i) – # discharges (i) ]; i = 1, 2, 3, …….

Simulated Census. Capacity 380 beds

320

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390

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120 124 128 132 136 140 144 148 152 156 160 164 168

days/ hours

ce

ns

us

capacity limit

Mon Tue Wed Thu Fri Sat Sun

Take Away: Percent of time Nursing Units are full (% diversion) is about 16%.

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• Subsystems are reconnected in a way that

recaptures the interdependency between them.

• The entire system is re-analyzed using the output of

one subsystem as the input for another subsystem.

Step 2

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• All subsystems are reconnected to each other.

• The output of one subsystem is the input for another subsystem.

Step 2 – continued

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Hospital System Simulation Summary

Performance Metrics

Current

State

Baseline

Too aggressive ED

improvement:

patients admitted

within 6 hours

Downstream

Units: Better

or worse than

current state?

Less aggressive

ED improvement:

patients admitted

within 10 hours

Downstream

Units: Better or

words than current

state?

95% CI of the number of

patients waiting to get to

ED (ED in)25 – 27 8 – 10 Better 17 – 19 Better

95% CI of the number of

patients waiting hospital

admissions (ED out)57 – 62 64 – 69 Worse 57 – 62 Neutral

Number of patients left

not seen (LNS) after

waiting more than 2

hours

23 – 32 0 Better 0 – 3 Better

95% CI for % ED

diversion 22% – 23% 0.4% – 0.5% Better 6.8% – 7.3% Better

95% CI for % ICU

diversion 28% – 32% 30% – 34% Worse 28% – 32% Neutral

95% CI for % OR

diversion 12% – 13% 13% – 15% Worse 12% – 13% Neutral

95% CI for % floor NU

diversion 11% – 12% 11% – 12% Neutral 11% – 12% Neutral

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Take Away

• Too aggressive ED improvement results in worsening

three out of seven hospital system performance metrics.

• Less aggressive ED improvement is more aligned with

the ability of downstream subsystems to handle

increased patient volume.

• This illustrates important Management System

Engineering Principles:

Take-Away from Hospital System

Simulation Summary

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• Improvement in the separate subsystems (local

optimization or local improvement) should not be

confused with the improvement of the entire system.

• A system of local improvements is not the best system;

it could be a very inefficient system.

• Analysis of an entire complex system is usually

incomplete and can be misleading without taking into

account subsystems’ interdependency.

Important System Engineering Principles

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Main Take-Away

Management Engineering helps to address the following typical

pressing hospital issues:

• How many beds are needed for each unit.

• How many procedure rooms are needed for each service.

• How many nurses/physicians should each unit schedule for the particular

day and night.

• How to reduce patient wait time and increase access to care.

• How to develop an efficient outpatient clinic schedule.

And so on, and so on…

And the Ultimate Goal:

How to manage hospital operations to increase profitability (reduce

costs, increase revenue) while keeping high quality, safety and

outcomes standards for patients.

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Summary of Some Fundamental Management

Engineering Principles

• Systems behave differently than the sum of their independent

components.

• All other factors being equal, combined resources are more efficient

than specialized (dedicated) resources with the same total

capacity/workload.

• Scheduling appointments (jobs) in the order of their increased duration

variability (from lower to higher variability) results in a lower overall

cycle time and waiting time.

• Size matters. Large units with the same arrival rate (relative to its

size) always have a significantly lower waiting time. Large units can

also function at a much higher utilization % level than small units

with about the same patient waiting time.

• Work load leveling (smoothing) is an effective strategy to reduce

waiting time and improve patient flow.

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• Because of the variability of patient arrivals and service time, a

reserved capacity (sometimes up to 30%) is usually needed to

avoid regular operational problems due to unavailable beds.

• Generally, the higher utilization level of the resource (good for the

organization) the longer is the waiting time to get this resource

(bad for patient). Utilization level higher than 80% to 85% results

in a significant increase in waiting time for random patient

arrivals and random service time.

• In a series of dependent activities only a bottleneck defines the

throughput of the entire system. A bottleneck is a resource (or

activity) whose capacity is less than or equal to demand placed

on it.


Engineering Principles – continued

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• An appointment backlog can remain stable even if the

average appointment demand is less than appointment

capacity.

• The time of peak congestion usually lags the time of the

peak arrival rate because it takes time to serve patients

from the previous time periods (service inertia).

• Reduction of process variability is the key to patient flow

improvement, increasing throughput and reducing delays.


Engineering Principles – continued

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APPENDIX

A Simulation Model is the computer model that mimics the behavior of a

real complex system as it evolves over the time in order to visualize and

quantitatively analyze its performance in terms of:

• Cycle times.

• Wait times.

• Value added time.

• Throughput capacity.

• Resources utilization.

• Activities utilization.

• Any other custom collected process information.

What is a Simulation Model?

• The Simulation Model is a tool to perform ‘what-if’ analysis and play

different scenarios of the model behavior as conditions and process

parameters change.

• This allows one to build various experiments on the computer model

and test the effectiveness of various solutions (changes) before

implementing the change.

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A few random numbers sampled from these two distributions are, for example: Inter-arrival time, min Service time, min

2.6 1.4

2.2 8.8

1.4 9.1

2.4 1.8

…. ….

and so on… and so on….

How Does a Typical Simulation Model Work?

A simulation model tracks the move of entities through the system at distinct points

of time (thus, discrete events.) The detailed track is recorded of all processing

times and waiting times. In the end, the system’s statistics for entities and

activities is gathered.

Example of Manual Simulation (step by step)

Let’s consider a very simple system that consists of:• a single patient arrival line.

• a single server.

Suppose that patient inter-arrival time is uniformly (equally likely) distributed between

1 min and 3 min. Service time is exponentially distributed with the average 2.5 min.

(Of course, any statistical distributions or non-random patterns can be used instead).

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We will be tracking any change (or 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 First customer arrives. Service starts that should end at time = 4.

2 4 Service ends. Server waits for patient.

3 4.8 Second patient arrives. Service starts that should end at time = 13.6.

Server idle 0.8 minutes.

4 6.2 Third patient arrives. Joins the queue waiting for service.

5 8.6 Fourth patient arrives. Joins the queue waiting for service.

6 13.6 Second patient (from event 3) service ends. Third patient at the head of

the queue (first in, first out) starts service that should end at time 22.7.

7 22.7 Patient #4 starts service…and so on.

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

DES models are capable of tracking hundreds of individual entities, each with its own unique set of

attributes, enabling one to simulate the most complex systems with interacting events and component

interdependencies.

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Basic Elements of a Simulation Model

• Flow chart of the process: Diagram that depicts logical flow of a process

from its inception to its completion.

• Entities: Items to be processed (i.e. patients, documents, customers, etc.)

• Activities: Tasks performed on entities (i.e. medical procedures, document

approval, customer checkout, etc.)

• Resources: Agents used to perform activities and move entities (i.e. service

personnel, operators, equipment, nurses, physicians.)

Connections:

• Entity arrivals: They define process entry points, time and quantities of

the entities that enter the system to begin processing.

• Entity routings: They define directions and logical condition flows for

entities (i.e. percent routing, conditional routing, routing on demand, etc.)

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Typical Data Inputs Required to Feed the Model

• Entities, their quantities and arrival times

Periodic, random, scheduled, daily pattern, etc.

• Time the entities spend in the activities

This is usually not a fixed time but a statistical distribution. The wider the time distribution, the higher the variability of the system behavior.

• The capacity of each activity

The maximum number of entities that can be processed concurrently in the activity.

• The size of input and output queues for the activities (if needed).

• The routing type or the logical conditions for a specific routing.

• Resource Assignments

The number of resources, their availability, and/or resources shift schedule.