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System Engineering
and Management Science
     for Healthcare
Examples and Fundamental Principles


  SHS/ASQ 2010 Conference and Expo
              February 26, 2010

             Alexander Kolker, PhD
     Outcomes Operations Project Manager
     Children’s Hospital and Health System
             Milwaukee, Wisconsin

                                             1
Outline


• 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.

                                                                   2
This presentation is adapted from
                        the following System Engineering Publications

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).


                                                                                             3
Main Concept

• 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).


  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.

                                                                            4
Some Definitions

What is Management?
Management is controlling and leveraging available resources (material,
financial and human) aimed at achieving the performance objectives.

Traditional (Intuitive) Management is based on
• Past experience.
• Intuition or educated guess.
• Static pictures or simple linear projections.

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).
                               System output




                                                  Resource input
                                                                            5
What is Management Engineering?



• 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.




                                                         6
Scientific Management is Based On

• 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.

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).

                                                                               7
Main Steps for System Engineering Analysis


Step 1

   • Large systems are deconstructed into smaller subsystems
     using natural breaks in the system.

   • Subsystems are modeled, analyzed, and studied separately.


Step 2

   • 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.



                                                                 8
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


                                                         9
Step 1

• Deconstruction of the entire hospital system into
  Main Subsystems.

• 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).




                                                      10
Subsystem 1: Typical Emergency Department (ED)




The high-level layout of
the entire hospital system:   ED structure and in-patient units


                                                                  11
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.


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.



                                                                   12
ED simulation model layout
      Typical ED Simulation Model Layout

                                   Simulation
                                   Digital clock




  ED pre-filled at the
  simulation start


          Arrival pattern
          wk, DOW, time

       Mode of transp
 Mode of Transportation

           Disposition



                                                   13
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.



                                                                 14
Modeling Approach – continued
                                                MODELING APPROACH (cont.)
Given original distribution density and the the random value of what is the conditional
Given original distribution density and the limiting value of limiting variable T, th e random variable T,
distribution of the restricted random variable T?
what is the conditional distribution of the restricted random va riable T ?

                      Original unbounded distribution
                            Distribution of LOS_ home, Hrs                              New re-calculated distribution
                                                                                        Re-calculated bounded distribution of LOS_ home, Hrs
                                   3-Parameter (T ) orig
                                           f Gamma                            500
                                                                              480
            500
                                                                              460
                                                                                                                            f (T )original
            480
            460
                                                                              440         f (T , LOS ) new 
            440                                                               420                                    LOS

                                                                                                                         f (T )
            420                                                               400
            400                                                               380
                                                                                                                                   originaldT
            380                                                               360
            360                                                               340
            340                                                               320
                                                                                                                        0




                                                                  Frequency
            320                                                               300
Frequency




            300                                                               280
            280                                                               260
            260                                                               240
            240
            220
                                 Imposed LOS limit 6 hrs                      220
                                                                              200
            200
                                                                              180
            180
                                                                              160
            160
                                                                              140
            140
                                                                              120
                                                                                                                             LOS limit
            120
            100                                                               100
             80                                                                80
                                                                               60
                                                                                                                    f (T ) new  0, if T LOS
             60
             40                                                                40
             20                                                                20
              0                                                                 0
                  0        2     4       6        8   10     12                     0          2         4          6         8        10      12
                                     LOS, Hrs                                                                  LO Hrs
                                                                                                                LOS,
                                     T, Hrs                                                                     T, Hrs
                                                                                                                                                15
Simulation Summary and Model Validation
                                 SIMULATION SUMMARY & MODEL VALIDATION
               Scenario/option    LOS for discharged    LOS for         Predicted ED     Note
                                  home NOT more than    admitted NOT    diversion, %
                                                        more than
                  Current, 07     24 hrs                24 hrs          23.7%            Actual ED
                  (Baseline)
                                                                                         diversion
                                                                                         was 21.5%
                       1          5 hrs                 6 hrs           ~ 0.5 %          Practically NO
                                  Currently 17%         Currently                        diversion
                                  with LOS more         24% with
                                  than 5 hrs;           LOS more
                                                        than 6 hrs;


                       2          6 hrs                 6 hrs           ~ 2%             Low single
                                                                                         digits
                                                                                         diversion
                       3          5 hrs                 24 hrs          ~4%              Low single
                                                                                         digits
                                                                                         diversion
                   Take-away:
                                                  Take Away
               • ED diversion could be negligible (~0.5%) if patients discharged home stay NOT more than 5
• ED diversionand admittednegligible (~0.5%) if patients discharged home stay not more
            hrs could be patients stay NOT more than 6 hrs.
            • Relaxing of these LOS limits results in low digits % diversion that still could be acceptable
  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.
                                                                                                              16
Simulation Summary – continued
  What other combinations of upper LOS limits are limits LOS arelow single digit percent ED
        What other combinations of upper possible to get a possible to get low
  diversion?                      single digits % ED diversion ?
Perform full factorial DOE with two factors (ULOS_home and ULOS_adm) at six at 6 levels each
   Performed full factorial DOE with two factors ( ULOS_home and ULOS_adm) levels each using
simulatedsimulated % diversion as a response function.
   using percent diversion as a response function.

                                   Simulated Div % as a function of upper LOS limits, hrs
                                                                                       ULO S_home, hrs
                           24.0
                                                                                                     5
                           22.5
                                                                                                     6
                           21.0                                                                      8
                           19.5                                                                     10
    Mean predicted Div %




                           18.0                                                                     12
                           16.5   Low single digits                                                 24
                           15.0   % diversion
                           13.5
                           12.0
                           10.5
                            9.0
                            7.5
                            6.0
                            4.5
                            3.0
                            1.5
                            0.0

                                    5       6           8      10     12   24
                                                      ULOS_adm, hrs


                                                                                                         17
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.




                                                                18
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




                                                        19
Typical ICU Challenges
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.


                                                                                           20
Baseline – Existing Number of Elective Cases

                                               ICU Census:
                            Elective surgeries current pattern - No daily cap
Red zone:
Critical census limit exceeded
                                 Closed due to No ICU beds: 10.5 % of time

      51
      50
      49
      48
      47
      46
      45
      44
cns




      43
      42
      41
      40
      39
      38
      37
      36 wk1 wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 wk10 wk11 wk12 wk13 wk14 wk15 wk16 wk17
      35
         0  168 336 504 672 840 1008 1176 1344 1512 1680 1848 2016 2184 2352 2520 2688 2856   3024

                                                  Hrs/ weeks
                                                                                                     21
Conclusions for Subsystem 2:
                            Intensive Care Unit


• 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%).



                                                                      22
Subsystem 3: Typical Operating Rooms (OR)


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.



                                                                       23
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%.

                                                                            24
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.
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.

                                                                                     25
Simulation Model Layout (Scenarios 1 – 3)




Operating Rooms: OpR-general; U_OR-urgent; CV_OR-cardiovascular; Cath_OR-catheterization; SPR-special procedure.
                                                                                                                   26
Conclusions for Subsystem 3:
                      Operating Rooms (OR)


• 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.




                                                            27
Subsystem 4: Medical/Surgical
                                    Nursing Units (NU)

Total number of specialized nursing units: 24
Total number of licensed beds: 380




                                                       Patient Length of Stay
                                                       (LOS) is in the range from
                                                       2 days to 10 days;
                                                       The most likely LOS is 5
                                                       days.




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).
                                                                                    28
Census (i) (current period) = census (i-1) (previous period) +
   [# admissions (i) – # discharges (i) ]; i = 1, 2, 3, …….

                                                     Simulated Census. Capacity 380 beds

            390
                              Mon               Tue                 Wed                 Thu                   Fri                  Sat                    Sun
            380
                                                                         capacity limit
            370
   census




            360
            350

            340
            330

            320
                  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


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

                                                                                                                                                                          29
Step 2




• 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.




                                                         30
Step 2 – continued
• All subsystems are reconnected to each other.
• The output of one subsystem is the input for another subsystem.




                                                                      31
Hospital System Simulation Summary

                                         Too aggressive ED    Downstream       Less aggressive       Downstream
                              Current
                                           improvement:        Units: Better   ED improvement:      Units: Better or
  Performance Metrics          State
                                          patients admitted   or worse than    patients admitted   words than current
                              Baseline
                                           within 6 hours     current state?    within 10 hours         state?

95% CI of the number of
patients waiting to get to    25 – 27          8 – 10            Better             17 – 19              Better
ED (ED in)

95% CI of the number of
patients waiting hospital     57 – 62         64 – 69            Worse              57 – 62             Neutral
admissions (ED out)

Number of patients left
not seen (LNS) after
waiting more than 2           23 – 32            0               Better              0–3                 Better
hours

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


                                                                                                                        32
Take-Away from Hospital System
                      Simulation Summary


                       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:




                                                            33
Important System Engineering Principles



• 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.




                                                           34
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.
                                                                            35
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.
                                                                              36
Summary of Some Fundamental Management
                    Engineering Principles – continued


• 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.


                                                                          37
Summary of Some Fundamental Management
             Engineering Principles – continued



• 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.




                                                                38
APPENDIX




           39
What is a Simulation Model?
 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.

• 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.
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).
  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….
                                                                                            41
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.
                                                                                                      42
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.)


                                                                                      43
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.
                                                                               44

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SHS ASQ 2010 Conference Presentation: Hospital System Patient Flow

  • 1. System Engineering and Management Science for Healthcare Examples and Fundamental Principles SHS/ASQ 2010 Conference and Expo February 26, 2010 Alexander Kolker, PhD Outcomes Operations Project Manager Children’s Hospital and Health System Milwaukee, Wisconsin 1
  • 2. Outline • 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. 2
  • 3. This presentation is adapted from the following System Engineering Publications 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). 3
  • 4. Main Concept • 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). 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. 4
  • 5. Some Definitions What is Management? Management is controlling and leveraging available resources (material, financial and human) aimed at achieving the performance objectives. Traditional (Intuitive) Management is based on • Past experience. • Intuition or educated guess. • Static pictures or simple linear projections. 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). System output Resource input 5
  • 6. What is Management Engineering? • 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. 6
  • 7. Scientific Management is Based On • 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. 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). 7
  • 8. Main Steps for System Engineering Analysis Step 1 • Large systems are deconstructed into smaller subsystems using natural breaks in the system. • Subsystems are modeled, analyzed, and studied separately. Step 2 • 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. 8
  • 9. 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 9
  • 10. Step 1 • Deconstruction of the entire hospital system into Main Subsystems. • 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). 10
  • 11. Subsystem 1: Typical Emergency Department (ED) The high-level layout of the entire hospital system: ED structure and in-patient units 11
  • 12. 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. 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. 12
  • 13. ED simulation model layout Typical ED Simulation Model Layout Simulation Digital clock ED pre-filled at the simulation start Arrival pattern wk, DOW, time Mode of transp Mode of Transportation Disposition 13
  • 14. 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. 14
  • 15. Modeling Approach – continued MODELING APPROACH (cont.) Given original distribution density and the the random value of what is the conditional Given original distribution density and the limiting value of limiting variable T, th e random variable T, distribution of the restricted random variable T? what is the conditional distribution of the restricted random va riable T ? Original unbounded distribution Distribution of LOS_ home, Hrs New re-calculated distribution Re-calculated bounded distribution of LOS_ home, Hrs 3-Parameter (T ) orig f Gamma 500 480 500 460 f (T )original 480 460 440 f (T , LOS ) new  440 420 LOS  f (T ) 420 400 400 380 originaldT 380 360 360 340 340 320 0 Frequency 320 300 Frequency 300 280 280 260 260 240 240 220 Imposed LOS limit 6 hrs 220 200 200 180 180 160 160 140 140 120 LOS limit 120 100 100 80 80 60 f (T ) new  0, if T LOS 60 40 40 20 20 0 0 0 2 4 6 8 10 12 0 2 4 6 8 10 12 LOS, Hrs LO Hrs LOS, T, Hrs T, Hrs 15
  • 16. Simulation Summary and Model Validation SIMULATION SUMMARY & MODEL VALIDATION Scenario/option LOS for discharged LOS for Predicted ED Note home NOT more than admitted NOT diversion, % more than Current, 07 24 hrs 24 hrs 23.7% Actual ED (Baseline) diversion was 21.5% 1 5 hrs 6 hrs ~ 0.5 % Practically NO Currently 17% Currently diversion with LOS more 24% with than 5 hrs; LOS more than 6 hrs; 2 6 hrs 6 hrs ~ 2% Low single digits diversion 3 5 hrs 24 hrs ~4% Low single digits diversion Take-away: Take Away • ED diversion could be negligible (~0.5%) if patients discharged home stay NOT more than 5 • ED diversionand admittednegligible (~0.5%) if patients discharged home stay not more hrs could be patients stay NOT more than 6 hrs. • Relaxing of these LOS limits results in low digits % diversion that still could be acceptable 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. 16
  • 17. Simulation Summary – continued What other combinations of upper LOS limits are limits LOS arelow single digit percent ED What other combinations of upper possible to get a possible to get low diversion? single digits % ED diversion ? Perform full factorial DOE with two factors (ULOS_home and ULOS_adm) at six at 6 levels each Performed full factorial DOE with two factors ( ULOS_home and ULOS_adm) levels each using simulatedsimulated % diversion as a response function. using percent diversion as a response function. Simulated Div % as a function of upper LOS limits, hrs ULO S_home, hrs 24.0 5 22.5 6 21.0 8 19.5 10 Mean predicted Div % 18.0 12 16.5 Low single digits 24 15.0 % diversion 13.5 12.0 10.5 9.0 7.5 6.0 4.5 3.0 1.5 0.0 5 6 8 10 12 24 ULOS_adm, hrs 17
  • 18. 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. 18
  • 19. 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 19
  • 20. Typical ICU Challenges 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. 20
  • 21. Baseline – Existing Number of Elective Cases ICU Census: Elective surgeries current pattern - No daily cap Red zone: Critical census limit exceeded Closed due to No ICU beds: 10.5 % of time 51 50 49 48 47 46 45 44 cns 43 42 41 40 39 38 37 36 wk1 wk2 wk3 wk4 wk5 wk6 wk7 wk8 wk9 wk10 wk11 wk12 wk13 wk14 wk15 wk16 wk17 35 0 168 336 504 672 840 1008 1176 1344 1512 1680 1848 2016 2184 2352 2520 2688 2856 3024 Hrs/ weeks 21
  • 22. Conclusions for Subsystem 2: Intensive Care Unit • 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%). 22
  • 23. Subsystem 3: Typical Operating Rooms (OR) 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. 23
  • 24. 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%. 24
  • 25. 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. 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. 25
  • 26. Simulation Model Layout (Scenarios 1 – 3) Operating Rooms: OpR-general; U_OR-urgent; CV_OR-cardiovascular; Cath_OR-catheterization; SPR-special procedure. 26
  • 27. Conclusions for Subsystem 3: Operating Rooms (OR) • 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. 27
  • 28. Subsystem 4: Medical/Surgical Nursing Units (NU) Total number of specialized nursing units: 24 Total number of licensed beds: 380 Patient Length of Stay (LOS) is in the range from 2 days to 10 days; The most likely LOS is 5 days. 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). 28
  • 29. Census (i) (current period) = census (i-1) (previous period) + [# admissions (i) – # discharges (i) ]; i = 1, 2, 3, ……. Simulated Census. Capacity 380 beds 390 Mon Tue Wed Thu Fri Sat Sun 380 capacity limit 370 census 360 350 340 330 320 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 Take Away: Percent of time Nursing Units are full (% diversion) is about 16%. 29
  • 30. Step 2 • 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. 30
  • 31. Step 2 – continued • All subsystems are reconnected to each other. • The output of one subsystem is the input for another subsystem. 31
  • 32. Hospital System Simulation Summary Too aggressive ED Downstream Less aggressive Downstream Current improvement: Units: Better ED improvement: Units: Better or Performance Metrics State patients admitted or worse than patients admitted words than current Baseline within 6 hours current state? within 10 hours state? 95% CI of the number of patients waiting to get to 25 – 27 8 – 10 Better 17 – 19 Better ED (ED in) 95% CI of the number of patients waiting hospital 57 – 62 64 – 69 Worse 57 – 62 Neutral admissions (ED out) Number of patients left not seen (LNS) after waiting more than 2 23 – 32 0 Better 0–3 Better hours 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 32
  • 33. Take-Away from Hospital System Simulation Summary 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: 33
  • 34. Important System Engineering Principles • 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. 34
  • 35. 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. 35
  • 36. 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. 36
  • 37. Summary of Some Fundamental Management Engineering Principles – continued • 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. 37
  • 38. Summary of Some Fundamental Management Engineering Principles – continued • 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. 38
  • 39. APPENDIX 39
  • 40. What is a Simulation Model? 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. • 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.
  • 41. 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). 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…. 41
  • 42. 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. 42
  • 43. 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.) 43
  • 44. 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. 44