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					SIMULATION OPTIMIZATION: NEW ADVANCES FOR REAL
WORLD OPTIMIZATION




OPTIMIZATIONSOFTWARE
                                  Fred Glover (OptTek)
                  Gary Kochenberger (OptTek & UCD)
                       (Special thanks to Marco Better)


                                                   OPTIMIZATIONSOFTWARE
                                                      www.OptTek.com
Outline

   OptTek Systems, Inc.
   What is simulation optimization?
   Why is it important?
   Classical approaches
   Metaheuristic approaches
   Applications
   Conclusions


                                       OPTIMIZATIONSOFTWARE
                                          www.OptTek.com
OptTek Systems, Inc. Snapshot

 Founded in 1992
 Leading provider of optimization software to the general simulation market.
 OptQuest®, the company’s flagship software product
      licensed to over 60,000 users
      the optimization standard for simulation modeling
 Alliance partners number over twenty including:
        Halliburton
        Oracle
        CSC
        Flextronics
        Dassault
        CACI                                              OptTek Systems, Inc.
        Lockheed Martin                                   1919 Seventh Street
        Rockwell Software                                 Boulder, CO 80302
        HP                                                www.OptTek.com
   Consulting and Technical Services

                                                                        OPTIMIZATIONSOFTWARE
                                                                           www.OptTek.com
    Simulation Optimization Software

                     Our Channel Partners:

   Alion, Micro Analysis and Design Division      Jada Management Systems
   CACI , SIMPROCESS                              Halliburton, Landmark Graphics Division
   Oracle, Decisioneering (Crystal Ball)          HP, Mercury Division
   Delmia, a subsidiary of Dassault Systèmes      Mesquite Software
                                                   Planview
   FlexSim Software Products
                                                   PROMODEL Corporation
   Flextronics/SimFlex
                                                   Risk Capital Management
   Frontline Systems (Premium Solver)
                                                   Rockwell Software (ARENA)
   GAMS
                                                   SIMUL8
   Glomark                                        XJ Technologies
   Incontrol Enterprise Dynamics




                                                                               OPTIMIZATIONSOFTWARE
                                                                                  www.OptTek.com
OptTek Customized Simulation Optimization
Software Applications


   Portfolio Management  securities and capital assets (projects,
    programs, initiatives, etc.)
   Workforce Optimization  Manpower planning, diversity planning
   Data Security
   Supply Chain Management
   Strategic and Operational Planning
   Financial Planning
   Manufacturing Process Flow
   Resource-Constrained Scheduling
   Business Process (re)Design


                                                              OPTIMIZATIONSOFTWARE
                                                                 www.OptTek.com
What is Simulation Optimization?

Which  of possibly many sets of model specifications (i.e.,
input parameters and/or structural assumptions) leads to
optimal performance?



                          Simulation
                          model




       Input                                  Measure of
       parameters                             performance



                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Simulation Optimization
Why is it required?

Complex   models contain many variables and constraints as
well as uncertainty

What-if  approach unlikely to result in an optimal answer due
to large number of possible solutions

Inabilityof pure optimization to model complexities,
uncertainties and dynamics of scenarios

Simulation-Optimizationremoves these inabilities by
combining both approaches




                                                             OPTIMIZATIONSOFTWARE
                                                                www.OptTek.com
Simulation-Optimization
Why is it required?


A   total solution requires both capabilities.


Integrated   two-Step Solution
Simulation
Optimization


Both   are necessary, neither is sufficient.



                                                  OPTIMIZATIONSOFTWARE
                                                     www.OptTek.com
Simulation Optimization
Benefits in Dealing with Uncertainty



Simulationenables understanding/modeling and
communications of uncertainty.



Optimization   enables management of uncertainty.




                                                     OPTIMIZATIONSOFTWARE
                                                        www.OptTek.com
Optimization on a Metamodel




                              OPTIMIZATIONSOFTWARE
                                 www.OptTek.com
Classical Approaches

   Stochastic approximation
    – Gradient-based approaches
   Sequential response surface methodology
   Random search
   Sample path optimization
    – Also known as stochastic counterpart
   Drawbacks:
        • Local in their search
        • Rely heavily on randomness
        • Lack of intelligent guidance
        • No learning ability

                                              OPTIMIZATIONSOFTWARE
                                                 www.OptTek.com
Metaheuristic Approaches

   Based on neighborhood search
    – Tabu search
    – Simulated annealing
   Based on combining solutions in a population
    – Genetic algorithms
    – Scatter search
   Other:
    – Swarm methods
    – Hybrid methods (e.g. tabu search + scatter search)

                                                    OPTIMIZATIONSOFTWARE
                                                       www.OptTek.com
Modular Design




                      Metaheuristic
                       Optimizer
   Input parameters                   Objective function value

                       Simulation
                         Model




                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Tabu Search

   Uses a systematic neighborhood search to
    choose the best neighbor
    – Size of the neighborhood is controlled by candidate
      list strategies
    – The selection of the best neighbor is constrained by
      tabu functions
   The best move may be nonimproving
   Memory functions (short and long term) are
    updated after every move


                                                     OPTIMIZATIONSOFTWARE
                                                        www.OptTek.com
Tabu Search:
Implementation Issues




                        Feasible point

                        Infeasible point

                        Current point

                        Optimal point

                          Nontabu move
                          Tabu move




                          OPTIMIZATIONSOFTWARE
                             www.OptTek.com
Scatter Search

   Combines solutions in a small reference set to
    create new trial solutions
   Uses generalized combination methods with
    controlled randomization
   The selection process is deterministic
   The updating of the reference set (aka the
    “evolution process”) is also deterministic and
    attempts to create a balance between solution
    quality and diversity


                                              OPTIMIZATIONSOFTWARE
                                                 www.OptTek.com
Basic Scatter Search


                                                                                  P
       Diversification Generation   Repeat until |P| = PSize
                 Method


                                    Improvement
                                      Method




                                    Improvement                                  Reference Set
                                      Method                                     Update Method


         Solution Combination
                Method


                                       Subset Generation
                                           Method
                                                                                      RefSet
                                                               Stop if no more
                                                                new solutions
                                                                                                 OPTIMIZATIONSOFTWARE
                                                                                                    www.OptTek.com
Linear Combination Method

   y
                                                                         x3 = x1 - r(x2 - x1)
   10                                                                    x4 = x1 + r(x2 - x1)
                                                                         x5 = x2 + r(x2 - x1)
   9
            x3
   8                                  x1 = (5,7)

   7

   6
                             x4
   5
                                                            x2 = (8,4)
   4

   3
                                                   x5
   2

   1


                                                                                                x
        1        2   3   4        5    6     7          8    9     10       11    12     13

                                                                                                    OPTIMIZATIONSOFTWARE
                                                                                                       www.OptTek.com
Issues Related to Metaheuristics for Simulation
Optimization

   Aggressiveness of the search
    – Balance between diversification and intensification
   Solution representation
    – Combination methods
   Use of metamodels to “save” on evaluations
   Constraint handling (soft vs. hard)
   Length of simulation and selection of best
    solution


                                                     OPTIMIZATIONSOFTWARE
                                                        www.OptTek.com
Aggressiveness of the Search
 Objective function value




                            Less aggressive
                             but diversified



                                               Aggressive and
                                               less diversified




                                               Calls to the simulator




                                                                  OPTIMIZATIONSOFTWARE
                                                                     www.OptTek.com
Solution Representation

   Continuous variables
   Discrete variables
    – Resources (e.g., number of machines, number of
      technicians, etc.)
    – Design choices (e.g., brand, category, etc.)
   Binary variables
    – Special case of discrete variables
   Permutation variables
    – Imply so-called all-different constraints

                                                     OPTIMIZATIONSOFTWARE
                                                        www.OptTek.com
Use of Meta-models


                                                     Neural networks,
                                                     Regression, Data
                                                     mining, etc.

         Metaheuristic   x
                                  Metamodel
          Optimizer


                                         fˆ ( x )
  f(x)
                                                        ˆ
                                                    d  f ( x)  f ( xbest )
                             No
          Simulation
                                   large d?
            Model


                                        Yes


                                  Discard x



                                                                               OPTIMIZATIONSOFTWARE
                                                                                  www.OptTek.com
Handling Constraints



                                                       F(x*)
    x       Constraint       x*                                   Penalty
                                                                                P(x*)
                                      Simulator        G(x*)
             Mapping                                             Function



                x = input parameters (possibly infeasible)
                x* = mapped input parameters (constraint feasible)
                F(x*) = objective function value
                G(x*) = value of other output variables used in constraints
                P(x*) = penalized objective function value

        May allow desirable infeasible solutions from management perspective.

                                                                                OPTIMIZATIONSOFTWARE
                                                                                   www.OptTek.com
Length of Simulation

   Simulation runs during the optimization process
    are typically shorter than those of confirmation
    runs
   A run can be terminated early if it can be
    predicted that the outcome will not improve upon
    the current best solution
    – This can be done with statistical analysis tools such
      as confidence intervals and hypothesis testing




                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
OptQuest®

  A potent search engine that can pinpoint the best
  decisions to optimize plans.


         Scatter Search
         Advanced Tabu Search
         Linear Programming
         Integer Programming
         Neural Networks
         Linear Regression


          Ten years of Research &
           Development funded by
           National Science Foundation
           (NSF) and Office of Naval
           Research (ONR)
                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
                              OptQuest vs. RiskOptimizer, Ex. 5 Prob. 14     Best solution = -8695.012285
            -3000




            -4000
                                                                                                            -4272.22 Risk Pop 50
                                                                                                            -4397.23 Risk Pop 10
                                                                                                            -4576.85 Risk Pop 20
                                                                                                            -4765.34 Risk Pop 100
            -5000

                                                Efficiency is Critical!
Objective




            -6000




            -7000




            -8000
                                                                                                            -8543.49 OptQuest
                                                                                                                  Pop 20
                                                                                                            -8695.01 OCL
                                                                                                             Boundary=.7
            -9000
                    0   200       400     600     800     1000        1200   1400   1600    1800    2000
                                                        Simulations                                                             OPTIMIZATIONSOFTWARE
                                                                                                                                   www.OptTek.com
OptQuest Applications

   Optimization of Monte Carlo Models
    – Project portfolio selection
    – Inventory order management
   Optimization of Discrete Event Models
    – Six Sigma in an Emergency Room
    – Job shop configuration
   Optimization of Agent-based Models
    – Workforce diversity planning
    – Manpower planning and scheduling

                                            OPTIMIZATIONSOFTWARE
                                               www.OptTek.com
Example 1 – Project Portfolio
Selection in Oil and Gas




                                OPTIMIZATIONSOFTWARE
                                   www.OptTek.com
Problem


   Given a set of opportunities and limited
    resources determine the best set of projects that
    maximize performance while controlling risk.


   Create a new portfolio


   Augment an existing portfolio



                                               OPTIMIZATIONSOFTWARE
                                                  www.OptTek.com
Traditional Approaches

   Net Present Value Analysis / Ranking Methods
    – Compute discounted cash flows and pick largest NPV
    – Ignores uncertainty


   Mean-Variance Optimization – Harry Markowitz (1952)

    Minimize s
    Such that m > Goal

    • Normality of returns of assets must be assumed
    • Quadratic Program
    • Addresses correlation but limited to variance as measure of risk.
    • Additional constraints such as cash flow and performance metrics
      may not be addressable.
                                                                   OPTIMIZATIONSOFTWARE
                                                                      www.OptTek.com
    Simulation-Based Portfolio Selection

   Use Monte Carlo simulation to model projects.
    – Unlimited ability to model complex situations
    – Risk can be defined in multiple ways


   Use OptQuest to select projects
    – Objectives based on outputs from simulation
    – Additional constraints based on cash flows, etc.




                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Components

   Simulation Model
   Integer Variables
    e.g., Only invest in one project within a group
   Constraints
    e.g., Cash Flow
   Multiple Objectives - “Requirements”
    e.g., Maximize Return Mean while keeping 5th percentile of return
       above some goal (risk control).




                                                               OPTIMIZATIONSOFTWARE
                                                                  www.OptTek.com
Application Information



   5 Projects
    – Tight Gas Play Scenario (TGP)
    – Oil – Water Flood Prospect (OWF)
    – Dependent Layer Gas Play Scenario (DL)
    – Oil - Offshore Prospect (OOP)
    – Oil - Horizontal Well Prospect (OHW)
   Ten year models that incorporate multiple
    types of uncertainty

                                                OPTIMIZATIONSOFTWARE
                                                   www.OptTek.com
Budget-Constrained Project Selection



    5 Projects
     – Expected Revenue and Distribution
     – Probability of Success
     – Cost
    $2M Budget




                                           OPTIMIZATIONSOFTWARE
                                              www.OptTek.com
Base Case


   Determine participation levels in each project
    [0,1] (Decision Variables) that
   Maximize E(NPV) (Forecast)
   While keeping sNPV < 10 M$ (Forecast)


   All projects must start in year 1.




                                               OPTIMIZATIONSOFTWARE
                                                  www.OptTek.com
                         Base Case
                                  Forecast: NPV
1,000 Trials                      Frequency Chart                        16 O utlie rs
     .028                                                                       28



     .021                                                                       21



     .014                                                                       14



     .007                                                                       7


                                          Mean = $37,393.13
     .000                                                                       0

        $15,382.13   $27,100.03      $38,817.92       $50,535.82   $62,253.71
                                         M$



TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.
E(NPV) = 37.4M s =9.5M




                                                                                         OPTIMIZATIONSOFTWARE
                                                                                            www.OptTek.com
Deferment Case


   Determine participation levels in each project [0,1] AND
    starting times for each project that
   Maximize E(NPV)
   While keeping sNPV < 10 M$


   All projects may start in year 1, year 2, or year 3.
    (5x3=15 Decision Variables)




                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
                         Base Case                                                                            Deferment Case
                                  Forecast: NPV                                                                             Forecast: NPV
1,000 Trials                      Frequency Chart                        16 O utlie rs   1,000 Trials                       Frequency Chart                             8 O utliers
     .028                                                                       28            .027                                                                            27



     .021                                                                       21            .020                                                                            20.25



     .014                                                                       14            .014                                                                            13.5



     .007                                                                       7             .007                                                                            6.75


                                          Mean = $37,393.13                                                                        Mean = $47,455.10
     .000                                                                       0             .000                                                                            0

        $15,382.13   $27,100.03      $38,817.92       $50,535.82   $62,253.71                    $25,668.28    $37,721.53      $49,774.78       $61,828.04       $73,881.29
                                         M$                                                                                        M$




TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.                                                 TGP1 = 0.6, DL1=0.4, OHW3=0.2
E(NPV) = 37.39M s =9.50M                                                                 E(NPV) = 47.5M s =9.51M 10th Pc.=36.1M




                                                                                                                                                             OPTIMIZATIONSOFTWARE
                                                                                                                                                                www.OptTek.com
    Probability of Success Case




   Determine participation levels in each project [0,1]
    AND starting times for each project that
   Maximize P(NPV > 47,455 M$)
   While keeping 10th Percentile of NPV > 36,096 M$


   All projects may start in year 1, year 2, or year 3.



                                                     OPTIMIZATIONSOFTWARE
                                                        www.OptTek.com
                         Base Case                                                                                              Deferment Case
                                  Forecast: NPV                                                                                                   Forecast: NPV
1,000 Trials                      Frequency Chart                                16 O utlie rs            1,000 Trials                            Frequency Chart                             8 O utliers
     .028                                                                               28                     .027                                                                                 27



     .021                                                                               21                     .020                                                                                 20.25



     .014                                                                               14                     .014                                                                                 13.5



     .007                                                                               7                      .007                                                                                 6.75


                                          Mean = $37,393.13                                                                                              Mean = $47,455.10
     .000                                                                               0                      .000                                                                                 0

        $15,382.13   $27,100.03      $38,817.92       $50,535.82           $62,253.71                             $25,668.28     $37,721.53          $49,774.78       $61,828.04       $73,881.29
                                         M$                                                                                                              M$




TGP = 0.4, OWF = 0.4, DL = 0.8, OHW = 1.                                                                  TGP1 = 0.6, DL1=0.4, OHW3=0.2
E(NPV) = 37.39M s =9.50M                                                                                  E(NPV) = 47.5M s =9.51M 10th Pc.=36.1M
                                                              Probability of Success Case
                                                                                             Forecast: NPV
                                                  1,000 Trials                               Frequency Chart                           13 O utlie rs
                                                        .032                                                                                  32



                                                        .024                                                                                  24



                                                        .016                                                                                  16



                                                        .008                                                                                  8


                                                                                                     Mean = $83,971.65
                                                        .000                                                                                  0

                                                              $43,258.81        $65,476.45       $87,694.09       $109,911.73    $132,129.38
                                                                                                     M$



               TGP1 = 1.0, OWF1=1.0, DL1=1.0, OHW3=0.2
                                                                                                                                                                                   OPTIMIZATIONSOFTWARE
                                                                                                                                                                                      www.OptTek.com
               E(NPV) = 83.9M s =18.5M P(NPV > 47. 5) = 99%                                                                         10th           Pc.=53.4M
Benefits


    Easy to use
    Quickly evaluate many planning alternatives
    Optimized financial performance
    Better risk control using familiar metrics


    Similar results found in larger problems
        • (e.g. oil & gas investment funnel with 256 projects).



                                                                  OPTIMIZATIONSOFTWARE
                                                                     www.OptTek.com
Example 2 – IT Project Portfolio Selection
in Pharmaceuticals




                                             OPTIMIZATIONSOFTWARE
                                                www.OptTek.com
Problem Setup

   Example 2: Monte Carlo Simulation
       • Portfolio of 20 potential projects
       • Pharmaceutical product development
            Relatively long and costly R&D
            Probability of Success factor after R&D is complete
       • Mutually exclusive (substitute) products
       • Dependent (complementary) products
       • Choose the best (0,1) set of projects to:
            Maximize return
            Control risk
            Maximize probability of high NPV




                                                                   OPTIMIZATIONSOFTWARE
                                                                      www.OptTek.com
Base Case

   Example 2: Summary Results
          (All cases subject to budget constraint).



    – Base Case:         Max E[NPV]
                         While St.Dev.(NPV)  $ 650


    – Result:            E[NPV] = $ 2,139
                         P(5) = $ 1,086
                         St.Dev. = $ 639


                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Case 2

   Example 2: Summary Results
          (All cases subject to budget constraint).



    – Case 2: Max E[NPV]
                         While P(5)  $ 1,086


    – Result:            E[NPV] = $ 2,346
                         P(5) = $ 1,159
                         St.Dev. = $ 725


                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Case 3

   Example 2: Summary Results
          (All cases subject to budget constraint).



    – Case 3: Max P(NPV > $2,139)


    – Result:            P(NPV > $2,139) = 62%
                         E[NPV] = $ 2,346
                         P(5) = $ 1,159
                         St.Dev. = $ 725


                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
Example 3 – Six Sigma in an
Emergency Room



        Optimization Driven
            SIX SIGMA
   Using Simulation Optimization to Achieve Quality Goals




                                                        OPTIMIZATIONSOFTWARE
                                                           www.OptTek.com
    Minimizing Cycle Time at an ER




Patient Arrival

                          Emergency Room
                                                              Admit


                                           Treatment

Approach= optimize current process,
redesign process and re-optimize.

                                                            Release


                                                       OPTIMIZATIONSOFTWARE
                                                          www.OptTek.com
DMAIC Framework


 Define the problem area
  – Current ER process is too costly, in terms of
    operating cost and variability in level of service.
  – Need to redesign ER process to reduce costs and
    guarantee service levels at a 95% confidence level or
    higher.




                                                      OPTIMIZATIONSOFTWARE
                                                         www.OptTek.com
DMAIC Framework

 Describe the current process
  – Arriving patients are assigned a priority level according to
    the criticality of their condition:
     • LEVEL 1: immediately taken to an ER Room.
     • LEVELS 2 AND 3: first sign in, then undergo a triage assessment before
       being taken to an ER Room.
     • Level 2 and 3 patients’ arrival rate is higher than Level 1 patients’.
     • Higher priority patients can preempt resources being used by lower priority
       patients.




                                                                                OPTIMIZATIONSOFTWARE
                                                                                   www.OptTek.com
DMAIC Framework


 Describe the current process (Cont’d.)
  – Current resources available:
     • Nurses (7)
     • Physicians (3)
     • Patient Care Technicians (PCTs) (4)
     • Administrative Clerks (4)
     • ER Rooms (20)
  – Rooms not used by ER can be used by other wards.




                                               OPTIMIZATIONSOFTWARE
                                                  www.OptTek.com
DMAIC Framework



               Current Process for Level 1 Patient




   Arrive at    Transfer to       Receive       Fill out                Y
                   room                                       OK?           Released
      ER                         treatment    registration
                                                                 N

                                                             Admitted
                                                               Into
                                                             Hospital




                                                                                 OPTIMIZATIONSOFTWARE
                                                                                    www.OptTek.com
DMAIC Framework


 Measure current performance
  – Costs (per 100 hours of operation):
     • Cost of personnel:               $51.7K
     • Fixed ER room cost:     $ 0.9K
     • Total operating cost:   $52.6K
  – Level of Service (CT of critical patients):
     • Average: 1.98 hours
     • 95% Confidence Interval: [1.94 – 2.02]




                                                  OPTIMIZATIONSOFTWARE
                                                     www.OptTek.com
DMAIC Framework


 Measure current performance (Cont’d.)
  – Process is too costly. Six Sigma team has set a new
    budget goal of $40.0K per 100 hours of operation.
  – Service level variability is too great.    New goal:
    at least 95% of Level 1 patients spend no longer than
    2 hours in the ER.




                                                  OPTIMIZATIONSOFTWARE
                                                     www.OptTek.com
DMAIC Framework

 Analyze problem to identify causes
  – Construct a workflow level simulation model of current
    process.
  – Use OptQuest® to optimize resource levels in order to
    minimize Level 1 patients’ CT. Why?
  – Enumeration of all possible scenarios may require:
     •   7x3x4x4x20 = 6,720 scenarios tested
     •   30 runs/scenario = 2 min. each
      28 workdays to obtain best solution!




                                                         OPTIMIZATIONSOFTWARE
                                                            www.OptTek.com
DMAIC Framework


 Analyze problem (Cont’d)
  – Minimize E[CT] for Level 1 Patients
  – Subject to:
     • Operating Cost <= $40.0K/100 hrs of operation
     • Number of Nurses between 1 and 7
     • Number of Physicians between 1 and 3
     • Number of PCTs between 1 and 4
     • Number of Clerks between 1 and 4
     • Number of ER Rooms between 1 and 20




                                                       OPTIMIZATIONSOFTWARE
                                                          www.OptTek.com
DMAIC Framework

 Analyze problem (Cont’d)
  – First, run 30 replications of the current operation:
     • 7 nurses
     • 3 physicians
     • 4 PCTs
     • 4 Admin. Clerks
     • 20 ER Rooms

  – Results:
     • E[OC] = $ 52.6K per 100 hrs. of operation
          (TOO COSTLY! New budget <= $40.0K)
     • E[CT] for Level 1 Patients = 1.98 hours
          New process should achieve this result, or better.



                                                                OPTIMIZATIONSOFTWARE
                                                                   www.OptTek.com
DMAIC Framework

 Analyze problem (Cont’d)
  – Next, set up OptQuest to run for 100 iterations and 30
    runs per iteration.
     • Each run simulates 100 hours of ER operation.
     • Results:
          Best solution found in 6 minutes
          3 nurses, 3 physicians, 1 PCT, 2 clerks, 12 rooms
          E[OC] = $ 36.2K (31% improvement)
          E[CT] for P1 = 2.08 hours (too high!)

  – Need to redesign process to assure quality goal is
    achieved on a 95% confidence level.



                                                               OPTIMIZATIONSOFTWARE
                                                                  www.OptTek.com
DMAIC Framework

   Improve the results by redesigning processes
     Arrive at   Transfer to     Receive          Fill out                Y
                                                                   OK?        Released
        ER          room        treatment       registration
                                                                    N

                                                               Admitted
                                                                 Into
                                                               Hospital
                        Current Process



                                     Receive
                                    treatment
     Arrive at   Transfer to                                        Y
        ER          room                                  OK?            Released
                                     Fill out                  N
                                   registration
                                                        Admitted
                                                          Into
                  Redesigned Process
                                                        Hospital
                                                                                    OPTIMIZATIONSOFTWARE
                                                                                       www.OptTek.com
DMAIC Framework


   Improve the results by redesigning processes
    – E[CT] for P1 improves from 2.08 to 1.98 hours;
      however, the upper limit of the 95% confidence interval
      is still above 2 hours.
    – Re-optimize new process using OptQuest.
    – Results:
       • Best solution found in 8 minutes
       • 4 nurses, 2 physicians, 2 PCTs, 2 clerks, 9 rooms
       • E[OC] = $ 31.8K (a 12% further improvement)
       • E[CT] for P1 = 1.94 hours (95% C.I. is 1.91 – 1.99)
       • MISSION ACCOMPLISHED!


                                                               OPTIMIZATIONSOFTWARE
                                                                  www.OptTek.com
DMAIC Framework


   Control the processes to ensure
    improvement goals are met
    – Implement changes and a performance
      measurement system to continuously assess real
      performance.
    – Readopt this simulation-optimization methodology
      whenever necessary to maintain adequate
      performance.




                                                 OPTIMIZATIONSOFTWARE
                                                    www.OptTek.com
Conclusions



     Able to find high-quality solution quickly.
     Able to improve the model and re-optimize to
      find better configurations.
     Highly unlikely to find solution of such high
      quality relying solely on simulation.




                                                OPTIMIZATIONSOFTWARE
                                                   www.OptTek.com
Conclusions




 There is still much to learn and discover about
how to optimize simulated systems both from the
  theoretical and the practical points of view.


         The opportunities are exciting!



                                           OPTIMIZATIONSOFTWARE
                                              www.OptTek.com
Questions & Feedback




            www.OptTek.com

             (303) 447-3255




                              OPTIMIZATIONSOFTWARE
                                 www.OptTek.com

				
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