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					Simulation Modeling &
Analysis
       Department of Industrial Engineering
          University of Central Florida
What is Simulation?
     Very broad term, set of problems/approaches
     Generally, imitation of a system via computer
     Involves a model --validity?
     Don’t aspire to analytic solution
       Don’t get exact results (bad)

       Allows for complex, realistic models (good)

     Approximate answer to exact problem is better
      than exact answer to approximate problem
     Very popular, powerful approach
Applications

    Manufacturing
    Supply chain and logistics
    Staffing
    Telecommunications
    Health care
    Military
    Consistently ranked as most useful, powerful of
     mathematical-modeling approaches
Systems

    Physical facility/process, usually evolving
     through time
    May or may not exist
    Study its performance
    May be controlled in real time
Models

    Abstraction/simplification of the system used
     as a proxy for the system itself
    Two types
        Physical (iconic)
        Mathematical - quantitative and logical
         assumptions
  Methods of Studying a System

                        SYSTEM


    Experiment with the               Experiment with a
      actual system                  model of the system



                     Physical model                      Analytical model

Mathematical model    Simulation model    Spreadsheets/Process maps   Hybrid model
Study a System vs. Model

     System study
         No question about validity
         May be impractical or impossible (system may not exist)
         High risk
     Model study
         Must be concerned with validity
         Generally much easier to work with
         Can “exercise” it for many more situations than system
         Analytical solution (simple model) or simulation?
Simulation Alternatives

   Mathematical models are an equation or set of equations which
    attempt to give a mathematical description of some real
    phenomenon.
   It can be very simple or very complex.
   Linear and non linear programming.
   Easiest and fastest for simple problems, gives exact and
    optimum solutions



      Mathematical models are not dynamic (static) and cannot account for changes
      in the system over time and they cannot model variability, e.g., probabilistic
      processing times, dynamic resource schedules/failures, etc.
Example: Transportation Problem

   Problem Definition
       Company XYZ has five distribution centers in
        different locations. The company would like to
        develop an optimum transportation plan to
        distribute building material to six of its customers.
        The inventory at each plant, the quantity required
        by each customer, and location of customers and
        plants are known.
       Example: Transportation Problem
                                                                                           C6 (30)


                                                           C5 (16)




                                                                                               30 miles
                                                                                                                   C1 (16)
                                                                                                                                                     S1
                        S5




                                                           1 mi
                                                                                                                                                          (36)
                                    (8)                                    8 miles                        1 mile                9 miles




                                                           8 miles
                        4 miles




                                                                                                                                          30 miles
                                                                                               S2
        S4                                     C4 (28)
             1 mile               3 miles
                                                                                                                   (31)
(25)
                                                                                                                                                     C2 (13)
             10 miles




                                                                                                                     15 miles
                                                 C3 (25)
                                                                                     5 miles              S3
                                    10 miles                         10 miles
                                                                                                                    (28)
Problem Formulation (General)
   Variables: Xij - where Xij is the quantity transported from plant i (i=1,2,..m)
    to customer j (j=1,2,…n).
                                                       m     n

   Objective function: Minimize Z=                     c x
                                                       i 1 j 1
                                                                   ij ij



       Where cij is the unit transportation cost between i and j


   Constraints:     n

                   x
                    j 1
                           ij    ai , i  1,2,...m

                    m

                   x
                    i 1
                           ij    b j , j  1,2,...n


       a: supply , b: demand
Problem Formulation (Company XYZ)

   Variables: Xij - where Xij is the quantity transported from plant i (i=1,2,3,4,5) to
    customer j (j=1,2,3,4,5,6).
   Assume 1 mile = $0.75
   Objective function: Minimize z  6.75x11  22.5x12  45x13  63x14  14.25x15  30 x16
                                      16.5 x21  45.75x22  68.25x23  86.25x24  10.5 x25  38.25x26
                                      44.25x31  15x32  7.5 x33  25.5 x34  52.5 x35  67.5 x36
                                      66.75x41  52.5 x42  15x43  3x44  74.25x45  90 x46
                                      70.5 x51  56.25x52  18.75x53  5.25x54  78x55  93.75x56


   Constraints:                      x11  x12  x13  x14  x15  x16  36
                                      x21  5 x22  x23  x24  x25  x26  31
                                      x31  x32  x33  x34  x35  x36  28
                                      x41  x42  x43  x44  x45  x46  25
                                      x51  x52  x53  x54  x55  x56  8
Problem Formulation (Company XYZ)

   Constraints:
                     x11  x21  x31  x41  x51  x61  16
                     x12  x22  x32  x42  x52  x62  13
                     x13  x23  x33  x43  x53  x63  25
                     x14  x24  x34  x44  x54  x64  28
                     x15  x25  x35  x45  x55  x65  16
                     x16  x26  x36  x46  x56  x66  30

                   and
                      xij  0
Problem Formulation (Table Representation)

        To
From          C1      C2      C3      C4      C5      C6     Supply


   S1        6.75    22.5     45      63     14.25    30      36

   S2        16.5    45.75   68.25   86.25   10.5    38.25    31

   S3        44.25    15      7.5    25.5    52.5    67.5     28

   S4        66.75   52.5     15      3      74.25    90      25

   S5        70.5    56.25   18.75   5.25     78     93.75     8

Demand        16      13      25      28      16      30
Optimum Transportation Plan
        Trucks From site to customer for minimum cost
        Total Transportation Cost = $1,859.25


                                   Customer
                To   C1    C2      C3      C4      C5   C6   Supply
        From

           S1        16     5                           15    36

           S2                                      16   15    31

 Site      S3               8      20                         28

           S4                       5      20                 25

           S5                              8                   8

        Demand       16    13      25      28      16   30
Simulation Alternatives

   Spreadsheets are fast, easy to use, and widely available.
   Any number of parameters and formulas with varying degrees of
    complexity can be included; at the same time these parameters
    and formulas can be updated quickly to test several scenarios.




      Spreadsheets are not very dynamic and cannot account for changes in the
      system over time and they neglect variability. They consider averages only
      (very bad) e.g., average arrival rates, average processing times, travel times,
      etc.
Simulation Alternatives

   Process maps represent a common understanding of systems
    operations.
   They are easy to use, widely available, and with no need of prior
    mathematics or programming knowledge.
   Can be used to map an end-to-end business process in greater
    details, mainly to convey a common understanding of the “as is”
    process and map alternative “to be” processes.




      Process maps are not dynamic, cannot account for changes in the system over
      time, and do not represent any variability.
      .
Is Simulation a Better Method?
   Yes, because
      Simulation fulfills other methods shortfalls and weaknesses
     Simulation is dynamic and account for changes in the system

       over time.
     Simulation models variability, far beyond averages.

   The following demonstration shows the power of simulation
    methodology over other competitive methodologies. The
    demonstration mainly shows that averages used by others method
    are not enough and always mislead decision makers.
Demonstration: Claims Department
   Assume an insurance company with a claim department of 3
    employees; each claim is processed by the three employees.
   Insurance claims arrive at the claims department every 10 minutes
    (inter-arrival time) for processing.
   When a claim arrives, it takes 1 min. to transfer the claim to the first
    employee. If the first employee is not free, the claim waits on his
    desk. When the first employee becomes free, it takes 10 min to
    process the claim. When the first employee finishes working on the
    claim, the claim is transferred to the second employee for further
    processing. This transfer takes 1 min.
   Once the second employee is available, it takes 10 min to complete
    his portion of the process. When the second employee finishes, the
    claim is transferred to the third and final employee. This transfer
    takes 1 min.
   Once the third employee is available, it takes 10 min to perform his
    portion of the process. When the third employee finishes, the claim
    is complete and is transferred to the mailroom where it is sent to the
    customer with the approval or disapproval decision.
Claims Department
     Spreadsheet



                                                                                                                 Formula B3+B4+…+B9 = 34




     Process map

 Claims arrival                             Process 1                                Process 2                             Process 3
                          1 min                                    1 min                                1 min                                         1 min   exit
 1 claim/10 min                              10 min                                   10 min                                10 min




     Simple graphical representation

                                                              0                           0                        0

                  Arri vi ng Cl ai m s                                                                                        Fi ni s hed Cl ai m s


                          0              Proc es s /em pl oyee 1       Proc es s /em pl oyee 2   Proc es s /em pl oyee 3
                                                                                                                                       0
Question
   What is your best estimate for the minimum,
    average, and maximum times for cycle time,
    i.e. a claim to arrive at the department,
    process through all 3 employees, and finally
    arrive at the mailroom, exiting the system
 Modeling Claims Department Using Arena
                                                                                   Transfer time = 1 min
Inter-arrival time =
10 min                   Create 1         Assign arrive time
                                                                    Transf er to
                                                                    employee1
                                    0




                                                                                    Transfer time = 1 min
                                        Claim processing         Transf er to
                       employee1        by employee_1            employee2

                                                0




processing time = 10                                                                Transfer time = 1 min
min                                     Claim processing         Transf er to
                       employee2        by employee_2            employee3

                                                    0


                                                                                    Transfer time = 1 min
processing time = 10
                                         Claim processing        Transf er to
min                    employee3         by employee_3            mailroom

                                                        0




processing time = 10                                                                Averages
                       mailroom                                send to client
min                                       Record 1


                                                                0
Simulation Run (Averages)
Simulation Output (Averages)




   From the animation and the output
     Queues are not building

     Cycle time is not fluctuating,

     No problems in the system.

   This output is similar to using a static tool like a spreadsheet or a process
    map.
In Reality “Averages Kill”

   In reality, the arrival of the claims and
    department operations would never work in
    perfect rhythm, there is variability.
   Variability occurs in every day situations and
    in any business. This is where the power of
    simulation over other methods arises.
   Variability and its effect on business
    operations and decision making will be
    demonstrated in the claims department
    simulation model.
    Claims Department Model with Variability
                                                                                      Transfer time =
   Inter-arrival time =                                                               Exponential (1)
   Exponential (10)         Create 1         Assign arrive time
                                                                       Transf er to
                                                                       employee1
                                       0




                                                                                       Transfer time =
                          employee1
                                           Claim processing         Transf er to       Exponential (1)
                                           by employee_1            employee2

                                                   0

processing time =
                                                                                       Transfer time = 1 min
Normal distribution
                                                                                       Exponential (1)
Mean=10 , Std.dev 2       employee2
                                           Claim processing         Transf er to
                                           by employee_2            employee3

                                                       0


processing time =                                                                      Transfer time = 1 min
Triangular distribution                                                                Exponential (1)
                                            Claim processing        Transf er to
                          employee3
Min=8, Mode=10,                             by employee_3            mailroom
Max=12                                                     0




processing time =
Uniform distribution      mailroom           Record 1             send to client      Distributions
Min = 8, Max = 12                                                  0
Question

   What is your estimates of the minimum,
    average, and maximum cycle time for this
    system.
Simulation Run (Distributions)
Simulation Output (Distributions)




   From the animation and the output
     Queues are building, especially at process 1

     Cycle time is fluctuating,

     There are problems in the system.

   This output is not similar to using a static tool like a spreadsheet, a process
    map, or even simulation run based on averages
Comparison of Simulation Models
Comparison of Simulation Output


 Averages




Distributions
(Variability)
“A little bit” of Statistics
   We ran the model 1 time only, i.e. 1 replication.
   This is not statistically correct. Since, we introduced
    variability in the model
   We have to make the output “statistically correct”
    and we need to be confident about the output
    values.
   This can be done by running the simulation model
    several times (replications), then take the average of
    these replications and build a confidence interval
    around the mean.
   The simulation output then will include the average,
    halfwidth, min., and max. Average ± halfwidth gives
    the confidence interval.
Simulation Output (Distributions, 30
replications)
I have output! Then what?
   Look at the output, analyze them, brainstorm
   Identify possible reasons, e.g. under staffing
   Identify possible alternative solutions, e.g. increase
    number of employees
   Perform what-if analysis of the possible alternatives
    in your laboratory (simulation model)
   Compare and select best alternative
   In the claims department example:
       Analyze: Queues are building
       Possible reason: Department under staffed
       Possible solution: Increase staffing level
       What-if more employees added: next slide
Simulation Output (Distributions, 30
replications, increase staffing level)




   The Cycle time decreases as number of employees/process increases
   Claims to be processes wait time decreases as number of
    employees/process increases
   The best alternative is (2, 2, 2), i.e. assigning 2 employees for each
    process
    Simulation Output (Cont.)




    Number in queue and wait time in queue decreases as number of
     employees/process increases
    The best alternative is (2, 2, 2), i.e. assigning 2 employees for each
     process
Simulation Modeling Process
                      Problem definition     Problem and
     Real System
                                              Objectives

                                                    Model scope and
                                                    level of details


                                           Conceptual model
               More runs/scenarios

                                                    Modeling &
                                                    Data collection


   Conclusions and     Running and         Simulation Model
    implementation     analyzing the
                          model
    Simulation Modeling Process
Planning the Study


     1. Defining Objectives/Problem Definition                                2. Identifying Constraints


                                                                      3. Preparing Simulation Specification
             4. Developing a schedule                                         3.1 Scope of model
                                                                              3.2 Level of details

                                 Defining the system                                            Model      Building


                                     5. Determining and CollectingPrimary Data                          6. Conceptual Model
                                                     Required                                               Development



                                             7. Determining Data Required



                                               8. Selection of data sources                             6.1. Conceptual Model
                                                                                                              Validation


                                        9. Data Collection        9.1. Data Validation


                                     10. Modeling required assumptions



                                    Converting data & assumptions to useful Form                         Model Translation



                                                                                                                                                            No


                                                                                                                                               Validated?                                                 Verified?
                                                                                                                                   No                                           Yes                                        No



                                                                                                                                                                           Experimental Design
                                                                                                                                   “As is”
                                                                                                                                   model

                                                                                                                                                                  Running & Analyzing of Output
                                                                                                                      Scenario 1


                                                                                                                      Scenario 2


                                                                                                                      Scenario 3                                             MoreRuns?
                                                                                                                                                     Yes                  “What if” analysis        Yes
                                                                                                                                                                         DifferentScenarios
                                                                                                                      Scenario n
                                                                                                                                                             No


                                                                                                                                               Documentation &                                 Implementation of best Scenario
                                                                                                                                             Reportring the results
Discrete Event Simulation

   Provides trade-off analysis
       Without DES analysis, process design is a “Black
        Box”
   Provides approximate answers to exact
    problems
       Better than exact answers to approximate
        problems
   Usually get random output
Advantages and Disadvantages of
Simulation Modeling
   Advantages:
       Flexibility to model things as they are (even if
        messy)
       Allows for uncertainty, non-stationarity in modeling
   Disadvantages:
       Don’t get simple closed-form formulas
       Don’t get exact answers, only estimates
Is Simulation that Simple?
   NO
   The case demonstrated is a very simple
    example.
   The complexity of simulation models
    increases with the complexity of the problem,
    scope of the problem, and the level of details
   simulation modeling solutions is applied for
    problems with varying degrees of complexity
Real World Simulation
Applications
Orlando International Airport (OIA)
   Objectives of the simulation study
       Capacity analysis of the key passenger
        processing components within the North Terminal
        Complex
       Determine the various bottlenecks and problems
        that would impede the processing of additional
        passengers per year.
       Detailed analysis of agent and electronic ticketing
       Detailed analysis of security check points
       Develop a GUI tool for the simulation model to
        enable the airport authority to use the model
        without prior simulation knowledge and to
        conduct unlimited “What if” analysis.
Data Collection

   Flight schedules
   Passengers arrival rates and behavior
   Agent Ticketing time
   Electronic ticketing time
   Security check time
   Vertical and Horizontal transports flow time
   Facilities usage time
   Proportions of various events
Data sources

   Time and motion study
   Questionnaires
   Airlines
   Airport authority
Data Analysis/Input modeling
   Statistical analysis of data using statistical
    analysis software e.g. Minitab
       Test of hypothesis
       Two sample t-test
       ANOVA …etc.
   For example, statistical analysis of the
    ticketing time data collected to answer the
    question:
       is the passenger grouping significant?
Data Analysis/Input modeling




  Grouping is significant
Airport Model
                       GUI



     Excel
                       Arena
Flight schedule
                  (Airport model)
  Seat Count
Airport Model
Model Output
Time in system
      Average and standard deviation of time in system

Ticketing time
      Average and standard deviation of Ticketing time
      Average and standard deviation of E-ticketing time

Waiting Time
      Average and standard deviation of waiting time in queue
      Maximum waiting time in queue

Number waiting in queues
      Average and standard deviation of number waiting in queue
      Maximum number waiting in queue

Passengers Count

Airport Resources utilization
OIA simulation model
GUI
   An easy to use graphical user interface was
    developed and integrated with the simulation
    model and Excel sheets.
   The graphical user interface is used to:
        Input model data and parameters
        Populate/load the simulation model
        Run the simulation model
        Obtain and customize model output
        On-line help
Model Validation
   The following approaches were used to
    validate the model:
       Regular interaction with airport SME to validate
        assumptions and results. The model results were
        compared to the actual system by running the
        model using June data and comparing the results
        obtained to the results visually observed within the
        real system.
       Ran numerous test scenarios

				
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