# Simulation

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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
   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

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
   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

   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
Simulation Modeling
   Flexibility to model things as they are (even if
messy)
   Allows for uncertainty, non-stationarity in modeling
   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
   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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