1. Chapter 1 – What Is Simulation?
OUTLINE
Basic Concepts in Modeling and Simulation
Building Simulation Models
Verification and Validation
Designing Experiments
Output Analysis
Applications of Simulation Modeling
Simulation with Arena, 3rd ed.
Chapter 1 – What Is Simulation?

2. SIMULATION
Imitate the operations of a facility or process, usually via computer
What’s being simulated is the system
To study system, often make assumptions/approximations, both logical and mathematical, about how it works
These assumptions form a model of the system
If model structure is simple enough, could use mathematical methods to get exact information on questions of interest — analytical solution
Simulation Modeling and Analysis – Chapter 1 – Basic Simulation Modeling

3. Ways to Study Systems Simulation is “method of last resort?” Maybe …
But with simulation there’s no need (or less need) to “look where the light is”

4. Work With the System?
Advantage — unquestionably looking at the right thing
But it’s often impossible to do so in reality with the actual system
System doesn’t exist
Would be disruptive, expensive, or dangerous

5. Computer Simulation
Methods and applications to imitate or mimic real systems usually via computer.
No longer regarded as the approach of “last resort”.
Today, it is viewed as an indispensable problem-solving methodology for engineers, designers, and managers.
Can be used to study simple models but should not use it if an analytical solution is available
Real power of simulation is in studying complex models

6. Applications of Simulation
Applies in many fields and industries
Manufacturing facility
Bank operation
Airport operations (passengers, security, planes, crews, baggage)
Transportation/logistics/distribution operation
Hospital facilities (emergency room, operating room, admissions)
Computer network
Freeway system
Business process (insurance office)
Criminal justice system
Chemical plant
Fast-food restaurant
Supermarket
Theme park
Emergency-response system

7. Advantages of Simulation
Flexibility to model things as they are (even if messy and complicated) - Allows uncertainty, nonstationarity in modeling
New policies, operating procedures can be explored without disrupting ongoing operation of the real system.
New hardware designs, physical layouts, transportation systems can be tested without committing resources for their acquisition.
Time can be compressed or expanded to allow for a speed-up or slow-down of the phenomenon
Advances in simulation software, computing and information technology are all increasing popularity of simulation

8. The Bad News Don’t get exact answers, only approximations, estimates
Model building requires special training.
Simulation modeling and analysis can be time consuming and expensive.
Simulation results can be difficult to interpret.
Get random output (RIRO) from stochastic simulations
Statistical design, analysis of simulation experiments

9. SIMULATION vs. OPTIMIZATION
In an optimization model, the values of the decision variables are outputs that will maximize (or minimize) the value of the objective function.
In a simulation model, the values of the decision variables (controllable ones) are inputs. The model evaluates the objective function for a particular set of values and provides various performance measures. RIRO (Random input Random Output)

10. Simulation Model Taxonomy
DDC: Newton’s cooling law
SDC: Pizza oven with random opens/closes

11. The System: A Simple Processing System
Arriving
Blank Parts
Departing
Finished Parts
Machine
(Server)
Queue (FIFO)
Part in Service 4 5 6 7
General intent:
Estimate expected production
Waiting time in queue, queue length, proportion of time machine is busy
Time units
Can use different units in different places … must declare
Be careful to check the units when specifying inputs
Declare base time units for internal calculations, outputs
Be reasonable (interpretation, roundoff error)
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

12. Model Specifics Initially (time 0) empty and idle
Base time units: minutes
Input data (assume given for now …), in minutes:
Part Number Arrival Time Interarrival Time Service Time
Stop when 20 minutes of (simulated) time have passed
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

13. Simulation by Hand: Setup
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

14. Simulation by Hand: t = 0.00, Initialize
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

15. Simulation by Hand: t = 0.00, Arrival of Part 1
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

16. Simulation by Hand: t = 1.73, Arrival of Part 2
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

17. Simulation by Hand: t = 2.90, Departure of Part 1
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

18. Simulation by Hand: t = 3.08, Arrival of Part 32
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

19. Simulation by Hand: t = 3.79, Arrival of Part 42
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

20. Simulation by Hand: t = 4.41, Arrival of Part 53 2
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

21. Simulation by Hand: t = 4.66, Departure of Part 25 4 3
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

22. Simulation by Hand: t = 12.57, Departure of Part 4
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

23. Simulation by Hand: t = 17.03, Departure of Part 5
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

24. Simulation by Hand: t = 18.69, Arrival of Part 6
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

25. Simulation by Hand: t = 19.39, Arrival of Part 76
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

26. Simulation by Hand: t = 20.00, The End7 6
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

27. Simulation by Hand: Finishing Up
Average waiting time in queue:
Time-average number in queue:
Utilization of drill press:
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

28. Randomness in Simulation
The above was just one “replication” — a sample of size one (not worth much)
Made a total of five replications:
Confidence intervals for expected values:
In general,
For expected total production,
Note
substantial
variability
across
replications
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

29. Steps in a Simulation Study
Understand the system
Be clear about the goals
Formulate the model representation
Translate into modeling software
Verify “program”
Validate model
Design experiments
Make runs
Analyze, get insight, document results
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

30. -Knowledge of the system under investigation
A Simulation Project Requires to Put together a Complete Mix of Skills on the Team
-Knowledge of the system under investigation
-System analyst skills (model formulation)
-Model building skills (model Programming)
-Data collection skills
-Statistical skills (input data representation, experimental design, output analysis)
-Management skills (to get everyone pulling in the same direction)
Introduction 11

31. Steps in a Simulation
Project

32. Data Collection:Input Data Modeling
Input Analysis activities consist of:
data collection
data analysis
goodness-of-fit testing (Chi-Square and the Kolmogrov-Smirnov tests).
The quality of the output is no better than the quality of inputs (GIGO principle).

33. Model Translation: Choose The Appropriate Simulation Tools
Assuming Simulation is the appropriate means, three alternatives exist:
1. Build Model in a General Purpose Language
2. Build Model in a General Simulation Language
3. Use a Special Purpose Simulation Package
Introduction 14

34. Simulation Languages
ARENA, Extend, AweSim, Micro Saint, GPSS/SLX, SIMPLE++, SIMUL8 and etc.
Less flexibility
Easier to learn
More costly

35. SPECIAL PURPOSE SIMULATION PACKAGES
NETWORK II.5: Simulator for computer systems
MEDMODEL: Health Care
OPNET: Simulator for communication networks, including wireless networks
SIMFACTORY: Simulator for manufacturing operations
Advantages: Short learning cycle, No programming
Disadvantages: High Cost, Limited Flexibility
Introduction 22

36. Two Simulation Modeling Approaches
Event-Scheduling Approach
2. Process-Interaction Approach
Chapter 2 – Fundamental Simulation Concepts
Simulation with Arena, 3rd ed.

37. Steps in a Simulation
Project

38. Verfication & Validation
Real-World System
Validation
Simulation Model
(Conceptual Model)
Verification
Simulation Program
Verfication & Validation
4/17/2017

39. Calibration and Validation of Models
<Iterative process of calibrating a model>
Verification and Validation 30

40. Example
Suppose, in our current system, average order-filling time is 16.2 hours for orders received via the web. We hope to reduce this by making changes in our logistics system.
We can check the validity of our simulation model via a hypothesis test.
We can set up the following test:
H0: simulation mean fill time = H1: simulation mean fill time  16.2
4/17/2017

41. Testing
Run R replications of the simulation model, collecting the average fill time Y1,…,YR on each replication.
If the data are approximately normally distributed, then we reject H0 if
4/17/2017

42. If we accept, then the model is valid?
What can we conclude?
If we accept, then the model is valid?
No! The model and the real system are not the same; if we make R large enough, we will eventually reject.
If we reject, then the model is invalid?
No! It may be close enough for the decision we need to make; we might have accepted if R was smaller.
4/17/2017

43. Steps in a Simulation
Project

44. Experimental Design in Simulation
There is a huge amount of literature on experimental design and most of it is applicable to simulation.
Experimental design allows us to efficiently explore the relationship between inputs and outputs.
In experimental design terminology, the input parameters and structural assumptions are called factors (qualitative, quantitative, controllable, uncontrollable) and the output performance measures are called responses.

45. Experimental I/O Examples
Inputs (factors)
Outputs (responses)
Chemical reaction
Pressure
Temperature
Catalyst concentration
Yield
Growing tomatoes
Fertilizer
Soil pH
Seed hybrid
Water
Hardiness
Simulation of a
manufacturing
system
Job dispatch rule
Number of machines
Machines’ reliability
Mean downtimes
Throughput
Time in system
Utilizations
Queue sizes

46. What Outputs (Responses) to Collect?
There are typically two types of output:
Discrete-Time Output Data
Continuous-Time Output Data

47. Discrete-time Output Data
There is a natural “first” observation, “second” observation, etc.—but can only observe them when they “happen”.
If Wi = time in system for the ith part produced (for i = 1, 2, ..., N), and there are N parts produced during the simulation i 1 2 3 N Wi

48. Continuous-time Output Data
Can jump into system at any point in time (real, continuous time) and take a “snapshot” of something-there is no natural first or second observation.
If Q(t) = number of parts in a particular queue at time t between [0,T] and we run simulation for T units of simulated time

49. DIDO Vs. RIRO Simulation
Simulation Model
Inputs:
Cycle
times
Interarrival
Batch
sizes
Outputs:
Hourly
production
Machine
utilization
RIRO

50. Steps in a Simulation
Project

51. Chapter 1 – What Is Simulation?
OUTPUT ANALYSIS
Terminating (Transient) Simulations (Starts at time 0 under well-specified initial conditions)
Example: Bank opens at 8:30 am with no customers present and all tellers are available, and closes at 4:30 pm
Non-terminating (Steady-state) Simulations (Initial conditions are defined by the analyst)
Examples: assembly lines that shut down infrequently, telephone systems, hospital emergency rooms, airport
Whether a simulation is considered to be terminating or non-terminating depends on
both the objectives of the simulation study and
the nature of the system.
Simulation with Arena, 3rd ed.
Chapter 1 – What Is Simulation?

52. Analysis for Steady-State Simulations
Objective: Estimate the steady state mean
Basic question: Should you do many short runs or one long run ?????

53. Simulation with ARENA©
What is ARENA©?
Arena is a Microsoft Windows based application package for simulation modeling and analysis. It is a product of Rockwell Software, Inc.
Current version: 14.5 (2014)
ARENA’s User interface: GUI, interactive and menu driven.

55. Cellular Manufacturing
Cells 1, 2, and 4 each have a single machine, Cell 3 has 2 machines. The two machines in Cell 3 are different: the newer one can process parts in 80% of the time of the older one.
The system produces 3 parts types, each visiting a different sequence of stations.
All the process times are triangularly distributed.
We will collect statistics on resource utilization, time and number in queue, as well as cycle time (time in system, from entry to exit) by part type. Initially, we’ll run the simulation for 2000 minutes.

56. Exercise 1: Wayne International Airport
Wayne International Airport primarily serves
domestic air traffic. Occasionally, however,
a chartered plane from abroad will arrive
with passengers bound for Wayne's great amusement
parks.
Whenever an international plane
arrives at the airport the two customs
inspectors on duty set up operations to
process the passengers.

57. Exercise 1: Wayne International Airport
Incoming passengers must first have their
passports and visas checked. This is handled by
one inspector. The time required to check
a passenger's passports and visas can be
described by the following probability distribution:
Time Probability
20 seconds
40 seconds
60 seconds
80 seconds

58. Exercise 1: Wayne International Airport
After having their passports and visas checked, the passengers next proceed to the second customs official who does baggage inspections. Passengers form a single waiting line with the official inspecting baggage on a first come, first served basis. The time required for baggage inspection is described by the following probability distribution:
Time Probability
No Time
1 minute
2 minutes
3 minutes

59. Exercise 1: Wayne International Airport
A chartered plane from abroad lands at Wayne
Airport with 80 passengers. Simulate the processing
of the first 10 passengers through customs. Use the
following random numbers:
For passport control:
93, 63, 26, 16, 21, 26, 70, 55, 72, 89
For baggage inspection:
13, 08, 60, 13, 68, 40, 40, 27, 23, 64

60. Exercise 1: Wayne International Airport
Question 1
How long will it take for the first 10 passengers to clear customs?
Question 2
What is the average length of time a customer waits before having his bags inspected after he clears passport control? How is this estimate biased?

61. Exercise 1: Wayne International Airport
Answer 1: Passenger 10 clears customs after 9 minutes and 20 seconds. Answer 2: (Baggage Inspection Begins) - (Passport Control Ends) = = 120 sec. Average Wait. Time/passenger=120/10 = 12 sec/passenger This is a biased estimate because we assume that the simulation began with the system empty. Thus, the results tend to underestimate the average waiting time.

62. EXERCISE 2: Hand Simulation of Ordering Policy
XYZ company sells CD players (with speakers), which it orders from Fuji Electronics in Japan. Because of shipping and handling costs, each order must be for five CD players. Because of the time it takes to receive an order, the warehouse outlet places an order every time the present stock drops to five CD players. It costs $100 to place an order. It costs the warehouse $400 in lost sales when a customer asks for a CD player and the warehouse is out of stock. It costs $40 to keep each CD player stored in the warehouse. If a customer cannot purchase a CD player when it is requested, the customer will not wait until one comes in but will go to a competitor. The probability distributions for demand and lead time have been determined as follows:

63. EXERCISE 2: Hand Simulation of Ordering Policy
Demand per Month
Probability
.04 1
.08 2
.28 3
.40 4
.16 5
.02 6
1.00

64. EXERCISE 2: Hand Simulation of Ordering Policy
Time to Receive an Order (month)
Probability 1
.60 2
.30 3
.10
1.00

65. EXERCISE 2: Hand Simulation of Ordering Policy
The warehouse has five CD players in stock. Orders are always received at the beginning of the week. Simulate ordering and sales policy for 10 months using the following random numbers and compute the average monthly cost.
RNs (Demand): 39, 72, 37, 87, 98,99, 93, 21,97, 41
RNs (Lead Time):73,75,15, 62, 47, 69, 95, 78, 16, 25

66. Exercise 3
George Nanchoff owns a gas station. The cars arrive at the gas station and they are served by one assistant. Use the following inter-arrival time and service distribution to simulate arrival of five cars.
Using the random number sequence: 92, 44, 15, 97, 21, 80, 38, 64, 74, 08 estimate:
the average customer waiting time ,
average idle time of the assistant,
the average time a car spends in the system.
Interarrival time (in minutes)
P(X)
Service Time (in minutes)
P (X) 4
.35 2
.30 7
.25
.40 10 6
.20 20
.10 8