ME-ESE-13
LECTURE I & II: Introduction to
modeling, simulation, and
optimization
Dr. Tayab Din Memon
Department of Electronic Engineering, MUET
Outline
• System and System Types
• Natural Vs. Artificial
• Open loop and Closed loop
• Static Vs. Dynamic
• Models and Model Types
• Physical Model
• Mathematical Model
• Deterministic vs. stochastic models
• Simulation
•
•
•
•
What is Simulation
Reasons for Simulation
Phases and Steps of Simulation
Develop Simulation Model
2
Reference Books
• Any suitable book may be referred
• Recommended Books for this course are:
1. Richard S. Muller and Theodore I. Kamins “Device
Electronics for Integrated Circuits”
2. Christopher M. Snowden “ Introduction to Semiconductor
Device Modeling”.
3
Systems
• What is System
• A system is a set of components which are related by some form of
interaction and which act together to achieve some objective or
purpose
• Components are the individual parts or elements that collectively make up
the system
• Relationships are the cause-effect dependencies between components
• Objective is the desired state or outcome which the system is attempting to
achieve
4
A Daily life System Example
• Collectors
• Capture sun’s thermal energy
• Storage tank
• Pump
• Move the water through the
tank
• Booster element
• Heat water
• Relief valve
• Cold water inlet
• Hot water outlet
Solar-Heated Water System
5
Systems
• Natural vs. Artificial Systems
• A natural system exists as a result of processes occurring in the natural
world (e.g. river, universe)
• An artificial system owes its origin to human activity (e.g. space
shuttle, automobile)
• Find-out few more differences between Natural and Artificial System
• Static vs. Dynamic Systems
• A static system has structure but no associated activity (e.g. bridge,
building, furniture, dishes and etc )
• A dynamic system involves time-varying behavior (e.g. machine, U.S.
economy, entertainment equipment (radios, televisions, tape
recorders, etc.)
• Find-out few more differences between Static and Dynamic Systems
6
Systems
• Open-Loop vs. Closed-Loop systems
• Inputs
• Variables that influence the behavior of the system
• e.g. wheel, accelerator, and brake of a car
• Outputs
• Variables that are determined by the system and may influence the
surrounding environment
• e.g. direction and speed of a car
• An open-loop system cannot control or adjust its own performance
• e.g. watch, car
• A closed-loop system controls and adjusts its own performance in
response to outputs generated by the system through feedback
• e.g. watch with owner, car with driver
• Feedback is the system function that obtains data on system
performance (outputs), compares the actual performance to the desired
performance (a standard or criterion), and determines the corrective
action necessary
7
System
Controller
Input
Output
Open-Loop System
Desired Reference
or Input
Error
+ Signal
-
System
Controller
Output
Feedback
Closed-Loop System
8
Models
• What is Model
• A model of a system is a representation of the construction and
working of the system
• Similar to but simpler than the system it represents
• Close approximation to the real system and incorporate most of its salient
features
• Should not be so complex that it is hard to understand or experiment with
it
• Physical Model
• A physical object that mimics some properties of a real system
• e.g. During design of buildings, it is common to construct small physical
models with the same shape and appearance as the real buildings to be
studied
• Through prototyping process
• Prototyping is the process of quickly putting together a working model (a
prototype) in order to test various aspects of a design, illustrate ideas or
features and gather early user feedback
9
Models
• Mathematical Model
• A description of a system where the relationship between variables of
the system are expressed in a mathematical form
• e.g. Ohm's law describes the relationship between current and voltage for
a resistor; Hooke's Law gives the relationship between the force applied to
an unstretched spring and the amount the spring is stretched when the
force is applied, etc.
• Through virtual prototyping
• Virtual prototyping is a technique in the process of product development.
It involves using computer-aided design (CAD) and computer-aided
engineering (CAE) software to validate a design before committing to
making a physical prototype [source Wikipedia].
10
Mathematical Models (Cont…)
• Deterministic vs. stochastic models
• In deterministic models, the input and output variables are not
subject to random fluctuations, so that the system is at any time
entirely defined by the initial conditions chosen
• e.g. the return on a 5-year investment with an annual interest rate of 7%,
compounded monthly
• In stochastic models, at least one of the input or output variables is
probabilistic or involves randomness
• e.g. the number of machines that are needed to make certain parts based
on the probability of machine failure
11
Fspring
Fspring
spring constant The amount spring
is stretched
FSpring = -k∙x
x= -FSpring/k
Hooke’s Law
12
Simulation
• What is Simulation
• A simulation of a system is the operation of a model of the system, as
an imitation of the real system
• A tool to evaluate the performance of a system, existing or proposed,
under different configurations of interest and over a long period of
time
• e.g. a simulation of an industrial process to learn about its behavior under
different operating conditions in order to improve the process
• Reasons for Simulation
• Experiments on real systems are too expensive, too dangerous, or the
system to be investigated does not yet exist
• e.g. Investigating ship durability by building ships and letting them collide
is a very expensive method of gaining information; training nuclear plant
operators in handling dangerous situations by letting the nuclear reactor
enter hazardous states is not advisable
13
Simulation
• Reasons for Simulation (Cont.)
• The time scale of the dynamics of the system is not compatible with
that of the experimenter
• e.g. It takes millions of years to observe small changes in the
development of the universe, whereas similar changes can be quickly
observed in a computer simulation of the universe
• Easy manipulation of parameters of models (even outside the
feasible range of a particular physical system)
• e.g. The mass of a body in a computer-based simulation model can be
increased from 40 to 500 kg at a keystroke, whereas this change might
be hard to realize in the physical system
• Suppression of disturbances
• Allow isolating particular effects and gaining a better understanding of
effects of particular interest as a result
• e.g. simulation of free-fall objects ignores the effect of air resistance
14
Simulation
• Dangers of Simulation
• Fall in love with a model
• Become too enthusiastic about a model and forget about the
experimental frame
• e.g. Hooke’s law applies only if the spring is not stretched beyond its
elastic limit
• Force reality into the constraints of a model
• e.g. Shaping of our societies after fashionable economic theories that
have a simplified view of reality and ignoring many other important
aspects of human behavior, society, and nature
• Forget the model’s level of accuracy
• All models have simplifying assumptions
• e.g. Free-fall motion is a simplified model (assuming air resistance is
negligible)
15
Phases and Steps of Simulation
• Phase 1. Develop Simulation Model
•
•
•
•
•
•
Step 1. Identify the problem
Step 2. Formulate the problem
Step 3. Collect and process real system data
Step 4. Formulate and develop a model
Step 5. Validate the model
Step 6. Document model for future use
• Phase 2. Design and Conduct Simulation Experiment
• A test or series of tests in which meaningful changes are made to the
input variables of a simulation model so that we may observe and
identify the reasons for changes in the performance measures
• Step 7. Select appropriate experimental design
• Step 8. Establish experimental conditions for runs
• Step 9. Perform simulation runs
16
Simulation
• Phase 3. Perform Simulation Analysis
• Step 10. Analyze data and present results
• Step 11. Recommend further courses of actions
17
Develop Simulation Model
• Step 1. Identify Problem
• Enumerate problems with an existing system
• Produce requirements for a proposed system
• Step 2. Formulate Problem
• Define overall objectives of the study and specific issues to be
addressed
• Define performance measures
• Quantitative criteria on the basis of which different system configurations
will be evaluated and compared
• Develop a set of working assumptions that will form the basis for
model development
• Model boundary and scope (width of model)
• Determines what is in the model and what is out
• Level of detail (depth of model)
• Specifies how in-depth one component or entity is modeled
• Determined by the questions being asked and data availability
• Decide the time frame of the study
• Used for one-time or over a period of time on a regular basis
18
Develop Simulation Model
• Step 3. Collect and Process Real System Data
• Collect data on system specifications, input variables, performance of
the existing system, etc.
• Identify sources of randomness (stochastic input variables) in the
system
• Select an appropriate input probability distribution for each stochastic
input variable and estimate corresponding parameters
• Standard distributions (e.g. normal, exponential, etc.)
• Empirical distributions
• Software packages for distribution fitting (e.g. @Risk, Arena, Matlab, etc.)
19
Develop Simulation Model
• Step 4. Formulate and Develop a Model
• Develop schematics and network diagrams of the system
• How do entities flow through the system
• Translate conceptual models to simulation software acceptable form
• Verify that the simulation model executes as intended
• Build the model right (low-level checking)
• Traces
• Vary input parameters over their acceptable ranges and check the output
20
Develop Simulation Model
• Step 5. Validate Model
• Check whether the model satisfies or fits the intended usage of system
(high-level checking)
• Build the right model
• Compare the model's performance under known conditions with the
performance of the real system
• Perform statistical inference tests and get the model examined by
system experts
• Assess the confidence that the end user places on the model and
address problems if any
• Step 6. Document Model for Future Use
• Objectives, assumptions, inputs, outputs, etc.
21
Design and Conduct Simulation
Experiment
• Step 7. Select Appropriate Experimental Design
• Performance measures
• Input parameters to be varied
• Ranges and legitimate combinations
• Document experiment design
• Step 8. Establish Experimental Conditions for Runs
• Whether the system is stationary (performance measure does not
change over time) or non-stationary (performance measure changes
over time)
• Whether a terminating or a non-terminating simulation run is
appropriate
• Starting condition
• Length of warm-up period
• Model run length
• Number of statistical replications
• Step 9. Perform Simulation Runs
22
Simulation Analysis
• Step 10. Analyze Data and Present Results
• Statistics of the performance measure for each configuration of the
model
• Mean, standard deviation, range, confidence intervals, etc.
• Graphical displays of output data
• Histograms, scatterplot, etc.
• Document results and conclusions
• Step 11. Recommend Further Courses of Actions
• Other performance measures
• Further experiments to increase the precision and reduce the bias of
estimators
• Sensitivity analysis
• How sensitive the behavior of the model is to changes of model
parameters
• etc.
23
Model Development:
A case study
LECTURE – II
An Example of Model Building
(continued)
• You are the owner of a new take-out restaurant, McBurgers,
currently under construction
• You want to determine the proper number of checkout stations
needed
• You decide to build a model of McBurgers to determine the optimal
number of servers
25
• Problem
Figure 12.3
System to Be Modeled
26
An Example of Model Building
(continued)
• A new customer arriving
• An existing customer departing after receiving food and paying
• Next: Develop an algorithm for each event
• Should describe exactly what happens to the system when this event
occurs
27
• First: Identify the events that can change the system
Figure 12.4
Algorithm for New Customer Arrival
28
An Example of Model Building
(continued)
• The algorithm for the new customer arrival event
uses a statistical distribution (Figure 12.5) to
determine the time required to service the
customer
• Can model the statistical distribution of customer
service time using the algorithm in Figure 12.6
29
Figure 12.5
Statistical Distribution of Customer Service Time
30
Figure 12.6
Algorithm for Generating Random Numbers That Follow the
Distribution Given in Figure 12.5
31
Figure 12.7
Algorithm for Customer Departure Event
32
An Example of Model Building
(continued)
• Must initialize parameters to the model
• Model must collect data that accurately measures
performance of the McBurgers restaurant
33
An Example of Model Building
(continued)
• When simulation is ready, the computer will
• Run the simulation
• Process all M customers
• Print out the results
34
Figure 12.8
The Main Algorithm of Our Simulation Model
35
Running the Model and
Visualizing Results
• Scientific visualization
• Visualizing data in a way that highlights its important characteristics
and simplifies its interpretation
• An important part of computational modeling
• Different from computer graphics
36
Running the Model and
Visualizing Results (continued)
• Scientific visualization is concerned with
• Data extraction: Determine which data values are important to
display and which are not
• Data manipulation: Convert the data to other forms or to different
units to enhance display
37
Running the Model and
Visualizing Results (continued)
• Output of a computer model can be represented
visually using
• A two-dimensional graph
• A three-dimensional image
• Visual representation of data helps identify
important features of the model’s output
38
Figure 12.9
Using a Two-Dimensional Graph to Display Output
39
Figure 12.10: Using a Two-Dimensional Graph to Display and
Compare Two Data Values
40
Figure 12.11
Three-Dimensional Image of a Region of the Earth’s Surface
41
42
Figure 12.12
Three-Dimensional Model of a Methyl Nitrite Molecule
Figure 12.13
Visualization of Gas Dispersion
43
Running the Model and
Visualizing Results (continued)
• Image animation
44
• One of the most powerful and useful forms of visualization
• Shows how model’s output changes over time
• Created using many images, each showing system state at a slightly
later point in time
Figure 12.14
Use of Animation to Model Ozone Layers in the Atmosphere
45
CASE STUDY – II
STEP WISE
A machine shop contains two drills, one straightener, and one finishing
operator. Type 1 parts require drilling, straightening, and finishing in sequence.
Type 2 parts require only drilling and finishing. The frequency of arrival and
the time to be routed to the drilling area are deterministic for both types of
parts.
Straightener
Drill #1
Drill #2
Finishing
Operator
Legend:
Type 1 parts
Type 2 parts
47
Step 1. Identify the problem
• Assess utilization of drills, straightener, and finishing operator
• The following modification to the original system is of interest: the frequency of arrival
of both parts is exponential with the same respective means as in the original system
Step 2. Formulate the problem
Objectives
• Obtain the utilization of drills, straightener, and finishing operator for the system
• Assess the modification
Performance measure
• Utilization of operations (the fraction of time the server is busy, i.e. busy time divided
by the total time)
Assumptions
• Two drills are identical
• There is no material handling time between the three operations
• Parts are processed on a first-come-first-serve basis
• Parts wait in a queue till one of the two drilling machines becomes available
48
Step 3. Collect and process real system data
• A type 1 part arrives every 30 min.
• A type 2 part arrives every 20 min.
• It takes 2 min. and 10 min. to route a type 1 part and a type 2 part to the drilling area,
respectively
• Drilling time is normally distributed with mean 10 min. and standard deviation 1 min.
• Straightening time is exponentially distributed with a mean of 15 min.
• Finishing requires 5 min. per part
Step 4. Formulate and develop a model
• A model of the system and the modification are developed using a simulation package
• A trace verifies that the parts flowed through the job shop as expected
Step 5. Validate the model
• The model of the original system is run for a sufficiently long period, and its utilization
performance measures are judged to be reasonable by the machine shop operators
Step 6. Document model for future use
• The models of the original system and the modification are documented as thoroughly as
possible
49
Step 7. Select appropriate experimental design
• Performance measures are the utilization of operations
• Vary input parameters: operating times for drilling, straightening, and arrival time of
parts (in modification)
• Document experiment design for the models of the original and modified systems
Step 8. Establish experimental conditions for runs
• The system is non-stationary
• There is no part in the machine shop initially
• 1000 min. warm-up period
• Each model is run three times for 4000 min.
Step 9. Perform simulation runs
• Runs are performed as specified in Steps 7 and 8
50
Step 10. Interpret and present results
Utilization Statistics of Models of Original and Modified Systems (in parenthesis)
Drilling
Straightening
Finishing
Mean Run #1
0.83 (0.78)
0.51 (0.58)
0.42 (0.39)
Mean Run #2
Mean Run #3
Std. Run #1
Std. Run #2
Std. Run #3
0.82 (0.90)
0.84 (0.81)
0.69 (0.75)
0.68 (0.78)
0.69 (0.76)
0.52 (0.49)
0.42 (0.56)
0.50 (0.49)
0.50 (0.50)
0.49 (0.50)
0.41 (0.45)
0.42 (0.40)
0.49 (0.49)
0.49 (0.50)
0.49 (0.49)
• Utilization of each drill is about 80%
• Utilization of straightener is about 50%
• Utilization of finishing operator is about 40%
• Average utilization of the original and modified systems does not differ significantly
• The standard deviation of the drilling operation seems to have increased because of the
increased randomness in the modification
51
Step 11. Recommend further course of action
• Other performance measures of interest may be: throughput of parts for the system,
mean time in system for both types of parts, average and maximum queue lengths for
each operation
• Other modification of interest may be: the flow of parts to the machine shop doubles
52
Simulation Tools
• General Purpose Programming Languages
• FORTRAN, PASCAL,C/C++ JAVA, etc.
• Advantages:
• Little or no additional software cost
• Universally available (portable)
• No additional training
• Disadvantages:
• Every model starts from scratch
• Very little reusable code
• Long development cycle for each model
53
Simulation Tools
• General Simulation Languages
• Arena, Extend, GPSS, SIMSCRIPT, SIMULINK (In Matlab), etc.
• Advantages
• Standardized features in modeling
• Shorter development cycle for each model
• Very readable code
• Disadvantages
• Higher software cost (up-front)
• Additional training required
• Limited portability
54
Simulation Tools
• Special Purpose Simulation Packages
• Manufacturing (e.g. AutoMod, FACTOR/AIM, etc.), Communications network
(e.g.COMNET III, NETWORK II.5, etc.), Business (BP$IM, ProcessModel, etc.),
Health care (e.g. MedModel)
• Advantages
• Very quick development of complex models
• Short learning cycle
• little programming
• Disadvantages
• High cost of software
• Limited scope of applicability
• Limited flexibility
55
Optimization
• What is Optimization
• Its objective is to select the best possible decision for a given set of
circumstances without having to enumerate all of the possibilities
• Involves maximization or minimization as desired
• How can a large manufacturing company determine the monthly product mix at its
Indianapolis plant that maximizes corporate profitability?
• Design of civil engineering structures such as frames, foundations, bridges, towers,
chimneys and dams for the minimum cost
• Components
• Decision variables
• Variables in the model which you have control over
• Objective function
• A function (mathematical model) that quantifies the quality of a solution in an
optimization problem
• Constraints
• Conditions that a solution to an optimization problem must satisfy
• Restrict decision variables by defining relationships among them
• Find the values of the decision variables that maximize (minimize) the objective
function value, while staying within the constraints
56
Optimization
• Linear Programming
• The objective function and all constraints are linear functions (e.g. no
squared terms, trigonometric functions, ratios of variables) of the
decision variables
Example:
Maximize z = 15x1+10x2
subject to
0≤ x1 ≤2, 0 ≤ x2 ≤ 3, x1+x2 ≤4
The objective function is z = 15x1+10x2
The constraints are:
0≤ x1≤2, 0 ≤ x2 ≤ 3, x1+x2 ≤4
57
x
5 2
x1=2
4
x2=3
3
Optimal point (x1=x2=2)
2
x1+ x2 = 4
Feasible Region
1
z = 40
0
0
1
z = 10
z = 20
z = 30
2
x1
3
4
5
58
zmax = 15*2 + 10*2 = 50
Excel Solver
• A Microsoft Excel Add-In
• Go to Tools >>Add-Ins , select Solver Add-in, click OK
• Originally designed for optimization problems but also useful for root
finding and similar mathematical problems
Target cell
• The objective or goal
• Maximize, minimize or set a specific
value to the target cell
Changing cells
• Can be adjusted until the constraints in the
problem are satisfied and the cell in the Set
Target Cell box reaches its target
Constraints
59
• The restrictions placed on the changing
cells