1. Dr. Tayab Din Memon Department of Electronic Engineering, MUET
ME-ESE-13 LECTURE I & II: Introduction to modeling, simulation, and optimization
Dr. Tayab Din Memon
Department of Electronic Engineering, MUET

2. Outline System and System Types Models and Model Types Simulation
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

3. Reference Books Any suitable book may be referred
Recommended Books for this course are:
Richard S. Muller and Theodore I. Kamins “Device Electronics for Integrated Circuits”
Christopher M. Snowden “ Introduction to Semiconductor Device Modeling”.

4. 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

5. 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

6. Systems Natural vs. Artificial Systems Static vs. Dynamic 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

7. Systems Open-Loop vs. Closed-Loop systems Inputs Outputs
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

8. System
Controller
Input
Output
Open-Loop System
System
Controller
Desired Reference
or Input
Output
Feedback
Closed-Loop System - +
Error
Signal

9. Models What is Model Physical 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

10. 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].

11. 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

12. The amount spring is stretched
Fspring
The amount spring is stretched
spring constant
Fspring
FSpring = -k∙x
x= -FSpring/k
Hooke’s Law

13. Simulation What is Simulation Reasons for 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

14. 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

15. 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)

16. 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

17. Simulation Phase 3. Perform Simulation Analysis
Step 10. Analyze data and present results
Step 11. Recommend further courses of actions

18. 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

19. 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 Arena, Matlab, etc.)

20. 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

21. 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.

22. 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

23. 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.

24. Model Development: A case study
LECTURE – II

25. An Example of Model Building (continued)
Problem
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

26. Figure 12.3
System to Be Modeled

27. An Example of Model Building (continued)
First: Identify the events that can change the system
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

28. Algorithm for New Customer Arrival
Figure 12.4
Algorithm for New Customer Arrival

29. 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

30. Statistical Distribution of Customer Service Time
Figure 12.5
Statistical Distribution of Customer Service Time

31. Figure 12.6
Algorithm for Generating Random Numbers That Follow the Distribution Given in Figure 12.5

32. Algorithm for Customer Departure Event
Figure 12.7
Algorithm for Customer Departure Event

33. An Example of Model Building (continued)
Must initialize parameters to the model
Model must collect data that accurately measures performance of the McBurgers restaurant

34. An Example of Model Building (continued)
When simulation is ready, the computer will
Run the simulation
Process all M customers
Print out the results

35. The Main Algorithm of Our Simulation Model
Figure 12.8
The Main Algorithm of Our Simulation Model

36. 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

37. 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

38. 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

39. Using a Two-Dimensional Graph to Display Output
Figure 12.9
Using a Two-Dimensional Graph to Display Output

40. Figure 12.10: Using a Two-Dimensional Graph to Display and Compare Two Data Values

41. Three-Dimensional Image of a Region of the Earth’s Surface
Figure 12.11
Three-Dimensional Image of a Region of the Earth’s Surface

42. Three-Dimensional Model of a Methyl Nitrite Molecule
Figure 12.12
Three-Dimensional Model of a Methyl Nitrite Molecule

43. Visualization of Gas Dispersion
Figure 12.13
Visualization of Gas Dispersion

44. Running the Model and Visualizing Results (continued)
Image animation
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

45. Use of Animation to Model Ozone Layers in the Atmosphere
Figure 12.14
Use of Animation to Model Ozone Layers in the Atmosphere

46. CASE STUDY – II STEP WISE

47. 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
Type 1 parts
Type 2 parts
Legend:

48. 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

49. 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

50. 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

51. 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
0.82 (0.90)
0.52 (0.49)
0.41 (0.45)
Mean Run #3
0.84 (0.81)
0.42 (0.56)
0.42 (0.40)
Std. Run #1
0.69 (0.75)
0.50 (0.49)
0.49 (0.49)
Std. Run #2
0.68 (0.78)
0.50 (0.50)
0.49 (0.50)
Std. Run #3
0.69 (0.76)
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

52. 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

53. 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

54. 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

55. 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

56. Optimization What is Optimization Components
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

57. 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

58. zmax = 15*2 + 10*2 = 50 x2 x1=2 x2=3 Optimal point (x1=x2=2)
Feasible Region x1
zmax = 15*2 + 10*2 = 50

59. 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
The restrictions placed on the changing cells