1. System Modeling
Nur Aini Masruroh

2. Materials Basic modeling concepts
Mathematical modeling: basic concepts
Mathematical modeling: deterministic
Mathematical modeling: stochastic
Parameter estimation
Verification and validation
Uncertainty modeling
Modeling decisions
Systems dynamics
Case studies

3. References
Murthy, D.N.P, Page, N.W, and Rodin, E.Y. (1990). Mathematical Modelling, Pergamon Press, Oxford.
Ross, S.M. Stochastic Processes, 2nd ed., John Wiley and Sons, Inc., Canada
Clemen, R.T. and Reilly, T. (2001). Making Hard Decisions with Decision Tools. California: Duxbury Thomson Learning.

4. System modeling
System
Model

5. What is a system? Collection of one or more related objects
Object: physical entity with specific characteristics and attributes
Attributes  parameters and variables
Parameters: attributes intrinsic to an object
Variables: attributes needed to describe interaction between objects
Think system instead of single object!

6. System and its environment
The system studied is usually a subset of the bigger system
Depends on the goal/objective of the study
System
Variables
Environment
Interaction between system and its environment is through the common variables
Similar case for interaction between objects

7. System characterization
Open-closed system
Static-dynamic
Discrete-continues

8. Open vs closed system Closed system:
Objects within system don’t interact with other objects of the super system
Open system: vice versa
Example: demand for soft drinks
If the demand for the future only depends on the past sales  closed system
If other variables such as population changes, weather conditions, advertising are considered  open system

9. Static vs dynamic Dynamic  time dependent Example: rocket launch
Variables: position, relative velocity
Earth
Interactions between objects: theory of dynamics
Static  time independent
Example: alloy selection
Variables: coefficient of expansion for the alloy, method for production, supplier

10. Discrete vs continues time
A priori taken before analysis
Depends on the objective and the degree of detail required
Examples:
Demand of a product is usually recorded as discrete time
River pollution (variable: pollutant concentration at a certain point) is recorded in continuous basis

11. Black box vs transparent box
Black box: inner structure of the system is ignored
More interested in the interaction between system and its environment
Lack of knowledge of the inner structure
Simplify the system description
Transparent box: describe all the objects within system and their attributes (variables and parameters)
Example:
Manufacturer in the supply chain structure is considered as a black box, only supply and demand are considered as entering and leaving variables
When designing a production schedule, manufacturer should be described in detail
Need to know the inside process

12. What’s a model?
Representation of a system

13. Why we need model?
Simple
Easy to “play”
Safer to test
Low-cost

14. Uses of
modeling
Analysis
Design
Research
Control
Optimization
Experimental
design
Finance

15. The type of model will depend on
The question that is being asked (the problem objective)
The level of detail required
The resource available (time, personnel, computers, etc)

16. Why don’t we just always build a detailed model?
Models cost money
The wages of the engineer who builds the model
The cost of other resources (computers, software, company overhead)
Implication:
In modeling there is always a trade-off between time and detail

17. So, we can simplify the model considerably, but …
We lose detail and accuracy
The model becomes more limited in its application
It may no longer be adequate for the problem
We should make our assumptions very clear to anyone who
Use the model
Use the result of the model

18. How much detail do we need?
The purpose of modeling is to be able to answer questions and make decisions
Once we have enough information to make the decision, the model is adequate
The model is not reality
We can never be 100% sure that our model gives a perfect prediction of reality
We should always attempt to indicate our confidence in the result

19. Assumptions Always try to justify assumptions
With practical explanation
With quick calculation to show that the neglected effects are negligible
Only make enough assumptions to simplify the model to the level justified by the problem objectives
Too many assumptions  might assume the answer as well  guess work
NEVER assume data!!!

20. Good model? Validate and verify
Have someone else to review or check the assumptions and results
Sensitivity analysis

21. Good model? Represents the actual systems Adequate for the goal
Physical
Scale down
Pictorial
Verbal
Mathematical formulation
Simulation
Validated and verified
Adequate for the goal
Focus on significant features only

22. Since the model is not reality….
The results are only as good as the model and data used (“garbage in  garbage out”)
If the model doesn’t give a good description of reality, there is no point in optimizing a design based on it!
Fix the model first

23. First questions to ask …
Have I solved this problem before?
If so, do the same think again
Has someone else solved this problem?
Look in textbooks, do a literature search, etc
Don’t waste time and money starting from scratch if someone has already solved the problem unless you have good reason to believe their model is not good

24. If it’s a completely new problem …
Understand the system and its characteristics
Set objective
Model formulation
Validate
Analysis
Adequate? If not revise the model

25. Model classification Material or physical model
Non-material or formal model
Focus on this model!

26. Mathematical model
Symbolic representation involving an abstract mathematical model
Classification: static, dynamic, deterministic, stochastic

27. Simulation model Imitation of real world system over time
Model is run instead of solved
Can be used as analysis tools for predicting the effect of change of the existing system and as a design tool to predict the performance of the new system under varying sets of circumstances

28. Simulation is needed when …
Dealing with complex systems
System is black box, only inputs and outputs to the system can be examined
New design or policy before implementation
Can be used to verify analytic solution

29. Concluding remarks
We try to use system approach to solve the real world problem
Definition of system has been presented
Modeling concept has been discussed
Focus on formal model