System ModelingSystem Modeling

Nur Aini Masruroh

LOGOMaterials

Basic modeling conceptsMathematical modeling: basic

concepts Mathematical modeling: deterministic Mathematical modeling: stochasticParameter estimationVerification and validationUncertainty modeling Modeling decisionsSystems dynamicsCase studies

LOGOReferences

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.

LOGO

System modeling

System Model

LOGOWhat 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!

LOGOSystem and its environment

The system studied is usually a subset of the bigger system Depends on the goal/objective of the study

System Variables Variables

Environment

Interaction between system and its environment is through the common variables

Similar case for interaction between objects

LOGOSystem characterization

Open-closed system Static-dynamic Discrete-continues

LOGOOpen 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

LOGOStatic vs dynamic

Dynamic time dependent Example: rocket launch

• Rocket– 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

LOGODiscrete 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

LOGOBlack 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

LOGOWhat’s a model?

Representation of a system

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tosubject

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LOGOWhy we need model?

Simple Easy to “play”

Safer to test Low-cost

LOGO

Uses of modeling

Analysis

Design

Research

Control

Optimization

Experimental design

Finance

LOGOThe 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)

LOGOWhy 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

LOGOSo, 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

LOGOHow 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

LOGOAssumptions

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!!!

LOGOGood model?

Validate and verify Have someone else to review or check the

assumptions and results Sensitivity analysis

LOGOGood model?

Represents the actual systems Physical

• Scale down Pictorial Verbal Mathematical formulation Simulation

• Validated and verified

Adequate for the goal Focus on significant features only

LOGOSince 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

LOGOFirst 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

LOGOIf it’s a completely new problem …

Understand the system and its characteristics

Set objective Model formulation Validate Analysis

Adequate? If not revise the model

LOGOModel classification

Material or physical model

Non-material or formal model Focus on this model!

LOGOMathematical model

Symbolic representation involving an abstract mathematical model

Classification: static, dynamic, deterministic, stochastic

LOGOSimulation 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

LOGOSimulation 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

LOGOConcluding 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