System Modeling Nur Aini Masruroh

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

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.

System modeling System Model

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!

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

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

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

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

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

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

What’s a model? Representation of a system

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

Uses of modeling Analysis Design Research Control Optimization Experimental design Finance

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)

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

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

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

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!!!

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

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

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

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

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

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

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

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

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

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