ETM 607 Modeling and Simulation

What is Modeling?

What is Simulation?

How do you evaluate a math model?

How do you evaluate a simulation model?

ETM 607 Modeling and SimulationMy History with Simulation• 1983-1984: courses on GPSS and Slam (Univ. of Fla.)• 1985: additional Siman courses (NC State)• 1986-1989: Ford Motor company operations research analyst, primarily responsible for simulation models

- Essex engine hot test loop- Thunderbird body decking line- Double eagle steel electro galvanizing plant- Nashville glass plant float line simulation

• Consulting 2003-current:- YKK - Marine depot (Albany,GA)- C130 Depot Maintenance- RCAN - Resource Constrained Activity Network

• Research: Scheduling Radar Warning Receivers

ETM 607 Modeling and Simulation

What is the expected value from the roll of two dice?

1) Develop a simple math model and solve.

2) Solve same model using a simulation approach as a comparison.

ETM 607 Modeling and Simulation

What is the expected value from the roll of two dice?

1)Develop a simple math model and solve.

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ETM 607 Modeling and Simulation

Class Exercise:

Develop math model on board.

Then perform simulation exercise:

1.Have each team role die 10 times and record average.2.Show averages of each team on board.3.Find average of averages.4.Compare to math model.

ETM 607 Modeling and Simulation

Considering the simulation of the average roll of two dice:

When should you stop performing experiments?

How would you use a computer to perform this simulation? (e.g. how do you obtain the random numbers 2 through 12?)

Others…

ETM 607 Modeling and Simulation

What is the major difference between this math model approach and the simulation approach?

• Solution if found by solving/resolving the math model, and by running the simulation model • Accuracy, one is exact, the other estimated• Time to obtain solution

What are common features between this math model and the simulation?

• Same goal (expected value)

Definition - "simplified representation of something real" www.dictionary.com -

Modeling

1. A small object, usually built to scale, that represents in detail another, often larger object.

2. a. A preliminary work or construction that serves as a plan from which a final product is to be made: a clay model ready for casting.

b. Such a work or construction used in testing or perfecting a final product: a test model of a solar-powered vehicle.

3. A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics

Why Model? 

- reduce cost- save time- too much complexity- avoid disrupting production system

Modeling

Types of models 

- Math programming (Linear, Integer, non-Linear)- Network- Queueing- MDP (Markov Decision Processes)- Regression- Forecasting- Inventory- Dynamic programming- Probability- Simulation

 

Modeling

Principles of Modeling (Ravindran, Phillips, Solberg)

1. Do not build a complicated model when a simple one will suffice.

2. Beware of modeling the problem to fit the technique.

3. The deduction phase of modeling must be conducted rigorously (conclusions one draws from results).

4. Models should be validated prior to implementation.

5. A model should never be taken too literally.

Principles of Modeling (Ravindran, Phillips, Solberg) cont.

6. A model should never be pressed to do, nor criticized for failing to do, that for which it was never intended.

7. Beware of overselling a model.

8. Some of the primary benefits of modeling are associated with the process of developing the model.

9. A model cannot be any better than the information going into it.

10. Models cannot replace decision makers.  

Simulation Is …• Simulation – very broad term – methods and applications to imitate or

mimic real systems, usually via computer

• Applies in many fields and industries• Broadly interpreted, computer simulation refers to methods for

studying a wide variety of models of systems– Numerically evaluate on a computer– Use software to imitate the system’s operations and characteristics,

often over time• Can be used to study simple models but should not use it if an

analytical solution is available• Real power of simulation is in studying complex models• Simulation can tolerate complex models since we don’t even aspire to

an analytical solution

Basic Simulation Terminology

• System – a collection of entities that act and interact toward the accomplishment of some logical end.

• State – the state of a system is the collection of variables necessary to describe the status of the system at any given time.

• Discrete – a discrete system is one in which the state variables change only at discrete or countable points in time.

• Continuous– a continuous system is one in which the state variables change continuously over time.

Basic Simulation Terminology

• Static – a static simulation model is a representation of a system at a particular point in time.

• Dynamic – a dynamic simulation is a representation of a system as it evolves over time.

• Deterministic – a deterministic simulation model is one that contains no random variables. All variables are known with certainty, or in other words, no probability is associated with them.

• Stochastic– a stochastic simulation model contains random variables (variables containing probability distributions).

How would you describe the die rolling simulation?

Different Kinds of Simulation

• Most operational models:– Dynamic, Discrete-change, Stochastic

• However, we will start with static models referred to as:- Monte Carlo Simulation, or- The Monte Carlo Method

ETM 607

Class Break

Monte Carlo Method / Simulations

Monte Carlo methods are a class of computational algorithms that rely on repeated random sampling to compute their results. Monte Carlo methods are often used when simulating physical and mathematical systems. Because of their reliance on repeated computation of random or pseudo-random numbers, these methods are most suited to calculation by a computer and tend to be used when it is infeasible or impossible to compute an exact result with a deterministic algorithm.[1]

From Wikipedia, the free encyclopedia

Monte Carlo Method / Simulations

Monte Carlo simulation methods are especially useful in studying systems with a large number of coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). More broadly, Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business.

• Example - Finding the expected time to detect enemy threats for Radar Warning Receivers.

From Wikipedia, the free encyclopedia

Monte Carlo Method / Simulations

These methods are also widely used in mathematics: a classic use is for the evaluation of definite integrals, particularly multidimensional integrals with complicated boundary conditions. It is a widely successful method in risk analysis when compared with alternative methods or human intuition. When Monte Carlo simulations have been applied in space exploration and oil exploration, actual observations of failures, cost overruns and schedule overruns are routinely better predicted by the simulations than by human intuition or alternative "soft" methods.[2]

The term "Monte Carlo method" was coined in the 1940s by physicists working on nuclear weapon projects in the Los Alamos National Laboratory.[3]

From Wikipedia, the free encyclopedia

Monte Carlo Method / Simulations

There is no single Monte Carlo method; instead, the term describes a large and widely-used class of approaches. However, these approaches tend to follow a particular pattern:

1.Define a domain of possible inputs. 2.Generate inputs randomly from the domain using a certain specified probability distribution. 3.Perform a deterministic computation using the inputs. 4.Aggregate the results of the individual computations into the final result.

From Wikipedia, the free encyclopedia

Monte Carlo Method / Simulations

For example, the value of π can be approximated using a Monte Carlo method:1.Draw a square on the ground, then inscribe a circle within it. From plane geometry, the ratio of the area of an inscribed circle to that of the surrounding square is π / 4. 2.Uniformly scatter some objects of uniform size throughout the square. For example, grains of rice or sand. 3.Since the two areas are in the ratio π / 4, the objects should fall in the areas in approximately the same ratio. Thus, counting the number of objects in the circle and dividing by the total number of objects in the square will yield an approximation for π / 4. Multiplying the result by 4 will then yield an approximation for π itself.

From Wikipedia, the free encyclopedia

Monte Carlo Simulations

• Static• Independent Runs• Tend to Determine Expected Values

Winston Handouts

Monte Carlo Simulations Class Exercise How would you find the expected daily production for the following?:

Two machines are required to produce a product. When both machines are running the total production rate is 25/hour. Uptime of each machine has distribution shown in Fig 1. When machine is down, repair takes on distribution show in Fig. 2. If one machine is down, the other can still produce parts at a degraded rate of 10/hour. Assume 16 hour day.

1. Describe a simulation model.2. Describe a math model.

Fig.1 – Machine Reliability Distribution

Fig.2– Repair Time Distribution

ETM 607

Monte Carlo Application

RWR Scheduling

Power Point Presentation