Lecture 7

When is it good to use Monte Carlo?

- Complex Problems; - No other techniques are appropriate; - Uncertainty and Probability Distributions; - Stochasticity;

Monte Carlo Steps:

- Define Problem - Define Variables (controllable vs uncontrollable) - Formulate the Model - Starting Condition - Simulate - Analysis of result and re-formulate if necessary - Take best course of action

Monte Carlo Process

- The Monte Carlo is not a type of simulation model but a technique for selecting numbers randomly from a probability distribution for use in a trial (computer run) of a simulation model - In the Monte Carlo process, values for a random variable are generated by sampling from a probability distribution

What is the purpose of the Monte Carlo Process?

- The purpose of the Monte Carlo process is to generate the random variable (i.e. demand, in our example) by sampling from the probability distribution P(x)

Artificially created random numbers must have the following characteristics:

1. The random numbers must be uniformly distributed. 2. The numerical technique for generating the numbers must be efficient. 3. The sequence of random numbers should reflect no pattern.

True or False: A small proportion of the applications of simulations are for probabilistic models

False. A large proportion of the applications of simulations are for probabilistic models

________ is not part of a Monte Carlo simulation. Analyzing results Analyzing a real problem Finding an optimal solution Evaluating the results "What if" scenarios implementations

Finding an optimal solution

True or False: Applications of simulation models reflecting continuous distributions are more common than those of models employing discrete distributions.

True

True or False: Outcomes of simulation modeling are statistical measures such as averages.

True

True or False: Random numbers generated by a mathematical process instead of a physical process are pseudorandom numbers.

True

Two Approaches to Simulations:

• Analogue simulation: replaces a physical system with an analogous physical system that is easier to manipulate (example: conditions of weightlessness were simulated using rooms filled with water, wind tunnels that simulate the conditions of flight, and treadmills that simulate automobile tire wear in a laboratory instead of on the road, etc.). • Computer mathematical simulation: when a system is replaced with a mathematical model that is analyzed with the computer. It offers a means of analyzing very complex systems that cannot be analyzed using other techniques...

Monte Carlo Attributes

• The more periods simulated, the more accurate the results. • Simulation results will not equal analytical results unless enough trials have been conducted to reach steady state. • It is often difficult to validate results of simulation - that true steady state has been reached and that simulation model truly replicates reality. • When analytical analysis is not possible, there is no analytical standard of comparison, thus making validation even more difficult.