Scribd
Upload
100 views2 pages

Monte Carlo Simulation History

Monte Carlo simulations model processes with random variables by repeatedly sampling random inputs to determine probability distributions of outcomes. They were first developed by mathematicians Stanislaw Ulam and John Von Neumann to study games of chance. A Monte Carlo simulation assigns random values to uncertain variables, runs the model, and averages the results to estimate outcomes when elements exhibit probabilistic behavior. The basic steps are to establish probability distributions for inputs, build cumulative distributions, define random number intervals, generate random numbers, and run simulation trials.

Uploaded by

Abdur Rahim
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
100 views2 pages

Monte Carlo Simulation History

Monte Carlo simulations model processes with random variables by repeatedly sampling random inputs to determine probability distributions of outcomes. They were first developed by mathematicians Stanislaw Ulam and John Von Neumann to study games of chance. A Monte Carlo simulation assigns random values to uncertain variables, runs the model, and averages the results to estimate outcomes when elements exhibit probabilistic behavior. The basic steps are to establish probability distributions for inputs, build cumulative distributions, define random number intervals, generate random numbers, and run simulation trials.

Uploaded by

Abdur Rahim
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 2

Monte Carlo Simulation

Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot
easily be predicted due to the intervention of random variables. It is a technique used to understand the
impact of risk and uncertainty in prediction and forecasting models.

A Monte Carlo simulation can be used to tackle a range of problems in virtually every field such as
finance, engineering, supply chain, and science. It is also referred to as a multiple probability simulation.

Monte Carlo Simulation History


Monte Carlo simulations are named after the popular gambling destination in Monaco, since chance and
random outcomes are central to the modeling technique, much as they are to games like roulette, dice, and
slot machines.

The technique was first developed by Stanislaw Ulam, a mathematician who worked on the Manhattan
Project. After the war, while recovering from brain surgery, Ulam entertained himself by playing
countless games of solitaire. He became interested in plotting the outcome of each of these games in order
to observe their distribution and determine the probability of winning. After he shared his idea with John
Von Neumann, the two collaborated to develop the Monte Carlo simulation.

Monte Carlo Simulation Method


The basis of a Monte Carlo simulation is that the probability of varying outcomes cannot be determined
because of random variable interference. Therefore, a Monte Carlo simulation focuses on constantly
repeating random samples to achieve certain results.

A Monte Carlo simulation takes the variable that has uncertainty and assigns it a random value. The
model is then run and a result is provided. This process is repeated again and again while assigning the
variable in question with many different values. Once the simulation is complete, the results are averaged
together to provide an estimate.

When a system contains elements that exhibit chance in their behavior, the Monte Carlo method of
simulation can be applied.
The basic idea in Monte Carlo simulation is to generate values for the variables making up the model
being studied. There are a lot of variables in real-world systems that are probabilistic in nature and that
we might want to simulate. A few examples of these variables follow
1. Inventory demand on a daily or weekly basis
2. Lead time for inventory orders to arrive
3. Times between machine breakdowns
4. Times between arrivals at a service facility
5. Service times 6. Times to complete project activities
7. Number of employees absent from work each day
Some of these variables, such as the daily demand and the number of employees absent, are discrete and
must be integer valued. For example, the daily demand can be 0, 1, 2, 3, and so forth. But daily demand
cannot be 4.7362 or any other no integer value. Other variables, such as those related to time, are
continuous and are not required to be integers because time can be any value. When selecting a method to
generate values for the random variable, this characteristic of the random variable should be considered.
Examples of both will be given in the following sections. The basis of Monte Carlo simulation is
experimentation on the chance (or probabilistic) elements through random sampling. The technique
breaks down into five simple steps.

Five Steps of Monte Carlo Simulation


1. Establishing probability distributions for important input variables
2. Building a cumulative probability distribution for each variable in step 1
3. Establishing an interval of random numbers for each variable
4. Generating random numbers
5. Simulating a series of trials

You might also like