PART ONE

 

1) What is Monte-Carlo Simulation?                                                                                                                                         

Monte-Carlo Simulation is an analytical method meant to imitate a real-life system. It answers “what-if” questions through deterministic analyses. Monte-Carlo Simulation randomly generates values for uncertain variables repeatedly in order to simulate a model. For variables that have a known range of values but an uncertain value for any particular time or event, Monte-Carlo Simulation is particularly useful.                                                                                                                                                                                                                                                                         

Monte-Carlo Simulation can be related to sensitivity and scenario analysis. With one-way sensitivity analysis, the most sensitive variable is at the top and variables then descend in sensitivity. This type of analysis measures the sensitivity/changes in the outcome due to changes in the input variable. This shows a sensitivity range, producing a “tornado-like” appearance. N-way sensitivity analysis makes changes in several inputs, helping with scenario evaluation. Controllable and uncontrollable variables are input into the model in order to predict certain outcomes. Sensitivity and scenario analyses are limited by the fact that probability distributions are not utilized. Monte-Carlo Simulation overcomes this obstacle by modeling uncertain variables using probability distributions.                         

                                                                                                                                               

2) How is Monte-Carlo Simulation performed?                                                                                                         

 

Monte-Carlo Simulation is performed by calculating multiple scenarios of a model by repeatedly sampling values from the probability distributions for the uncertain variables and using those values for the cell. Simply stated, a Monte-Carlo simulation allows for hypothetical values to be input into a model. These variables allow for the calculation of various outcomes.                                                                                                                                                                                                                                                            

For each uncertain variable with a range of possible values, the possible values are defined with a probability distribution. The type of distribution that is selected is based on the conditions surrounding that variable. Distributions can be normal, triangular, uniform, or lognormal.

I am using @Risk to perform Monte-Carlo Simulation, an add-in for Microsoft Excel. Monte-Carlo Simulation selects a value for an input, recalculates the outputs for the DSS, plots the forecast, and then repeats for as many iterations as are selected by the user.

The user selects an input in the support system. The distribution of values must be selected by clicking on the "Define Distributions" tab. There are a number of options to choose from. The most common distribution is the "normal" distribution, which looks like a bell-shaped curve. This means that when the simulation begins, it will select a range of random values centered around the peak of the bell-shaped curve. Minimum and maximum values can also be changed if needed. Triangle and uniform distributions are also common.

Outputs must be defined. First, select the output of interest in the spreadsheet. Then, click on the "Add Output" tab. A dialogue box appears asking for a name for the output. Usually the one given is correct.

Click on the "@Risk Model Window" and verify that all inputs and outputs are accounted for before simulating.

Click on the "Simulation Settings" tab. The most important item here is the number of iterations. Select the number of iterations desired. The more iterations that are performed, the longer Monte-Carlo Simulation takes.

Click on "Start Simulation"! When it is finished, you can then view multiple graph types and statistics that show the results of the simulation.                                                                                                                                                              

3) Why is Monte-Carlo Simulation appropriate for managing uncertainty in complex situations?                                     

Monte-Carlo Simulation takes the guessing out of business situations, while allowing decision-makers to choose the most promising calculated risk. Monte-Carlo Simulation emphasizes optimization as a process that finds the best solution. When variables exist that can be controlled, and you want a maximum or minimum goal that relies on those variables, Monte-Carlo Simulation is ideal.                                                                                

 

PART TWO

Inputs

Price - input variable has normal distribution with a mean of $377.78 and SD of 6.1032
Advertising - cost input variable has normal distribution with a mean of $93325.78 and SD of 9828.045

Outputs

Market Share
Relative Demand

Summary Statistics

In this simulation model I used #iterations as 4000 and #simulation as 1. The table below summarizes the quality of data that was used and the output generated off of the simulation model. The minimum, maximum, range and the kind of distribution of the inputs can be controlled in the simulation.

Variables

Cell

Minimum

Mean

Maximum

Relative Demand

G7

-5.35E-02

0.9980822

1.993445

Market Share

G9

-5.35E-03

9.98E-02

0.1993445

Price

B12

356.0646

377.7847

401.882

Advertising

B13

58808.89

93329.42

142045.1

Diagrams

Graphs below show the normal distribution of the outputs and inputs in the simulation. They include both the histogram and fitting distribution diagrams.

 

 

 

 

 

 

 

The distribution of the outcome can be very critical to businesses when making important decisions like launching a new product or for increasing market share. Monte-Carlo simulation helps companies get a feel of a near real-life situation before making any capital investments.

Application

We have seen above how Monte-Carlo simulation can be effectively used to study the effect of uncertainty in the inputs on the distribution of the output variables. Businesses can plan their entire operations based on the expected demand and plan their revenue targets and strive to achieve them.

Conclusion

One of the limitations of the human mind is that it can process only one piece of information at a time. As models get increasingly complex, it is difficult to manually factor in the uncertainty of inputs and their effect on the distribution of the outcomes. Monte-Carlo simulation helps us factor in the uncertainty in the inputs using their probability distributions and repeat it for a large number of iterations.