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Project#3B

Monte Carlo Simulation

 

What is Monte Carlo Simulation?

 Monte Carlo Simulation is a technique for managing uncertainty in a complex situation. Monte Carlo Simulation (MCS) is also a way for evaluating possible values of the outcome. With help of the MCS we can use both Sensitivity and Scenario analyses together. In other words, MCS is a way of doing complex analyses. In our situation we want to predict possible future changes of our company's market share and future demand for our product. We have uncertain variables (Average Industry Price & Average Industry Advertising), decision variables (Our Price & Advertising), and forecast variables (market share of our company and our firm's demand).

 It is possible to use Scenario analyses for this operation, but Scenario analyses is somewhat limited compare with MCS. If we use Scenario analyses we have to create different scenarios for every possible change on uncertain variables. If we have several uncertain variables and they can change in wide interval, then we have to create too many scenarios. Using MSC we don’t need to do this. We have opportunity to try all these scenarios within one simulation.

 

 

How is Monte Carlo Simulation performed?

 According to the situation and data that we used in previous assignments (Project#2 & Project#3a) we have 2 main uncertain variables (Avg. Price & Average Ad.) that are critical to the outcome. We will use these variables to forecast our firm's demand and market share. (Spreadsheet model).

 

Table#1

 

 We can also use in this simulation our decision variables (our price & advertising), but let us take them constant in order to see the affection of uncertain variables to our forecast variables more clearly. To input uncertain variables we need to choose their probability distribution and consequently, appropriate numbers for each variable.

Average Industry Price. Since Average Price has very close mean and median (378 & 378.9) according to descriptive statistics measures (Table#2) we define its distribution as a normal.

Average price

Average Advertisement

Mean

377.78421

Mean

93325.79

Standard Error

1.4001726

Standard Error

2254.708

Median

378.9

Median

93400

Mode

#N/A

Mode

#N/A

Standard Deviation

6.1032107

Standard Deviation

9828.045

Sample Variance

37.249181

Sample Variance

96590470

Kurtosis

-0.124622

Kurtosis

-0.97172

Skewness

-0.73522

Skewness

-0.33836

Range

22.5

Range

31770

Minimum

365

Minimum

76800

Maximum

387.5

Maximum

108570

Sum

7177.9

Sum

1773190

Count

19

Count

19

Table#2

 

Chart#1

 Average Industry Advertising. Since Average Industry Advertising has very close mean and median (93326 & 93400) according to descriptive statistics (Table#2) measures we define its distribution as a normal. Note that Crystal ball takes both variables inside three standard deviations.

 

 

Chart#2

 

 We choose market share and firm's demand as a Forecast variables (outcome variables). As a result of simulation we receive the results. According the results (500 trials) our market share depending on uncertain variables can change between 0% to 18%, and our firm's demand might be between 1000-3250. (Crystal Ball Report). Now we can try different variants to forecast our outcome variables. For example, let us assume that our market share would be between 5% and 17%. To do this we need just move grabbers to the appropriate positions. Then we will get the following results:

 

 

Chart#3

 

 According to the results, we can be 95.3% certain that under these conditions our market share will be between 5% and 17%. The same thing we can do with our firm's demand. We want that our Firm's demand be 1500 and 2850. The results will be followings:

 

Chart#4

 As it is seen from Chart#4 we can be 90% certain that our demand will be between these frames.

 

 

Why Monte Carlo Simulation?

 MCS is a way that allows to make complex analyses. MCS is very convenient for managers because building just one scenario they can see results for many possible variants. They also can easily change variables and manipulate results depending on their purposes. Moreover, MSC presents  not one outcome, but distribution of possible outcomes. Using this distribution, managers can define what variants have the most probability to happen and to build their activity according to these conditions. MSC also presents frequency and probability of each outcome. It is very commodious to create different charts and graphs within MSC, which helps to understand the situation clearly. Summarizing all the above mentioned  it can be restated that MSC is a  very useful tool for managing uncertainty in complex situation.