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 dont 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.