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Simulation Programming and Analysis

How confident are you about uncertainty?

Simulations programming can be used to find mathematical problems that cannot easily be solved. The profit distribution of your business is one good example.

Monte Carlo Simulation Programming

A Monte Carlo algorithm is often used to find solutions to mathematical problems (which may have many variables) that cannot be easily solved. This Monte Carlo simulation section illustrates two examples of how Excel VBA can be utilized for building simulation models, specifically in hydraulic engineering and market analysis.

Monte Carlo Simulation Example (1)

The hydraulic engineering simulation project utilized Pearson Type III distribution. Provided the mean, standard deviation, skewness, and other inputs, the discharge-frequency curve with 95% confidence interval uncertainty bans is constructed. The screen shot is shown on Figure 1. below.

Fig 1. Screen shot of the hydraulic simulation project

Monte Carlo Simulation Example (2)

This model is taken from our XL Modeling VBA program. Given the market assumption, profit equation, and input variables distributions (uniform, normal, and truncate normal), we derived the probability distribution of the profit and generate the histogram.

From the probability distribution, we can obtain the probability of the profit that excesses any given number of value. We can also obtain the median and average of the profit from the distribution.

Fig 2. Screen shot of the profit/market simulation program

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Monte Carlo Simulation

A Monte Carlo algorithm is often a numerical Monte Carlo method used to find solutions to mathematical problems (which may have many variables) that cannot easily be solved, for example, by integral calculus, or other numerical methods. For many types of problems, its efficiency relative to other numerical methods increases as the dimension of the problem increases. Or it may be a method for solving other mathematical problems that relies on (pseudo-)random numbers. Monte Carlo methods are useful for modeling phenomena with significant uncertainty in inputs, such as the calculation of risk in business. Monte Carlo methods have also proven efficient in solving coupled integral differential equations of radiation fields and energy transport, and thus these methods have been used in global illumination computations which produce photorealistic images of virtual 3D models, with applications in video games, architecture, design, computer generated films, special effects in cinema, business, economics and other fields. The advantage Monte Carlo methods offer increases as the dimensions of the problem increase.
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