Equipment Installation at Globus Enterprises
Equipment Installation at Globus Enterprises
Introduction
Risk Analysis is a fragment of each choice we make. We are always challenged with improbability and unpredictability. And even though we have access to information (especially nowadays), we can’t precisely foresee the future. Monte Carlo simulation lets you see all the potential outcomes of every decision you make and assess the impact of risk, giving you more commonsensical options for better decision making (Wittwer, 2003).
The Simulation
For question number 1, in order to create a distribution portraying total estimated project costs, we will use ten iterations to show us range of possible outcomes. The project might be completed in as cheap as $87,000 or as costly as $116,000.
The Monte Carlo Simulation is based on multiple trials that are trying to determine expected value of a random variable. The basis of the relationship is governed by the formula:
Since the “Usual (Most Likely)” value is the point estimate normally required, we only need two additional estimates: “Cheapest (Minimum)” and “Expensive (Maximum)”.
The first step is to generate random values for each Phase and its Cost. For this case, I used the MS Excel Application for solving. We can use the RAND() function to generate random numbers and multiply this by range of each variable. The range is the difference between Expensive and Cheapest values. The excel formula for the random cost for each Phase is:
Using the random variables, we now get the new percentage for the probability of cost for the Design Phase. As you can see in the Table below (Table 3), the Design has now 50% of chance to be cheaper(5 out of 10). It was raised by 20% from the historical cost of 30% chance only. The “1” served as the counting number for the probability when the value was greater than 9,000 but not more than 10,000 (since in the historical data, 10,000 was the usual cost). There is also zero chance for the Design Cost to be expensive compared to the historical data of having a probability of 30% and 50% to be the same as the usual phase cost.
The same with Build Phase (Table 4), it has now 50% chance of being cheap compared to the historical data of 20%, zero chance for being expensive, and 50% for being the Usual Cost of 70,000 from being 70% probability.
For Test Phase (Table 5), it has now 100% of being cheap compared to the historical data of only having 20%, 50% for Usual, and 30% for Expensive costing.
We can see from Figure 1, that Random 1, 3, 8, 9 and 10 have same probability of 10% being the cost for the Design Project, summing the total of 50%. It is the same with Build and Test Phase, wherein the random numbers have 10% chance of being the cost of the said phase(Dienemann, 2008).
We will use the formula for solving the Standard Deviation, as stated in Question 3:
SD = √Σ(Xi – X-bar)2/N,
where SD = standard deviation, √ = square root symbol, Σ = the summation sign, Xi = the ith value of X, X-bar = the mean of the X values, and N = the number of values being considered. To compute the mean of each Phase, Mean (average) is the sum of all the variables given divided by the number of variables.
Now we will solve the percentage of error in this estimate using the formula below where b is the standard deviation of the random variable and N, the number of iterations. There is no need to compute for iteration since we only used ten random variables in each phase.
For the Design Phase, we can see that there is a .61% error in this estimate. It is computed by multiplying the Standard Deviation solved earlier to 3 (635 x 3) and divide it by the square root of 10 (3.16), having a total of 603 to be divided by the Sum of the Random Variables (99,558). Same process was done with the computation for the error in estimate for Build Phase (.88%) and Test Phase (.15%).
References
Dienemann, P. (2008). Estimating Cost Uncertainty Using Monte Carlo Techniques. Retrieved
/RM4854.pdf
Wittwer, J. (2003). A Practical Guide to Monte Carlo Simulation. Retrieved from
http://www.vertex42.com/ExcelArticles/mc/MonteCarloSimulation.html
