The Monte Carlo Simulation

The concept of operations behind the Monte Carlo simulation is quite simple: by using a Monte Carlo computer simulation program, ^[4] the network schedule is "run" or calculated many times, something we cannot usually do in real projects. Each time the schedule is run, a duration figure for each task is picked from the possible values within the pessimistic to optimistic range of the probability distribution for the task. Now each time the schedule is run, for any given task, the duration value that is picked will usually be different. Perhaps the first time the schedule is calculated, the most pessimistic duration is picked. The next time the schedule is run, perhaps the most likely duration is picked. In fact, over a large number of runs, wherein each run means calculating the schedule differently according to the probabilistic outcomes of the task durations, if we were to look at a report of the durations picked for a single task, it would appear that the values picked and their frequency of pick would look just like the probability distribution we assigned to the task. The most likely value would be picked the most and the most pessimistic or optimistic values would be picked least frequently. Table 7-1 shows such a report in histogram form. The histogram has a segregation or discrete quantification of duration values, and for each value there is a count of the number of times a duration value within the histogram quantification occurred.

Table 7-1: Monte Carlo Outcome for Tasks

"Standard" Normal Distribution of Outcome Milestone
Normalized Outcome Value[a] (As Offset from the Expected Value)	Histogram Value * 100[b]	Cumulative Histogram * 100[b] (Confidence)
-3	0.110796	0.110796
-2.75	0.227339	0.338135
-2.5	0.438207	0.776343
-2.25	0.793491	1.569834
-2	1.349774	2.919607
-1.75	2.156932	5.07654
-1.5	3.237939	8.314478
-1.25	4.566226	12.8807
-1	6.049266	18.92997
-0.75	7.528433	26.4584
-0.5	8.80163	35.26003
-0.25	9.6667	44.92673
0	9.973554	54.90029
0.25	9.6667	64.56699
0.5	8.80163	73.36862
0.75	7.528433	80.89705
1	6.049266	86.94632
1.25	4.566226	91.51254
1.5	3.237939	94.75048
1.75	2.156932	96.90741
2	1.349774	98.25719
2.25	0.793491	99.05068
2.5	0.438207	99.48888
2.75	0.227339	99.71622
3	0.110796	99.82702
[a]The outcome values lie along the horizontal axis of the probability distribution. For simplicity, the average value of the outcome (i.e., the mean or expected value) has been adjusted to 0 by subtracting the actual expected value from every outcome value: Adjusted outcomes = Actual outcomes - Expected value. After adjusting for the mean, the adjusted outcomes are then "normalized" to the standard deviation by dividing the adjusted outcomes by the standard deviation: Normalized outcomes = Adjusted outcomes/σ. After adjusting for the mean and normalizing to the standard deviation, we now have the "standard" Normal distribution. [b]The histogram value is the product of the horizontal value (outcome) times the vertical value (probability); the cumulative histogram, or cumulative probability, is the confidence that a outcome value, or a lesser value, will occur: Confidence = Probability outcome ≤ Outcome value. For better viewing, the cell area and the cumulative area have been multiplied by 100 to remove leading zeroes. The actual values are found by dividing the values shown by 100.