Project planning is the key discipline by which simulations have found entrance into daily practice. Since something new is to be created, the individual activities, their duration and ultimately the costs are associated with great uncertainty. Additionally, unexpected events may occur with a singular impact on certain variables. Here we would like to know if a project is completed before a certain date.
Let us imagine that we must implement a project according to the specifications below for a test drilling. A tricky project, of course. Starting with the preparatory phase, communication measures have to be implemented in advance. These are intended to enlighten the population and thus prevent a rejection of the project. A "bad" condition is expected with a 10% probability during the drilling, which increases the cost of the realization task by 25%. However, we expect that this has no effect on the duration of the realization task. On the other hand, it is assumed that the success of the ex-ante communication is negatively correlated with the realization task. A "bad" or omitted communication leads to protests of the affected population, which may block the access roads and thus hinder further work. And, a high duration of the realization task also has a positive correlation with "ex-post" communication measures. Both correlation relationships have been defined under "Correlation" and we asume that both values have been derived from past data.
The duration of the individual tasks is described by a PERT distribution. However, the cost per hour varies due to the different job requirements profiles. The costs are calculated multiplying the uncertain hourly rates by the number of hours according to the corresponding PERT distribution. This is an important distinction. A direct multiplication of the uncertain hours with the uncertain hourly rates, on the other hand, would outweigh the risk, since the probability that an action of 39 hours (as for the task "preparation") would have an hourly wage of exactly 115 for each hour is extremely low. Therefore, hourly rates between 115 and 127 should be assumed for a given task duration of 39 hours.
The expectation value of all input variables yield to the project termination date 09/25/2017. However, the potential contractor would already like to start a new project on October 18, 2017 (ending after approx. 134 days since project start, weekend and holidays have been omitted). He would like to submit an offer, but only if we are sure in 95% that he doesn't need more than 134 days for project termination. The costs are, however, acceptable in all cases. Will he submit an offer?
After a simulation with 3,000 iterations the following results are shown: In the "worst-case" scenario the duration is 136 days, ie there is a "probability" of 5% that the project lasts longer than 136 days. Conversely, the probability of a project duration of more than 134 days must be over 5%, which is apparent from the point estimation (9%). The generation of several empirical distributions would not diminish the meaningfulness of our results, as can be seen from the confidence interval.
Note: the differentiation of the duration of the project and the costs per task leads also to different t-shaped distributions for the variable "task_c_com_pos".
Conclusion: The potential contractor would not carry out the project given the above premises. However, if he has enough money to significantly reduce the duration of the realization (as can be seen in the tornado graph, there is a important correlation between the total duration and the duration of the realization), he might still accept the offer.