## Risk assessment in network planning through Monte Carlo simulation

As a solution for this problem, Lanza (2003) proposes a Monte Carlo approach. In essence, this involves the following steps:

1. Establish most optimistic/most likely/most pessimistic estimates for the duration of all project activities;

2. Calculate the Critical Path using the most-likely-estimates. So far the procedure is the same as in traditional PERT planning;

3. Establish one or more other paths through the network that may actually become critical paths as a result of high variability in the duration of activities in those paths;

4. Conduct a Monte Carlo simulation on each of these paths.

The resulting probability distributions for the project duration according to these paths provide answers to relevant questions related to the risk involved, such as:

1. Which project duration can be achieved with a 90% probability and what is the associated path of activities through the network?

2. What is the probability of meeting the deadline for completion of the project as required by the financing party and what is the associated path of activities through the network?

In both cases the critical path may be different from the Critical Path calculated with the most-likely-estimates. The Monte Carlo approach constitutes an improvement over the traditional CPM and PERT techniques because it provides additional information that is relevant to both the project manager and the financing stakeholder. The project manager's attention is drawn to activities that are not on the Critical Path but nevertheless may become critical and the financing stakeholder gets an estimate of the probability of financing problems due to a substantial delay in project completion.

The Monte Carlo approach proposed by Lanza leaves, however, one important question unanswered: Are the considered paths through the network really the most relevant ones?

When the network is extensive and complicated, a path of (statistically) critical activities could easily be overlooked. This difficulty can be avoided by applying Monte Carlo simulation in such a way that (statistically) critical paths are identified in a systematic way. This is achieved by conducting Monte Carlo simulation on the entire project instead of on one path of the network only.