The concept of path ranking

We define two different rankings of relevant paths through the network:

Slack ranking

Keeping in mind that other paths through the network than the Critical Path calculated with the most-likely-estimates may become critical when variability of activity durations is accounted for, we define the following paths:

1. Primary Path. This is the Critical Path calculated with the most-likely-estimates. The slack (or float) of the activities on this path is zero.

2. Secondary Path. This is the path with the least total slack compared to the Critical Path.

3. Tertiary Path. This is the path which has the least total slack after the Secondary Path.

This ranking will be referred to as slack ranking. The Secondary Path follows from the dual values (shadow prices) as described in Chapter 7 of Open Design, a Collaborative Approach to Architecture. By removing the slack from the Secondary Path, it becomes part of the Critical Path. The dual values then identify the Tertiary Path.

Risk ranking

If the slack in the secondary and tertiary paths is small and the variability of activity durations substantially more than in the primary path, the secondary and tertiary paths may become more relevant to project control than the primary path. In other words: if variability of activity durations is taken into account, a ranking of the various paths can be established reflecting the risk involved. We will call this the risk ranking of the various paths of the network. The risk ranking and the associated risks are found in the following way.

For all activities the project is composed of, three estimates are made for the duration of the activity concerned: a most pessimistic, a most likely (best guess) and a most optimistic estimate. The pessimistic and optimistic estimates are defined as having a 10% probability of being exceeded. Whenever an activity duration is estimated in this way, a skewed probability distribution, such as the beta distribution, is assumed through the three given estimates. The Monte Carlo simulation is then conducted by carrying out a critical path calculation, say, 2 000 times, using activity durations that are obtained from the skewed distributions (by drawing a random number which is corrected for the skewed distribution). The frequency distribution of the 2 000 calculations provides the probability distribution for the duration of the entire project. A counter keeps track of how many times (out of the 2 000) a given path through the network was the critical path. This provides the risk ranking of the paths and the associated risks, that is, the likelihood that they will be the critical path in reality.

As will be shown in Chapter 11, the path ranking on slack can be very different from the path ranking on risk (frequency of being the critical path in the Monte Carlo simulation).

The risk ranking of the paths, with their associated risks, is important to the project manager as it indicates how much attention should be paid to monitoring activities on the various paths. The probability distribution for the completion of the entire project is, of course, of great interest to the financial stakeholder.

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