Since uncertainty is what typifies projects in progress, risk management is key to the success of a project. A technique known as Schedule Risk Analysis connects the risk information of project activities to the baseline schedule and provides sensitivity information of individual project activities as a way to assess the potential impact of uncertainty on the final project duration. The protection of a project’s deadline using a technique called Critical Chain/Buffer Management assures that delays in project activities are captured by buffers that are cleverly inserted into the project baseline schedule.
The analysis of a project schedule’s risk and its management through the use of detailed risk information and the incorporation of buffers is key to the success of a project. However, risk management is not a goal in itself, but rather it serves as a tool to improve and steer the project control phase. Indeed, the combination of the baseline schedule and the risk information should be interpreted and used as a point-of-reference to reveal threats and opportunities during the project progress.
Schedule risk analysis
Schedule Risk Analysis is a technique that allows you to refine the traditional Critical Path Method (CPM) to degrees of criticality and risk. It connects the risk information of project activities to the baseline schedule and provides sensitivity information of individual project activities as a way to assess the potential impact of uncertainty on the final project duration and cost. In doing so, it gives the project manager an idea on how dangerous/sensitive/risky an activity is for the project objective.
Buffer management
The Critical Chain/Buffer Management approach assumes the construction of a resource feasible schedule but incorporates a certain degree of flexibility in the activity start times in order to easily monitor schedule deviations and quickly respond by taking corrective actions to keep the whole project on schedule. It is based on the novel “Critical Chain” by E. Goldratt using his Theory of Constraints.
How to measure your baseline schedule’s sensitivity?
- Baseline schedule: Construct an activity timetable
- Define uncertainty: Define activity time and cost probability distributions
- Run Monte-Carlo simulations: Run multiple project progress simulations
- Interpret the simulation results: Interpret the sensitivity measures
Step 1. Baseline schedule
The construction of a project baseline schedule involves the definition of start and finish times for each project activity, using earliest and latest start calculations with or without the presence of limited resources. There is a wide range of techniques available (PERT, CPM, etc…) which will not be discussed in this article.
The project baseline schedule serves as a point of reference to which the simulated project progress of step 3 is compared to. Although it is generally accepted that it is very unlikely that everything will go according to plan, the baseline schedule plays a central role in schedule risk analysis and the lack of it would lead to incomparable data or even biased results.
Step 2. Define risk/uncertainty
Since time and cost estimates are often, if not always, subject to a margin or error, people feel more comfortable with a range of duration and cost estimates for project activities. Range estimates and risk assessment require analytical skills and basic knowledge of statistics which is often perceived as mathematically complex and sometimes theoretical and hence far from practice. However, a basic understanding of probability and distribution functions already allows the project manager to improve estimating the effects of unexpected events on the project outcome.
Step 3. Monte-Carlo simulations
Monte-Carlo simulation is a simple technique to quickly generate multiple runs simulating real project progress. Each simulation run generates a duration and cost for each project activity given its uncertainty profile defined in step 2. During each simulation run, the simulation engine records all project schedules and critical paths during progress in order to be able to measure the degree of activity sensitivity and the expected impact of activity variation on the project objective, as reported in step 4.
Step 4. Sensitivity results
The output of a schedule risk analysis is a set of measures that define the degree of activity criticality and sensitivity. These measures refine the black-and-white view of the critical path (which defines that an activity is either critical or not) to a degree of sensitivity, as follows:
Criticality Index (CI): Measures the probability that an activity is on the critical path.
Significance Index (SI): Measures the relative importance of an activity.
Schedule Sensitivity Index (SSI): Measures the relative importance of an activity taking the CI into account.
Cruciality Index (CRI): Measures the correlation between the activity duration/cost and the total project duration/cost.
Each measure gives the project manager an indication of how sensitive the activity is towards the final project duration or total cost. The values of the sensitivity measures are available upon completion of the simulation run and are used as triggers to focus on the risky activities which probably require higher attention in order to achieve successful project fulfillment.
Criticality Index (CI)
The Criticality Index measures the probability that an activity lies on the critical path. It is a simple measure expressed as a percentage denoting the likelihood of being critical. Although the CI has been used throughout various studies and implemented in many software tools, the CI often fails in adequately measuring the project risk. The main drawback of the CI is that its focus is restricted to measuring probability, which does not necessarily mean that high CI activities have a high impact on the total project duration (e.g. think of an activity with a very low duration always lying on the critical path, but with a low impact on the total project duration due to its negligible duration).
More precisely, the criticality index measures the probability that an activity lies on the critical path. It is a simple measure expressed as a percentage denoting the likelihood of being critical.
Significance Index (SI)
In order to reflect the relative importance between project activities, the Sensitivity Index of a project activity can be calculated as follows:
SI = E{(ActivityDuration * ProjectDuration) / ((ActivityDuration + ActivitySlack) * E(ProjectDuration))}
with E(x) denoting the expected value of x. The SI has been defined as a partial answer to the criticism on the CI. Rather than expressing an activity’s criticality by the probability concept, the SI aims at exposing the significance of individual activities on the total project duration. In some examples, the SI seems to provide more acceptable information about the relative importance of activities. Despite this, there are still examples where counter-intuitive results are reported.
or SI = E{(AD * SD) / ((AD + SL) * E(SD))}
with SD: Simulated project Duration, AD: Activity Duration, SL: Activity Slack,
E(x): Expected value of x
Schedule Sensitivity Index (SSI)
The Project Management Body Of Knowledge (PMBOK) mentions quantitative risk analysis as one of many risk assessment methods, and proposes to combine the activity duration and project duration standard deviations (StDevActivityDuration and StDevProjectDuration) with the CI. The Schedule Sensitivity Index is calculated as follows:
SSI = (StDevActivityDuration * CI) / StDevProjectDuration
Cruciality Index (CRI)
Another measure to calculate the duration sensitivity of individual activities is given by the correlation between the activity duration and the total project duration and can be calculated as follows:
CRI = |correlation(ActivityDuration, ProjectDuration)|
with |x|: The absolute value of x, AvgAD: Average activity duration, AvgSD: Average simulated project duration
This measure reflects the relative importance of an activity in a more intuitive way and calculates the portion of total project duration uncertainty that can be explained by the uncertainty of an activity.
Pearson’s product-moment CRI(r) is a traditional measure of the degree of linear relationship between two variables. The correlation is 1 in the case of a clear positive linear relationship, −1 in the case of a clear negative linear relationship, and some value in between in all other cases, indicating the degree of linear dependence between the activity duration and the total project duration. The closer the coefficient is to either −1 or 1, the stronger the correlation between these two variables. When the absolute value is taken, the CRI(r) lies between 0 and 1.
The Pearson’s product-moment cruciality index CRI(r) can be calculated as follows:
CRI(r) = |sum{(AD – AvgAD) * (SD – AvgSD)} / SQRT{sum(AD – AvgAD)2 * sum(SD – AvgSD)2}|
with sum{x} the sum of all x-values over all simulation runs.
However, the relation between an activity duration and the total project duration often follows a non-linear relation. Therefore, non-linear correlation measures such as the Spearman rank correlation coefficient or Kendall’s tau measure can also be calculated. These two correlation measures can be calculated as follows:
Spearman’s rank correlation CRI(ρ) (rho) assumes that the values for the variables (i.e. activity durations and project durations) are converted to ranks, followed by the calculation of the difference between the ranks of each observation of the two variables. The measure is a so-called non-parametric measure to deal with situations where the strict statistical assumptions of the parametric CRI(r) measure are not met. The CRI(ρ) measure has a similar meaning to the CRI(r) measure, i.e. -1 ≤ CRI(ρ) ≤ 1 or, when the absolute value is taken, 0 ≤ CRI(ρ) ≤ 1.
Kendall’s tau rank correlation CRI(τ) (tau) index measures the degree of correspondence between two rankings and assesses the significance of this correspondence. This non-parametric measure has a similar meaning to the CRI(r) measure, i.e. -1 ≤ CRI(τ) ≤ 1 or, when the absolute value is taken, 0 ≤ CRI(τ) ≤ 1.