# Project Evaluation and Review Technique

Complex projects will have a significant number of activities that need to be performed, both in sequence and in parallel. These tasks can be modelled as a network which reflects all the paths that the project needs to take, and all the dependencies in the project. Whilst it is possible to determine the critical path through such a network, real life projects tend to be subject to uncertainty, which makes it difficult to complete an accurate analysis based on deterministic networks. As a result of this, the program evaluation and review technique, or PERT, was developed by the US Navy in the late 1950s to model projects with large numbers of contractors, where there was significant uncertainty in the times various tasks would take. As such, PERT was designed to incorporate this uncertainty, whilst reducing the time taken and costs incurred in completing a project.

As with the critical path method, PERT requires a network diagram to be produced. However, whilst the critical path method typically displays the activities on nodes, with the arcs between nodes representing dependencies, PERT tends to display the activities on arcs, with the nodes representing milestones and dependencies. However, PERT can also be displayed using the activity on node method similar to CPM. As with a Gantt chart, a PERT chart can be composed of a number of separate pages with many tasks and sub tasks.

When the diagram is constructed, the milestones are numbered to ensure that the end of an activity occurs at a milestone with a higher number that the beginning milestone. This can be achieved by using increments of ten in between each milestone, so new milestones can be inserted as required whilst maintaining the numbering system. Once the diagram has been completed, the PERT planning process can begin.

__PERT Planning Process__

The planning process is composed of the following six steps:

1. Identify the individual tasks required

2. Identify any dependencies, and hence the sequences of tasks

3. Draw a network diagram to represent these tasks.

4. Obtain estimates of the time each task will take

5. Identify which path is the critical path: usually the path with the longest duration

6. Keep the network diagram and critical path up to date throughout the project

Identifying the individual tasks is generally done from the work breakdown structure. This enables a list of all tasks to be constructed. Within the PERT process, the activities need to be numbered, and spaces need to be left for additional tasks. This list can also be used to determine which activities are dependent on others. The network diagram is constructed to show the various sequences of serial and parallel tasks. The activities are shown as lines with arrows for their direction, and the milestones as circular nodes where activities start and end. Software packages are often used to speed up this process.

The time each task is likely to take can be estimated from previous projects, extrapolated from the technical requirements of the task, or simply estimated by a subject matter expert. In PERT analysis, three time estimates are used. The first is the optimistic time, which is the shortest time in which the activity could reasonably be expected to be completed. The second is the most likely time, which is the completion time with the highest probability, not the expected time. The last one is the pessimistic time, which is the latest the activity could realistically take. Most of the times are determined using probability distributions to represent the optimistic and pessimistic times. In this case, the optimistic time is three standard deviations lower than the mean time, and the pessimistic time is three standard deviations above. This implies that there is around a 1% likelihood of the activity being completed within the most optimistic time, and a 1% chance it will take longer than the most pessimistic time.

The critical path can be determined by adding the time for each task in each sequence, then determining which path is the critical path. This path is the one with the longest total duration of all activities. As this path has the longest duration, it will correspond to the length of the project, and any delays to the critical path will hence delay the project. The critical path is determined by finding the earliest start time, earliest finish time, latest start time and latest finish time for all activities, based on the requirements of other activities. For example, the first activity in the project will have earliest and latest start times of 0, and the earliest and latest start times will be the duration of the project. The earliest start and finish times for other tasks will then depend on the speed at which all the preceding activities can be completed. This can be used to find the earliest start and finish time for all tasks in the project. The latest start and finish times can then be identified from the latest time that tasks would have to start and finish to avoid delaying the task in front of them. Most tasks will have some difference between their earliest and latest times, as tasks ahead of them will depend on other tasks that finish later. However, there will be one path through the network where the earliest and latest times are all the same. This is the critical path. The critical path is also defined as the path through the network where there is no slack time for any of the activities, i.e. there is no flexibility around the start and end time for each activity.

The uncertainty in the completion times of the various tasks, and the project as a whole, is calculated by adding the variances in all dependent tasks and, for the project as a whole, for the tasks in the critical path. This variance allows project managers to calculate the likelihood of a project being completed by the due date, and by any given date assuming the variances are normally distributed. However, this assumption relies on their being more than thirty activities in the critical path in order for central limit theorem to hold and for the total probability distribution to be a normal distribution.

If the probability estimates indicate that the project is unlikely to be completed by the due date, extra resources can be used to reduce the duration of the critical path, and hence of the project as a whole. This is referred to as crashing the project, and generally incurs additional costs. As a result, the project manager needs to weigh up whether the costs associated with crashing the project are preferable to the risk of failing to meet the deadline.

The PERT chart needs to be updated continuously as the project moves forward, particularly if the estimated times for any tasks change. The critical path also needs to be regularly calculated because, if the project moves ahead of or behind schedule, the previous critical path may be replaced by a new one. In this case, resources should be devoted to this path in order to make further improvements to project time. In particular, if there are delays to a non critical path this may become the critical path, and additional resources may have to be directed towards it to ensure the project is not delayed.

__Benefits and limitations of PERT__

The main benefit of PERT is that is provides a project manager with an expected completion time for a project, whilst also indicating how likely it is that the project will be completed by a certain date. PERT also helps project managers to determine the critical path for the project, and how likely it is that this path can be shortened by diverting resources from not critical paths.

However, PERT’s main limitation comes from the fact that all the estimates for the task durations and the probability distributions of these durations are quite subjective. As such, if there is little experience of the tasks involved in a project, then the estimates may be poor, and they may also be biased if the estimates are performed by people responsible for performing the activity. In addition, even if the probability distribution of the times is known not to a beta distribution, PERT applies a beta distribution anyway, which can cause inaccuracy.

There is also a fundamental issue with the use of the beta distribution which is that, even if the task durations have beta distributions, the overall probability distribution for the project duration will not necessarily be the same as the distribution for the critical path. In particular, delays to other activities and improvements to the critical path can cause other paths to become critical, hence PERT tends to consistent underestimate the overall project duration. This is a serious flaw in the PERT method, and often requires the use of Monte Carlo simulations to eliminate any bias and accurately reflect the likely project duration.

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