PERT chart
Complex projects require a series of activities, some need to be performed in the order and others which can be done in parallel with other activities. This collection of series and parallel tasks can be modeled as a network.
In 1957 the method of critical path (CPM) has been developed a network for project management model. CPM is a deterministic method that uses an estimate of the time set for each activity. While CPM is easy to understand and use, it does not consider the time variations that can have a big impact on the time of execution of a complex project.
The program evaluation and Review Technique (PERT) is a network model that allows for random in the time of end of activity. PERT was developed during the late 1950s to Polaris project of the US Navy with thousands of entrepreneurs. It has the potential to reduce the time and costs required to complete a project.
Network diagram
In a project, an activity is a task that must be carried out and an event is a milestone marking the end of one or more activities. Before an activity can begin, all predecessor activities must be completed. Project models network represent the activities and milestones of nodes and arcs. PERT was originally an activity on the network of the arc, in which activities are represented on the lines and milestones on the nodes. Over time, some people have begun to use PERT as an activity on the network of the node. For this discussion, we will use the original form of the activity on the arc.
The PERT network can have multiple pages with many subtasks. Here is a very simple example of a PERT diagram:
PERT chart
Milestones are usually numbered so that the end of an activity node has a higher number than the start node. Increment numbers by 10 allows for the new insert without changing the numbering of all the diagram. The activities in the above diagram are labelled with letters as well as the expected time to complete the activity.
Steps in the process of planning PERT
PERT planning involves the following steps:
1. Identify the specific activities and milestones.
2. Determine the correct order of activities.
3. Build a network diagram.
4 Estimate the time required for each activity.
5. Determine the critical path.
6 Update the PERT network during the project.
1. Identify the activities and milestones
Activities are the tasks necessary for the implementation of the project. Milestones are the events marking the beginning and the end of one or more activities. It is useful to list the tasks in an array can be extended to include information on the sequence and duration in later stages.
2. Determine the sequence of activity
This step can be combined with the identification step activity, the sequence of activity being obvious to some tasks. Other stains may require a more in-depth analysis in order to determine the exact order in which they should be performed.
3 Build network diagram
Using the sequence of activity information, a network diagram can be pulled by showing the sequence of activities series and parallel. For the original model of the activity-on-arc activities are represented by arrows lines and milestones are represented by circles, or "bubbles".
If hand-made several projects may need to correctly portray the relationships between the activities. Software packages simplify this step by automatically converting the activity tabular information in a network diagram.
4. Estimate the activity times
Weeks are a unit commonly used time for the completion of the activity, but any coherent unit of time can be used.
A peculiarity of the PERT is its ability to cope with the uncertainty in the time of end of activity. For each activity, the model includes typically three time estimates:
Optimistic time - usually a minimum of time in which the activity may be carried out. It is common to specify once optimistic in three standard deviations from the average so that there is about a 1% chance that the activity will be completed within the optimistic period.
The most likely time - the execution time with the highest likelihood. Note that this time is different from the scheduled time.
Time pessimistic - the longer that an activity may require. Three standard deviations of the mean is commonly used for the pessimistic time.
PERT assumes a probability distribution of beta time estimates. For a beta distribution, time planned for each activity can be fixed using the weighted average follows:
Scheduled time = (Optimistic + 4 x more likely + pessimistic) / 6
This should time can be displayed in the network diagram.
To calculate the variance of each time of completion of the activity, if three times standard deviation have been selected for both optimistic and pessimistic, there are six gaps between them, if the variance is given by:
[(Pessimiste-optimiste) / 6] 2
5. Determine the critical path
The critical path is determined by adding the durations of activities in each sequence and determine the longest path in the project. Critical path determines the required total calendar for the project. If activities outside the critical path, speed up or slow down (limits), the total time of the project does not change. The duration for which a non-critical path activity can be delayed without delaying the project corresponds to the soft time.
If the critical path is not immediately obvious, it may be useful determine the following quantities of four for each activity:
ES - start time earlier
EF - complete first time
LS - the last start time
LF - last end time
These times are calculated using the time scheduled for the relevant activities. The earlier departure and the arrival time of each activity are determined by working forward through the network and determine the earlier during which an activity can start and finish account in light of the activities of its predecessor. The last departure and arrival times are the last time that an activity can start and finish without delaying the project. LS and LF are working backwards through the network. The difference in the oldest and most recent of each activity finish is soft for this activity. The critical path is the path through the network in which no activities have slack.
The variation in time of project can be calculated by adding gaps in times of activities in the critical path. Given this gap, can calculate the probability that the project will end by a certain date assuming a probability distribution of normal critical path. The normal distribution assumption holds if the number of activities in the path is big enough so that the central theorem limits to apply.
Given that critical path determines the date of completion of the project, the project can be speeded up by adding resources to reduce the time for activities in the critical path. Such a shortening of the project sometimes corresponds to draft crashing.
6 Update as and project
Make adjustments in the PERT chart during the project. As the project unfolds, some times may be replaced by real time. In cases where there are delays, additional resources may be required to remain on the calendar and the PERT chart can be changed to reflect the new situation.
Advantages of PERT
PERT is useful because it provides the following information:
Expected project completion time.
Probability of completion before a specified date.
Critical path activities that directly affect execution time.
Activities that have margin and can lend resources to the activities of path critical.
Activity start and end dates.
Limits
Here are some weaknesses of the PERT:
Activity time estimates are somewhat subjective and judgment. In cases where there is little experience in the exercise of an activity, the figures can only be a guess. In other cases, if the person or group running the activity, estimated the time it can be bias in the estimate.
Even if the time of activity are well estimated, PERT assumes a beta distribution for these time estimates, but the actual distribution may be different.
Even though the beta distribution hypothesis holds, PERT assumes that the probability distribution of the time of completion of project is the same as the critical path. Because the other paths can become the critical path if their activities are delayed, PERT always underestimates the expected project execution time.
The underestimation of project due to other paths execution time becomes critical is perhaps the most serious of these issues. To work around this limitation, simulation Monte Carlo can be performed on the network to eliminate this optimistic bias in time of performance expected from the project.
can only be a guess. In other cases, if the person or group running the activity, estimated the time it can be pa
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