Pert & CPM


Q2 Pert & CPM
CPM - Critical Path Method DuPont developed a Critical Path Method (CPM) designed to address the challenge of shutting down chemical plants for maintenance and then restarting the plants once the maintenance had been completed. Complex project, like the above example, require a series of activities, some of which must be performed sequentially and others that can be performed in parallel with other activities. This collection of series and parallel tasks can be modeled as a network. CPM models the activities and events of a project as a network. Activities are shown as nodes on the network and events that signify the beginning or ending of activities are shown as arcs or lines between the nodes. The Figure shows an example of a CPM network diagram:


Steps in CPM Project Planning
 1. Specify the individual activities.
 2. Determine the sequence of those activities.
 3. Draw a network diagram.
 4. Estimate the completion time for each activity.
 5. Identify the critical path (longest path through the network)
 6. Update the CPM diagram as the project progresses.
1. Specify the individual activities All the activities in the project are listed. This list can be used as the basis for adding sequence and duration information in later steps.
2. Determine the sequence of the activities Some activities are dependent on the completion of other activities. A list of the immediate predecessors of each activity is useful for constructing the CPM network diagram.
3. Draw the Network Diagram Once the activities and their sequences have been defined, the CPM diagram can be drawn. CPM originally was developed as an activity on node network.
4. Estimate activity completion time The time required to complete each activity can be estimated using past experience. CPM does not take into account variation in the completion time.
 5. Identify the Critical Path The critical path is the longest-duration path through the network. The significance of the critical path is that the activities that lie on it cannot be delayed without delaying the project. Because of its impact on the entire project, critical path analysis is an important aspect of project planning. The critical path can be identified by determining the following four parameters for each activity:
ES - earliest start time: the earliest time at which the activity can start given that its precedent activities must be completed first.
 EF - earliest finish time, equal to the earliest start time for the activity plus the time required to complete the activity.
LF - latest finish time: the latest time at which the activity can be completed without delaying the project.
LS - latest start time, equal to the latest finish time minus the time required to complete the activity.
 The slack time for an activity is the time between its earliest and latest start time, or between its earliest and latest finish time. Slack is the amount of time that an activity can be delayed past its earliest start or earliest finish without delaying the project.
The critical path is the path through the project network in which none of the activities have slack, that is, the path for which ES=LS and EF=LF for all activities in the path. A delay in the critical path delays the project. Similarly, to accelerate the project it is necessary to reduce the total time required for the activities in the critical path.
 6. Update CPM diagram As the project progresses, the actual task completion times will be known and the network diagram can be updated to include this information. A new critical path may emerge, and structural changes may be made in the network if project requirements change.
CPM Benefits • Provides a graphical view of the project
 • Predicts the time required to complete the project.
 • Shows which activities are critical to maintaining the schedule and which are not.
CPM Limitations While CPM is easy to understand and use, it does not consider the time variations that can have a great impact on the completion time of a complex project. CPM was developed for complex but fairly routine projects with minimum uncertainty in the project completion times. For less routine projects there is more uncertainty in the completion times, and this uncertainty limits its usefulness.
 PERT The Program Evaluation and Review Technique (PERT) is a network model that allows for randomness in activity completion times. PERT was developed in the late 1950's for the U.S. Navy's Polaris project having thousands of contractors. It has the potential to reduce both the time and cost required to complete a project. The Network Diagram In a project, an activity is a task that must be performed and an event is a milestone marking the completion of one or more activities. Before an activity can begin, all of its predecessor activities must be completed. Project network models represent activities and milestones by arcs and nodes. PERT is typically represented as an activity on arc network, in which the activities are represented on the lines and milestones on the nodes. The Figure shows a simple example of a PERT diagram.


Chart The milestones generally are numbered so that the ending node of an activity has a higher number than the beginning node. Incrementing the numbers by 10 allows for new ones to be inserted without modifying the numbering of the entire diagram. The activities in the above diagram are labeled with letters along with the expected time required to complete the activity.
Steps in the PERT Planning Process PERT planning involves the following steps:
1. Identify the specific activities and milestones.
2. Determine the proper sequence of the activities.
3. Construct a network diagram.
 4. Estimate the time required for each activity.
5. Determine the critical path.
6. Update the PERT chart as the project progresses.
 1. Identify activities and milestones The activities are the tasks required to complete the project. The milestones are the events marking the beginning and end of one or more activities
 2. Determine activity sequence This step may be combined with the activity identification step since the activity sequence is known for some tasks. Other tasks may require more analysis to determine the exact order in which they must be performed.
 3. Construct the Network Diagram Using the activity sequence information, a network diagram can be drawn showing the sequence of the serial and parallel activities.
 4. Estimate activity times Weeks are a commonly used unit of time for activity completion, but any consistent unit of time can be used. A distinguishing feature of PERT is its ability to deal with uncertainty in activity completion times. For each activity, the model usually includes three time estimates
: • Optimistic time (OT) - generally the shortest time in which the activity can be completed. (This is what an inexperienced manager believes!)
 • Most likely time (MT) - the completion time having the highest probability. This is different from expected time. Seasoned managers have an amazing way of estimating very close to actual data from prior estimation errors.
• Pessimistic time (PT) - the longest time that an activity might require. The expected time for each activity can be approximated using the following weighted average: Expected time = (OT + 4 x MT+ PT) / 6 This expected time might be displayed on the network diagram. Variance for each activity is given by: [(PT - OT) / 6]2 5. Determine the Critical Path The critical path is determined by adding the times for the activities in each sequence and determining the longest path in the project. The critical path determines the total time required for the project. If activities outside the critical path speed up or slow down (within limits), the total project time does not change. The amount of time that a non-critical path activity can be delayed without delaying the project is referred to as slack time. If the critical path is not immediately obvious, it may be helpful to determine the following four quantities for each activity:
• ES - Earliest Start time • EF - Earliest Finish time • LS - Latest Start time • LF - Latest Finish time These times are calculated using the expected time for the relevant activities. The ES and EF of each activity are determined by working forward through the network and determining the earliest time at which an activity can start and finish considering its predecessor activities. The latest start and finish times are the latest times that an activity can start and finish without delaying the project. LS and LF are found by working backward through the network. The difference in the latest and earliest finish of each activity is that activity's slack. The critical path then is the path through the network in which none of the activities have slack. The variance in the project completion time can be calculated by summing the variances in the completion times of the activities in the critical path. Given this variance, one can calculate the probability that the project will be completed by a certain date. Since the critical path determines the completion date of the project, the project can be accelerated by adding the resources required to decrease the time for the activities in the critical path. Such a shortening of the project sometimes is referred to as project crashing. 6. Update as project progresses Make adjustments in the PERT chart as the project progresses. As the project unfolds, the estimated times can be replaced with actual times. In cases where there are delays, additional resources may be needed to stay on schedule and the PERT chart may be modified to reflect the new situation. Benefits of PERT
 PERT is useful because it provides the following information:
 • Expected project completion time.
 • Probability of completion before a specified date.
 • The critical path activities that directly impact the completion time.
 • The activities that have slack time and that can lend resources to critical path activities.
 • Activities start and end dates.
Limitations of PERT
The following are some of PERT's limitations:
 • The activity time estimates are somewhat subjective and depend on judgment. In cases where there is little experience in performing an activity, the numbers may be only a guess. In other cases, if the person or group performing the activity estimates the time there may be bias in the estimate.

• The underestimation of the project completion time due to alternate paths becoming critical is perhaps the most serious.

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