Critical path method (CPM) was created in 1957 by J. E. Kelly of Remington Rand and M. R. Walker of DuPont to assist in the building and repairs of DuPont’s chemical plants. In the following year, the Special Projects Office of the U.S. Navy created PROGRAM EVALUATION AND REVIEW TECHNIQUE (PERT) to help coordinate the duties of the thousands of contractors working on the Polaris missile program. Today CPM and PERT are essential planning tools used to help managers overcome the limitations of Gantt charts (horizontal bar charts used to track the progress of projects) and to determine which critical activities must be completed in order for a project to be finished in a timely and cost-effective manner. Although CPM and PERT do have some differences, which will be pointed out, they are often discussed synonymously because both are necessary quantitative techniques used for effective PROJECT MANAGEMENT.
In project management, determining CPM and PERT requires the creation of a network diagram, which gives the order of critical activities and the estimated time for completion of each activity. Loosely defined, a critical activity is any job in a project’s schedule whose completion is necessary in order to have the entire project completed on time. Critical activities are found along a critical path, which therefore is “the longest path route through the network” because it is the path that will take the most time to complete. To reduce the time needed to complete a project, the number of activities found on the critical path would first have to be reduced.
Critical path method uses two time estimates for determining the time it will take to finish a project. The first is the “normal completion time” and the other is the “crash time.” As the name implies, the normal completion time is the estimated time it will take to complete a project under “normal” conditions, or rather, a situation in which nothing unexpected happens to interrupt the course of the project. The crash time is the shortest time it would take to finish an activity if more money and other resources where added to complete the project.
Finding CPM and PERT requires project managers to perform a few simple calculations. CPM requires managers to find four quantities.
1. Earliest Start Time (ES): the earliest time an activity can start without violating any of the initial requirements for beginning the activity.
2. Earliest Finish Time (EF): the earliest time an activity is expected to end.
3. Latest Start Time (LS): the latest time the activity could begin without having the entire project lag.
4. Latest Finish Time (LF): the latest an activity could end without having the entire project lag (Render and Stair Jr., p. 635).
To calculate the earliest start and finish times for each activity in a project, project managers should begin by drawing a graph that looks something like this:

The Earliest Start Time is set at zero. Project managers should keep in mind that the earliest start time for each activity in the project will always be set at zero. Say, for instance, that activity “A” takes two weeks to complete; therefore, its earliest finish time is represented as 2. The following calculation can be used to find the Earliest Finish Time: Earliest Finish Time = Earliest Start Time + Expected Activity Time, or EF = ES + t.
When computing the ES and EF for the activities in a project, there is one rule that must be followed. Before project managers begin one activity, all critical activities preceding that one must be completed first. For CPM, project managers are looking for the “longest path to an activity in determining ES” (Render and Stair Jr., p. 636). To calculate the ES and EF times for each activity in the entire project, project managers will make a “forward pass” through the network, where at each step EF = ES + t. Thus, say a project consists of projects A, B, C, D, E, and F; activity “F” cannot begin until the 11th week after starting the project, and it is expected to take two weeks to complete. The whole project will take exactly 13 weeks to be finished, since EF = ES + t; in this case, 13 = 11 + 2.
However, once the earliest finish time has been calculated, project managers still need to calculate the latest start and finish times for each activity in order to find the critical path. Now they will begin at the last activity, in this case activity “F,” and work backward to activity “A.” The formula used to find the latest start time is Latest Start Time = Latest Finish Time – Expected Activity Time, or LS = LF – t. For example, because LF equals 13 for activity “F,” the latest start time for the activity is 11 weeks since LS = 13 – 2. The general rule here is that “the latest finish time for an activity equals the smallest latest starting time for all activities leaving that same event” (Render and Stair Jr., p. 637).
Another calculation that should be determined when finding the critical path of a project is the slack time, or the amount of time an activity can be put on hold without holding up the project as a whole. The calculation for slack is: Slack = LS – ES or Slack = LF – EF. However, it cannot be stressed enough that no critical activities can have any slack time because they are critical, and any delay in completing them will delay the completion of the entire project. Slack time can only be applied to those activities that are not considered critical to the outcome of the project.
Once the times for all activities on the critical path are computed, managers will apply PERT techniques to each activity to determine the variance of the entire project. Project variance is found by adding all the variances for each critical activity. Project variance equals sigma variances of each activity found on the critical path. The standard deviation for the project is the square root of the project variance. Once these calculations are made, project managers can determine whether the project will be completed on time.
While using CPM and PERT techniques is a necessary part of project management, it may not be necessary for a company to apply these tools to every job undertaken. Clearly there is a lot of analysis involved finding both CPM and PERT, and it takes a lot of experience on the part of the project managers to make the correct calculations. Managers who have little skills and knowledge working with the projects will surely make plenty of mistakes applying CPM or PERT because these techniques assume that managers already have plenty of understanding about the projects at hand and that each critical activity will be done in a known sequence, independent of one another. If the sequence is disrupted for any reason, the project could easily fail. Only when a job is expensive or important should this kind of detailed analysis be applied. Once these skills are crafted, however, project managers will have an extremely valuable tool that will enable them to remain in control of their projects from start to finish (Anderson, p. 338).