Learning Objective
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The critical path is the path through the network that results in the latest completion date of the project. If any activity on the critical path is delayed, the completion of the project will be delayed by an equal amount. It is the path with the greatest total duration. To determine the critical path, add the amount of time estimated for the duration of each activity to the previous activity to determine which path through the network has the longest total duration, as shown in Figure 8.15 “Critical Path”. Durations are indicated in days. The critical path through these tasks takes at least eight days. Activities on the critical path are shaded. Figure 8.15 Critical Path
Early Start DatesStarting dates can be assigned to each activity by doing a forward pass proceeding from left to right in the network diagram beginning with the project start date. The dates derived by this method are the early start (ES) dates. The early start date for an activity is the earliest date the activity can begin. The estimate considers durations and resource availability calendars. To calculate early start dates, begin with the project start date and assign that date as the start date of activities that have no predecessor activities. Follow these steps to calculate the early start dates of subsequent activities, assuming finish-start relationships:
Forward Pass for John’s MoveJohn begins planning his move to Atlanta the same day he accepts the job. The start date in this example is Monday, November 29, 2010. Tasks 1.1 and 2.1 can both start on that day, so the early start dates for tasks 1.1 and 2.1 are November 29. John calculates the early start date for the activities. A partial list is provided below. Compare the figure below and the figure in the next sidebar. Observe that John is willing to work on weekends, but activity 2.2.3 is delayed by two days because one of the moving companies did not provide bids on the weekend. Observe that activity 2.3 has a lead time of one day, but that relationship is between activity 2.1 and 2.3. The network path from activity 1.3 is longer, so the lead time with activity 2.1 is not considered in calculating the early start date of 2.3. Figure 8.16 Early Start Dates Determined by a Forward Pass
Doing this process manually is error prone and time consuming. Fortunately, there are computer programs to assist in the process, but the project manager must understand the process well enough to recognize computer errors. Computer software must be combined with common sense or good judgment. FloatFloat, sometimes called slack, is the amount of time an activity, network path, or project can be delayed from the early start without changing the completion date of the project. Total FloatTotal float is the difference between the finish date of the last activity on the critical path and the project completion date. Any delay in an activity on the critical path would reduce the amount of total float available on the project. A project can also have negative float, which means the calculated completion date of the last activity is later than the targeted completion date established at the beginning of the project. Float in John’s MoveThe last activity in John’s move has an early start date of December 28 and a duration of one day. John could start work on Wednesday, December 29. John’s first day at work is Monday, January 3, so the project has a total float of five days. Figure 8.17 Total Project Float
Late Start DatesThe next step is to work through the network diagram from right to left beginning with the mandated completion date, which is a milestone that is set in the project plan. Subtract the duration of each activity in each path to determine the latest date the activity could begin and still meet the project completion date. Resource calendars must be considered in the backward pass as well as the forward pass. To calculate late start dates, begin with the project completion milestone and assign that date as the finish date of its predecessor activities. Follow these steps to calculate the late start dates of predecessor activities, assuming finish-start relationships:
The difference between the early start date and the late start date for activities on the critical path is usually the same as the total float, unless the activities are affected by the resource calendars differently in the forward and backward pass. For example, if a piece of key equipment is only available for a few days, activities that depend on it have the same start and finish dates in the forward and backward passes. Free FloatIf activities that are not on the critical path have a difference between their early start date and their late start date, those activities can be delayed without affecting the project completion date. The float on those activities is called free float. Key Takeaway
Exercises
Project Float Consider a project in which you have been involved that experienced unexpected delays. Describe how the project’s manager dealt with the delays. Specifically, consider if the delay was due to an activity that was on the project’s critical path, if people or resources were diverted from other tasks, or if free float existed in the original schedule. Describe the ultimate effect on the project’s completion date. What is the time by which complication of an activity can be delayed without affecting the start of succeeding activities?Free float: It is the amount of time that the activity completion time can be delayed without affecting the earliest start time of the immediate successor activities in the network.
What is the amount of time that a task can be delayed without affecting the subsequent tasks?So, A float (or slack) in a critical path method (CPM) is the amount of time that a task can be delayed without causing any delay to Subsequent tasks and project completion date. 2.
What is the amount of time an activity can be delayed before affecting the overall schedule?Float, sometimes called slack, is the amount of time an activity, network path, or project can be delayed from the early start without changing the completion date of the project.
What is preceding and succeeding activities?Preceding and Succeeding ActivitiesActivities performed before given events are known asprecedingactivities(Figure 8.4), and activities performed after a given event areknown assucceeding activities.
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