Learning Objective

Calculate instrumental path, job float, beforehand begin dates, and late begin days.

The crucial pathSequence of tasks through the network that results in the latest completion day of the task. is the route with the network that outcomes in the latest completion day of the job.

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If any kind of task on the crucial course is delayed, the completion of the job will certainly be delayed by an equal amount. It is the route via the biggest full duration. To recognize the instrumental path, include the amount of time estimated for the duration of each activity to the previous task to recognize which path via the netjob-related has actually the longest complete duration, as shown in Figure 8.15 "Critical Path". Durations are indicated in days. The instrumental course through these work takes at least eight days. Activities on the important route are shaded.

Figure 8.15 Critical Path


Early Start Dates

Starting days have the right to be assigned to each activity by doing a forward passThe procedure of determining the earliest beginning day for each activity by beginning at the project begin date and also adding the activity durations, resulting with the beforehand complete day for the project. proceeding from left to best in the network diagram start via the task begin date. The days derived by this strategy are the beforehand start (ES) datesThe soocolony day an activity deserve to start established by the task begin date and also the durations of its predecessor activities.. The at an early stage begin date for an activity is the earliest date the activity deserve to start. The estimate considers durations and resource availcapability calendars. To calculate beforehand begin dates, begin with the job begin date and also asauthorize that date as the begin day of activities that have no predecessor activities. Follow these steps to calculate the early on start dates of subsequent activities, assuming finish-begin relationships:

Add the predecessor activity’s duration to its start day. Add the lag time or subtract the lead time. Refer to the reresource calendar (or calendars) that applies to the world and also equipment crucial for the task, and add the variety of off-days that the activity would expectations on those calendars. Asauthorize the calculated date as the beforehand start day of the successor task.

Forward Pass for John’s Move

John begins planning his relocate to Atlanta the very same day he accepts the project. The begin day in this example is Monday, November 29, 2010. Tasks 1.1 and 2.1 have the right to both begin on that day, so the early on start dates for tasks 1.1 and 2.1 are November 29. John calculates the beforehand start day for the activities. A partial list is provided below. Compare the number listed below and also the figure in the next sidebar. Observe that John is willing to work-related on weekends, yet activity 2.2.3 is delayed by 2 days because one of the moving companies did not provide bids on the weekend. Observe that task 2.3 has a lead time of at some point, however that relationship is in between task 2.1 and 2.3. The netoccupational route from task 1.3 is much longer, so the lead time with task 2.1 is not thought about in calculating the early begin day 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 system programs to assist in the process, however the task manager must understand the procedure well enough to acknowledge computer system errors. Computer software program have to be merged with common sense or great judgment.


FloatThe amount of time an task can be delayed from an early begin without delaying the completion day., periodically referred to as sabsence, is the amount of time an task, network-related course, or job have the right to be delayed from the at an early stage start without transforming the completion date of the job.

Total Float

Total floatThe amount of time the project start day can be delayed without delaying the task completion date. is the difference in between the finish day of the last task on the crucial course and the task completion day. Any delay in an activity on the instrumental path would mitigate the amount of complete float accessible on the project. A job have the right to additionally have actually negative floatThe amount through which the early completion day exceeds the project completion day., which suggests the calculated completion date of the last activity is later than the targeted completion day established at the start of the task.

Float in John’s Move

The last activity in John’s relocate has actually a very early start day of December 28 and a duration of one day. John could start work on Wednesday, December 29. John’s first day at work-related is Monday, January 3, so the task has actually a full float of 5 days.

Figure 8.17 Total Project Float


Late Start Dates

The next action is to job-related through the network-related diagram from best to left start with the mandated completion day, which is a milerock that is collection in the job plan. Subtract the duration of each activity in each route to determine the latest day the activity could start and also still accomplish the job completion date. Resource calendars have to be taken into consideration in the backward pass as well as the forward pass.

To calculate late begin dates, start via the task completion milestone and assign that day as the finish date of its predecessor activities. Follow these procedures to calculate the late begin dates of predecessor tasks, assuming finish-start relationships:

Subtract the predecessor activity’s duration from its late finish date. Subtract the lag time or include the lead time to the late finish date. Refer to the resource calendar (or calendars) that uses to the human being and also tools important for the activity, and subtract the number of off days that the task would certainly expectancy on those calendars. Asauthorize the calculated day as the late begin day of the predecessor task.

The difference between the at an early stage start day and also the late start day for activities on the critical route is normally the exact same as the full float, unmuch less the activities are affected by the reresource calendars in different ways in the forward and backward pass. For example, if a piece of key tools is only accessible for a couple of days, tasks that depend on it have the same begin and complete dates in the forward and also backward passes.

Free Float

If tasks that are not on the crucial course have a distinction in between their beforehand begin day and their late start date, those activities have the right to be delayed without affecting the task completion day. The float on those tasks is called complimentary floatThe time an task that is not on the crucial course can be delayed without delaying the begin of a follower activity..

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Key Takeaway

To calculate complete project float, begin at the begin day and add the duration of each activity in each feasible course with the netjob-related diagram, including nonfunctioning days from the resource calendars, to identify the early job finish date. The longest course with the network-related is the critical path. The distinction in between the at an early stage end day and also the forced completion day of the project is the full task float, and also the begin day of each task is the beforehand begin day. To calculate the late begin days, start with the required project completion day and work backward, subtracting the duration of each task through each possible pathmethod.


The course with the netoccupational diagram that has the longest total duration is the __________ course. The difference in between the sum of the activity durations alengthy the instrumental course and the task completion date is the project _______. If 2 sequential activities overlap and also the successor task can start 3 days prior to the predecessor begins, those 3 days are referred to as _________ time. If the last task in the crucial route has actually a completion day that is five days later on than the task completion date, the task has actually a _______ _________ (two words) of 5 days. What is the difference between free float and task float? If an activity has actually a duration of 3 days, just how carry out you calculate the finish date in a method that considers availcapacity of the sources for that activity? What would certainly be an instance of lag time between 2 activities?

Project Float

Consider a project in which you have actually been involved that skilled unexpected delays. Describe just how the project’s manager faced the delays. Specifically, consider if the delay was because of an activity that was on the project’s critical path, if people or sources were diverted from various other tasks, or if complimentary float existed in the original schedule. Describe the ultimate result on the project’s completion day.