6.5 Develop Project Schedule Process

The Develop Project Schedule Process results in the project schedule, which is the planned start and finish dates for all project activities.

Scheduling involves the project manager and the project team, but it's not very likely that the schedule will be completed and approved in one sitting.

In fact, creating a schedule is usually the most difficult of the project management processes because it’s one of the more iterative and integrative processes both in its initial development and because most changes that occur in the project will, in the end, impact the schedule.

Creating the schedule relies on outputs from other processes, including the activity list, project schedule network diagrams, activity resource requirements, resource calendars, duration estimates, and the project scope.

Schedule development doesn’t just rely on the resource requirements and duration of the activities. It must also consider the activity attributes, milestones, assumptions, constraints, and risks.

This entire collection of documents supporting the schedule logic is called the schedule data.

At a minimum, the schedule data includes the milestones, activities, activity attributes, assumptions, and constraints.

Performance Measurement Baseline

Performance Measurement Baseline

Schedule network analysis is the various techniques used to analyze and apply scenarios to the schedule.

Schedule network analysis includes the critical path method, critical chain method, resource leveling and smoothing, what-if analysis, and schedule compression, as well as any other analysis methods employed by the project manager.

The project schedule will undergo some manner of approval or sign-off. Once approved, the schedule baseline comes into existence.

The schedule baseline is not a document that is specifically created. It just comes into existence when the schedule is approved, and it's the project schedule with approved changes incorporated into it.​

Another way of thinking about the schedule baseline is that it's the latest approved version of the project schedule.

Schedules may change as a direct or indirect result of variance analysis, corrective actions, preventative actions, or approved changes to any project component.

Once the schedule baseline is established any requested changes affecting the schedule should be directed through Integrated Change Control.

Complex projects may require a schedule change control system. Like other change control systems, this one is part of the project change control system, and it ensures that the review, approval, and documentation processes for schedule changes are followed.

Some people also mistakenly refer to the project plan and project schedule interchangeably, but the two are not the same.

We know from the chapter four that the project plan is a comprehensive document that drives the entire execution, management, and control of the project, of which the project schedule is just one component.

There is no single best way for the schedule to be represented. There can also be alternative views of the schedule for different audiences though they are derived from the detailed project schedule.

Milestone charts, bar charts, and project schedule network diagrams are commonly used.

At a minimum, the project schedule must clearly show the planned start and finish dates for all project activities.

Develop Schedule process

Develop Project Schedule Process Decomposition

Develop Project Schedule Process: Inputs

  • Activity list
    The activity list is the complete list of project activities that are needed to produce the work packages.
    It's decomposed from the WBS work packages. It’s the source document this process needs to identify what activities need put on the schedule.
  • Activity attributes
    The activity attributes document is a companion to the activity list. It provides sufficient detail to fully describe the activity, and any supplementary information about activity, such as its relationships, constraints, assumptions, dependencies, and responsible people.
  • Project schedule network diagrams
    Project schedule network diagrams (PND) are schematics that show the sequencing of activities and their interrelationships. These are created when activity sequencing takes place.
  • Activity resource requirements
    The activity resource requirements document describes the resource needs at the activity level, which can be aggregated up to the work package level. It focuses on the resource types and quantities needed.
  • Resource calendars
    This may be one or more calendars that identify when people, equipment, and material are available and for what lengths of time.
    For example, a resource calendar would indicate when supplies were expected to arrive and in what quantity.
    There is also a composite resource calendar that shows the availability of named human resources on the project as well as their skills.
    These calendars are useful in duration estimating because scarcity or unavailability of resources may increase the duration of activities.
  • Activity duration estimates
    Activity duration estimates are the work periods required to complete a scheduled activity. There are many factors that influence duration, including resource availability, multi-tasking, and risks.
  • Project scope statement
    Assumptions and constraints are factors in activity durations. The project scope statement details the measurable goals, objectives, deliverables, and requirements of the project, and what the acceptance criteria of deliverables will be.
    It also describes the work required to meet all objectives and deliverables of the project, and it also contains milestones, assumptions, risks, and costs.
  • Enterprise environmental factors
    Any of the many enterprise environmental factors and systems that influence the project should be considered when developing the schedule, the most common of which is a scheduling application.
  • Organizational process assets
    Organizational process assets are the source of existing policies, processes, organizational data, and knowledge.
    These assets include the entire collection of formal and informal methodologies, policies, procedures, plans, and guidelines, as well as the organization's "knowledge base," which includes historical performance data, labor information, service and maintenance history, issue and defect history, project files, and financial data.

Develop Project Schedule Process: Tools and Techniques

  • Schedule network analysis
    These are any analysis techniques applied to preliminary schedule models that result in a final project schedule.
    Techniques include the critical path method, critical chain method, resource leveling, resource smoothing, and schedule compression.
  • Critical path method
    CPM is a schedule network analysis technique uses the critical path, early and late starts, and early and late finishes to manage critical activities within the schedule.
  • Critical chain method
    CCM is a schedule network analysis technique that addresses resource scarcity. It uses buffers strategically placed on the critical chain to allow for potential bottlenecks.
  • Resource leveling
    Resource leveling is a schedule network analysis technique that aims for a consistent and steady demand for resource types instead of having high demand periods followed by low demand periods.
  • What-if scenario analysis
    What-if scenario analysis: A technique for schedule network analysis which applies simulations to the project schedule to assess the feasibility and agility of the project schedule under adverse situations.
    Monte Carlo analysis is a form of what-if scenario analysis.
  • Applying leads and lags
    Leads and lags speed up and slow down when activities can start.
  • Schedule compression
    Schedule compression uses crashing (adding more resources) or fast-tracking (allowing activities to be done in parallel) in order to reduce the duration of the project.
  • Scheduling tool
    Project scheduling most often requires the use of automated scheduling tools to assist in developing, analyzing, and tracking scheduled activities.

Develop Project Schedule Process: Outputs

  • Project schedule
    The project schedule specifies the planned start and finish date for each scheduled activity.
    As specific resources are assigned, the project schedule includes those assignments. Project schedules are presented in different manners, some in summary form and some in detailed form.
    These include project schedule network diagrams or bar charts, such as Gantt charts.
  • Schedule baseline
    The schedule baseline is the approved project schedule that will continue to be updated as any scheduling change requests are approved.
  • Schedule data
    The schedule data contains supporting information for the project schedule. It at least contains the milestones, activities, activity attributes, assumptions, and constraints.
  • Project document updates
    Developing and managing the project schedule is likely to result in changes to project documents.

Activity Constraints

We usually face limitations on when activities can start and end.

Those constraints can be imposed by the customer, sponsor, regulations, vendors, industry guidelines, market conditions, environmental or weather conditions, and even the project team.

Milestones, whether established by the sponsor, customer, or the project team, may also result in activity constraints.

Constraints can also be applied to the project as a whole, such as a project must be started or completed by a predetermined date.

When constraints are applied to activities, they serve to restrict when the activities can begin or end.

Use of constraints may also force mandatory leads and lags in the schedule.

There are four types of constraints:

  1. Start No Earlier Than (SNET or SNE)​
    The activity can't start until a predetermined date.
  2. Start No Later Than (SNLT or SNL)​
    The activity must be started before but not later than a predetermined date.
  3. Finish No Earlier Than (FNET or FNE)​
    The activity must be finished after a predetermined date.
  4. Finish No Later Than (FNLT or FNL)​
     The activity must be finished before a predetermined date.

Float and Slack

Float, also referred to as slack, is how much leeway an activity's duration has before it causes delays in successor activities or the project itself.

There are three types of float we need to know as well as how to calculate them.

A calculating float is discussed fully in the section on the Critical Path Method, but a brief overview is necessary here.

To determine float, we have to return to project schedule network diagrams.

Project Schedule Network Diagram

Project Schedule Network Diagram

In this project schedule network diagram, activity A has a duration of 10 days, activity B has a duration of 12 days, and activity C has a duration of 5 days.

activity C has a normal finish-to-start relationship with both activity A and B (both A and B have to finish before activity C begins).

 There are two progressions of activities that will occur on this project:

  1. Start to activity A to activity C to End, which will take 15 days,
  2. Start to activity B to activity C to End, which will take 17 days.
  • Free Float
    Free float or free slack is how much leeway an activity has before an extension to its duration delays the start of a successor activity. In the sample diagram, Activity A has a free float of two days before any delay impacts Activity C.
    This is because Activity B will take 12 days to complete, so Activity A can slide by up to two days before it causes a delay in starting work on Activity C.
    We should take notice that Activity B has no float because any delay in its completion will cause a delay to Activity C's start.
  • Total Float
    Total float or total slack is how much leeway an activity has before an extension to its duration delays the end date of the project.
    By looking at the sample diagram, we can see that the total project duration is 17 days.
    Since the combined duration of Activity A and Activity C is 15 days, Activity A has a total float of two days as does Activity C because either or both can slide a total of two days without lengthening the duration of the project.
    Total float and free float are not always the same, as coincidentally they are in this example.
  • Project Float
    Project float or project slack is how much leeway the overall project has before delays will cause it to exceed the ending constraint date.
    Continuing to use the example, if the customer required the project to be completed 20 days after it started, but total duration is only 17 days, the project has 3 days of project float.
  • Negative Float
    A negative float can occur, but it's indicative of a scheduling problem usually the result of unrealistic milestones or other constraints forced into the schedule.
    The negative float should be resolved by reworking the schedule or some form of schedule compression (crashing or fast-tracking).
    For example, a milestone for the signing of a contract is set for August 15th, but its preceding activity (drafting the contract) isn’t scheduled to complete before August 18th. The activity has a float of negative three.

Critical Path

Many people mistakenly use the term critical path to refer to an important set of activities within a project.

However, the critical path actually refers to the set of sequenced activities in which an extension to their durations will cause the project’s duration to extend.

In other words, the critical path is the set of sequenced activities that have no float.

There can be multiple critical paths within a project, and it's possible for the critical path to change as schedule changes occur.

It's important to know what the critical path is a project so that its activities can be monitored closely.

Critical Path

Critical Path

The critical path in this project is Start - Activity B - Activity C - End because an extension to the duration in any of these activities will cause the project's duration to extend.

Finding the critical path is done by evaluating the combined durations of all the different paths, and finding the one with the longest duration.

Continuing to use the same example, there are only two possible paths through this diagram:

Start to A to C to End ⇒ 0 + 10 + 5 + 0 = 15

Start to B to C to End ⇒ 0 + 12 + 5 + 0 = 17

With a duration of 17 days, activities B and C are on the critical path.

Let's now look at the critical path on a slightly more complicated example;

Project Schedule Network Diagram

Project Schedule Network Diagram

We’ll start again by finding each unique path through the diagram:

  • START - A - E - H - END
  • START - B - D - G - H - END
  • START - C - F – H - END
  • START - B - D - E - H - END
  • START - B - D - F - H – END

Next, let’s determine the duration of each path:

  • START - A - E - H – END ⇒ 0 + 6 + 8 + 4 + 0 = 18
  • START - B - D - G - H – END ⇒ 0 + 4 + 2 + 1 + 4 + 0 = 10
  • START - C - F – H - END ⇒ 0 + 10 + 12 +4 + 0 = 26
  • START - B - D - E - H - END ⇒ 0 + 4 + 2 + 8 + 4 + 0 = 18
  • START - B - D - F - H - END ⇒ 0 + 4 + 2 + 12 + 4 + 0 = 22

The path that is 26 periods is the longest in duration, so it is the critical path.

Schedule Compression Techniques

Schedule compression is used to decrease the duration of the project or specific activities.

It can also be used as a corrective action to bring what is actually occurring back in line with what was planned for in the schedule.

There are two ways to compress the schedule:

  1. Crashing: Adding more resources to the activity or project.
  2. Fast-Tracking: Allowing activities to occur in parallel that would normally have been done sequentially.

Crashing adds more resources, usually personnel, in order to decrease an activity's duration.

For example, an activity assigned to one person with a duration of 10 days might be reduced to six days if two people were assigned to it. 

When crashing is an option, the decrease in the activity's duration is not always linear to the increase in resources.

If it would take two people two weeks to complete an activity, adding four people to the activity does not automatically decrease its duration to one week.

This is because there's almost always a productivity loss as more resources are added, and there is a point when additional resources will actually begin increasing the activity's duration.

Crashing results in more cost, whether in labor or equipment, so there are also budgetary considerations.

Fast-tracking allows multiple activities to occur simultaneously when they were previously sequential.

Fast-tracking essentially cheats the finish-to-start (FS) relationship by creating leads.

For example, if the printing of a catalog cover is not normally started until after the catalog's contents have been printed, fast-tracking would allow the catalog cover to be printed before the catalog itself had been printed.

Since fast-tracking is essentially adding leads to activities, it has the same drawbacks –namely increasing risks and the likelihood of quality and rework issues if the risks aren't properly managed.

What-If Scenarios

Applying what-if and other scenarios against the schedule can be used to point out potential trouble spots should certain conditions occur.

What-If Scenarios

What-If Scenarios

For example, inclement weather scenarios could be applied against a project schedule that relies on fair weather conditions to see what impact a 1-, 2-, or 3-day rain delay would have during portions of the project.

Scenarios can also help identify alternative approaches.

Though more commonly discussed in terms of risk, Monte Carlo analysis is one schedule scenario technique.

Monte Carlo analysis is a computer-driven simulation technique that applies different variables to the schedule, and the results can identify high-risk and vulnerable areas within the schedule.

Monte Carlo analysis requires specialized skills to perform; however, effective scenarios for most projects can also be accomplished by making temporary changes to the schedule and viewing the results.

Resource Leveling

In the activity resource estimating process the resource types needed for each activity were identified, and now that activity duration is known and the activity is sequenced on the schedule timeline, we can see when resource types will be needed.

Resource intensity shows when and how many resources are needed at a particular time within the project.

For example, if we have three concurrent activities on the schedule that each needs four programmers to complete, the resource intensity for programmers at that point in the project is 12.

Resource leveling

Resource leveling

But what happens if only eight programmers are available?

Resource leveling techniques match the resource needs of the project with the organization's ability to provide resources.

When specific resource types are scarce, there are only a few options if the project budget doesn't allow for procuring them from outside the project.

One is that the higher priority activities can have the scarce resources allocated to them, first and the dates of the other activities staggered so that the resource intensity is lowered.

Another option is to use different but underutilized resource types for some activities, though this is not always possible.

In the preceding example where 12 programmers are needed in week three but only eight are available, if activity A were most critical then four programmers would be assigned to it so that its duration and sequencing remains intact.

How the remaining pool of four programmers would be allocated depends on the importance of the remaining two activities, how much float they have, and what resource requirements the successor activities need.

Critical Path Method

The critical path method (CPM) involves identifying and analyzing the activities that have the least flexibility in the project schedule. We've already seen some simple examples of how to identify the activities on the critical path.

But the critical path method combines many of the techniques we've seen along with some new analysis techniques.

CPM requires us to be proficient in project schedule network diagramming, calculating float, and determining the early start, early finish, late start, and late finish for activities and the project.

Let's first review some terms and look at a few new ones:

  • Project schedule network diagram
    The schematic showing the sequenced project activities.
    There are two diagramming methods: Precedence Diagramming Method (PDM), which produces activity-on- node (AON) diagrams, and the Arrow Diagramming Method (ADM), which produces activity-on-arrow (AOA) diagrams.
  • Network path​
    The sequence of activities from the start of the project to the end of the project. Only in the cases of very simple projects will there be only one network path.
  • Critical path
    The network path in which any lengthening of its duration will extend the project's end date. The common definition of the critical path is those set of sequenced activities that have zero floats.
  • Critical activity
    Any activity that is on the project's critical path(s).
  • Float/Slack
    A general term that indicates how much flexibility there is in the activity's duration. Free float identifies how long the activity's duration can extend before successor activities are delayed.
    Total float refers to how much float the activity has without affecting the project's duration.
  • Forward / Backward pass: Refers to whether we traverse forward through the network diagram, from start to end, or whether we traverse back through the network diagram, from end to start. Some calculation methods for a late start and late finish require backward passes.
  • Early start (ES)
    The earliest an activity can begin without affecting any dependencies.
  • Early finish (EF)
    The earliest an activity can complete without affecting any dependencies.
  • Late start (LS)
    The latest activity can begin without affecting any dependencies.
  • Late finish (LF)
    The latest an activity can complete without affecting any dependencies.

Critical Chain Method

While the critical path is the sequence of activities with the longest duration, the critical chain is the longest sequence of dependent (and not necessarily sequential) activities that prevent the project's duration from being any shorter.

Critical Chain Method

Critical Chain Method

The Critical Chain Method (CCM) recognizes that crucial events may not be sequential nor may they be even within the same project. The primary difference between the critical chain method and the critical path method is its approach to the schedule.

The critical chain method can be thought of as encouraging a relay race within the project team against the schedule while the critical path method focuses on maintaining and meeting the schedule.

First proposed in 1997 in the book "Critical Chain" by Eliyahu Goldratt, the critical chain is a continuum of his Theory of Constraints in manufacturing that focuses on addressing production bottlenecks in order to improve the throughput of the overall production system.

When applied to project management, this constraint is most usually a scarcity of human resources, so critical chain puts buffers of reserve time at the end of the project and at important junctures on the critical chain.

Creating critical chain buffers is also a way to mitigate risks relating to resource scarcity.

If we think about what we've learned thus far about scheduling, the methods available to us for dealing with uncertainty were to pad activity durations or use a large chunk of reserve time within the project.

Buffers move this reserve time out of the activity duration estimates and put it at strategic junctures on the critical chain.

While both approaches have the same end in mind of adding slack within the schedule, the critical chain method takes this slack (as buffers) and makes it visible to all and explicitly managed.

Buffers also serve as an additional management tool. If activities extend their duration, they draw time from a downstream buffer, and this shows up as a penetration into the buffer.

This penetration, along with the work completed, establishes a "buffer burn rate" letting us know at a glance at what might be a schedule performance problem.​

For example, if there’s buffer penetration of 60% when the work completed on the critical chain stands at only 10%, this would probably be an indication of a performance problem or a buffer that wasn’t set too low for the potential risks.

There are many different approaches to the critical chain method:

Durations

  • Drastically reduce activity duration estimates by up to 50%. Track the amount of time cut because it will be the basis for buffers that will later be inserted into the schedule.

Resources

  • Eliminate resource contentions in the project.

Critical Chain

  • Make several passes through the project looking for major dependencies and risks related to those dependencies.
  • Build an initial critical chain of these dependencies from the start to the end of the project.
  • Look for the minimum resource needs for critical chain activities.
  • Thoroughly review deliverables, activity inputs and outputs, and risks with the resources of critical chain activities. This may uncover additional dependencies.
  • Identify high-risk junctures in the critical chain, for instance, where a delay in a deliverable hand-off will adversely affect downstream activities.

Buffers

  • From the "bucket" of time cut from the original duration estimates, reduce it by another 25-35%. For example, if the original duration estimates were reduced by a total of 100 days, reduce it to 75 days.
  • Allocate the reserve time in two areas: At critical, high-risk junctures in the schedule, and as an overall project buffer just before the end of the project.

Buffer Management

  • Monitor the buffer penetration, consumption, or "burn-rate." Buffer consumption indicates that a planned-for risk has occurred.
  • Depending upon how much of the buffer has been consumed, and how much more is expected to be consumed, it may be necessary for corrective actions to be taken.

Precedence Diagramming Method

There are different approaches to calculating early start, late start, early finish, and late finish, the method shown here is the "brute-force" method. It requires us to fully diagram the path and run through all the calculations.

Overall, this takes longer, but it is less to memorize. As we get better and more familiar with the technique, there are lots of shorter methods we can learn.

When presented with a critical path, float, or ES, LS, EF, LF question, we're going to solve it by:

  1. Creating the project PDM diagram.
  2. Determining the critical path(s).
  3. Calculating each activity's float.
  4. Determining the early start and early finish of each activity.
  5. Determining the late start and late finish of each activity.

Creating a PDM Diagram

To make our diagramming easier, we need to create a table of all the activities, their predecessors, and their durations. 

Creating a PDM Diagram

Creating a PDM Diagram

On the PMP examination, some questions may provide this information textually, so we’ll need to convert it to tabular form;

  1. Begin by drawing the starting node. 
  1. Next, draw the activity nodes that have the starting node as their predecessor and connect the nodes. As activities are added, put the duration above the activity node.
  1. Continue adding the successor activity nodes and drawing the relationships. Any time there are multiple predecessors; there'll be a dependency between the successor activity and one or more other paths in the diagram.
    The relationship should be assumed to be a finish-to-start unless otherwise indicated.
    A few more activities from the table are shown in this diagram.
  1. After the activities are diagramed, double-check everything against the table of activities.

Finding the Critical Path

The critical path is the network path with the longest duration, so we’ll have to find each path in the diagram and sum the duration of each of its activities.

We’ll continue to use the PDM diagram we created in the earlier section throughout this example.

  1. Start by making a forward pass (Start to End) through the diagram and find all the unique paths through it.
    There are three paths through this diagram:
  • Start - A - B - C - D - End
  • Start - E - F - C - D - End
  • Start - G -H - I - D - End
  1. Next, sum the duration of each activity on the path:
  • Start - A - B - C - D – End ⇒ 2 + 5 + 3 + 4 = 14
  • Start - E - F - C - D – End ⇒ 4 + 6 + 3 + 4 = 17
  • Start - G -H - I - D – End ⇒ 1 + 8 + 2 + 4 = 15
  1. The critical path(s) is the one that has the longest duration.

The path Start - E - F - C - D - End is the critical path with duration of 17 units.

The activities E, F, C, and D are thus critical activities and will have zero floats.

Calculating Float

Calculating float requires either a completed node with some combination of an early start, early finish, late start, and late finish supplied, or we have to utilize the network diagram.

There are three kinds of float: free float, total float, and project float;

  • Project Float
    Project float is easy. It's only applicable when there's a duration constraint on the entire project.
    Using our continuing example, we know that the critical path (longest duration) is 17 periods. If the project had a constraint of 20 periods, then the project float would be three periods.
  • Free Float
    Free float is how long an activity's duration can increase without impacting the start of any successor activities. Free float requires that we know the early start of activities because it’s calculated by taking the early start of the successor activity minus the early start plus the duration of its predecessor activity.
    The steps for calculating the early start are shown in the next section, but below is a completed diagram with the early starts for all activities filled in.
Calculating Float

Calculating Float

To calculate the free float for activity H:

  • Activity H Free Float = ES of Activity I – (ES of Activity H + Duration of Activity H)
  • Activity H Free Float = 10 – (2+8)
  • Activity H Free Float = 0
  • Activity H has no free float even though it isn’t on the critical path.
  • Let’s see the free float for the activity I:
  • Activity I Free Float = ES of Activity D – (ES of Activity I + Duration of Activity I)
  • Activity I Free Float = 14 – (10+2)
  • Activity I Free Float =2
  • Total Float
    For total float, we're looking for how much an activity's duration can extend without pushing out the project's duration.
    In order to get the total float, we have to know the duration of the critical path and the duration of the network path the activity in question is on.
    Total Float = (Duration of Critical Path – Duration of Network Path Containing the Activity in Question)
    Let's return to the unique network paths through our diagram:
    Start - A - B - C - D - End: Duration = 14
    Start - E - F - C - D - End: Duration = 17 (critical path and project duration)
    Start - G -H - I - D - End: Duration = 15
    What's the total float for activity B? It'll be 3 because the total float for any non-critical activity on the first path will be three; 17 - 14 = 3
    Activities G, H, and I would each have a total float of 2 because of 17 - 15 = 2.
    What about the total float for activity C? Don't get fooled by questions such as this. Any activity on the critical path has zero floats even if that activity is on other paths.

Calculating Early Start and Early Finish

The early start is calculated by making a forward pass through the diagram and adding the activity's duration to the early start of the predecessor activity and adding one.

Calculating Early Start and Early Finish

Calculating Early Start and Early Finish

Let's look again our project schedule network diagram immediately after we added durations to the activities.

  1. Starting with the left-most activities with the Start node as their predecessor, set their early start to 1.
  2. The early finish of an activity is its early start plus its duration minus one. So for activity A, its EF is 1 + 2 – 1 = 2.
  3. The early start of subsequent activities is the EF of its predecessor activity plus one. Activity B’s ES is 3 (activity A EF of 2 plus 1).
  4. When an activity has multiple predecessors (like activity C does), its ES is based on the greatest early finish of its predecessors. For activity C, we use the EF of activity F.

Calculating Late Start and Late Finish

Unlike the earlier calculations where we worked forward through our diagram, we have to work backward through our diagram to get the late start and late finish for each activity.
Let’s begin with the network path with the longest duration (which is the critical path).

Calculating Late Start and Late Finish

Calculating Late Start and Late Finish

  1. First, we can easily address the late finish of the last critical path activity. In our example, activity D’s late finish will be the same as its early finish (which is 17).
    Activity D is the last activity node in our diagram, but if there were other non-critical activities that had the end node as their successor; their late finishes would also be the same as the LF for the last critical path activity (which is 17).
  1. For the last critical path activity, its late start will also be the same as its early start, which is 14.
  2. Now we can continue working backward along the critical path. From activity D, we’ll move back to activity C and calculate its late start and late finish.
  • For activity C, its late finish is activity D’s late start minus 1.
    Activity C LF = 14 – 1 = 13
  • Activity C’s late start is its late finish minus its duration plus 1.
    Activity C LS = 13 – 3 + 1 = 11
  • Activity F’s late finish is activity C’s late start minus 1.
    Activity F LF = 11 -1 = 10
  • Activity F’s late start is its late finish minus its duration plus 1.
    Activity F LS = 10 - 6 + 1 = 5
  • Activity E’s late finish is activity F’s late start minus 1.
    Activity E LF = 5 –1 = 4
  • Activity E’s late start is its late finish minus its duration plus 1.
    Activity E LF = 4 – 4 + 1 = 1
  1. Now we’ll do the same thing for the next longest path (Start - G -H - I - D – End) followed by the last path in our example (Start - A - B - C - D – End).
  • If an activity’s LS and LF have already been calculated from a prior backward pass, don’t recalculate them; use the prior calculation and carry it on in your current backward pass.
  • If an activity has multiple successors, we use the LF from the successor that is the least (as shown in step 5).
  1. Though not applicable in our example, when calculating the late finish for an activity that has two or more successor activities, you use the LS of the successor activity with the least start date.

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