Precedence Diagram Method and Critical Success Factors

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Precedence Diagram Method and Critical Success Factors

Project Management · Chapter 5: Project Management Tools and Analytical TechniquesSection 5.2 · lesson 31 of 7313 min · free with a free account

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In this lesson

Calculating early and late dates and identifying what must go right.

  • Calculate early start and early finish dates with a forward pass, including merge points
  • Calculate late start and late finish dates with a backward pass, including burst points
  • Identify the critical path where early and late dates match and apply lags to date calculations
  • Distinguish critical success factors from project objectives and the critical path, and give each factor a measure

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Transcript

Everything said in the video, section by section (1,941 words). Read along, or search it.

Opening Question

When Will the Hall Refit Finish

A volunteer committee is refitting a community hall. Seven jobs, a few days each, some waiting on others. When will the whole refit be done? And which jobs can't slip by a single day without moving that finish? A drawing alone can't say. This lesson turns the drawing into dates.

Definition

A Node Network With Date Calculation

The precedence diagram method is the node-based network, extended with date calculation. Every activity box carries its duration and four calculated dates, so the drawing that shows the logic also gives a schedule. A calculated schedule applies fixed arithmetic rules to the durations and the logic. It shows which activities govern the finish. And it's repeatable. Two people applying the same rules to the same inputs get the same dates, so the schedule can be checked and challenged.

Node Contents

Seven Items Including Four Dates

Each node carries seven items: an identifier, a name, and a duration in working days. Then four dates. Early start is the earliest day it can begin, and early finish the earliest it can be complete. Late start is the latest it can begin without pushing the project finish, and late finish the latest it can be complete. Early dates come from working forward from the start, and late dates from working backward from the finish.

Day Convention

Starting at Day Zero

Dates only mean something if everyone counts days the same way, so state the convention first. Here, the project starts at day 0, the very beginning of the first working day. Day 3 means the end of the third working day. Early finish equals early start plus duration. Start at 0 with 3 days of work, and you finish at day 3, having used days 1, 2 and 3. A successor with an early start of 3 begins at the start of day 4. The other common convention counts the first day as day 1. Mixing the two causes errors of exactly one day. Late dates use the mirror formula: late start equals late finish minus duration.

Pass Rules

Largest Finish Forward, Smallest Start Backward

The forward pass moves from the first activity to the last. An activity with no predecessor starts at day 0. One with a single predecessor starts when that predecessor finishes. A merge point, with two or more predecessors, waits for all of them, so its early start is the largest of their early finishes. Taking the smaller is a classic mistake. The backward pass mirrors it, from the last activity to the first. The last activity's late finish is the project duration. A burst point, with two or more successors, must finish early enough for every one of them, so its late finish is the smallest of their late starts. If one successor must start by day 9 and another by day 6, the activity must be done by day 6.

Worked Example

Seven Hall Refit Activities

Here's the hall refit, with every link finish-to-start, in working days. A, measure the hall, takes 3 days. B, the layout plan, takes 4, after A. C, order supplies, takes 2, after A. D, install wiring, takes 5, after B. E, build the stage, takes 3, after both B and C. F, paint the walls, takes 4, after C. And G, the final check, takes 2, after D, E and F.

Forward Pass

Early Dates and a Fourteen-Day Duration

Forward pass. A has no predecessor, so it starts at day 0, and finishes at 0 plus 3: day 3. B and C follow A, so both start at 3. B finishes at 7, and C at 5. D follows B: start 7, finish 12. E is a merge point. B finishes at 7, C at 5, and the larger governs. So E starts at 7, and finishes at 10. F follows C: start 5, finish 9. G merges D, E and F, which finish at 12, 10 and 9. The largest, 12, governs, so G runs from 12 to 14. So the project duration is 14 working days.

Backward Pass

Late Dates Working From Day Fourteen

Backward pass, from the end. G's late finish is the project duration, 14. Its late start is 14 minus 2: 12. D, E and F each feed only G, so each must finish by 12. D's late start is 7, E's is 9, and F's is 8. B is a burst point. It feeds D, which must start by 7, and E, by 9. The smaller governs, so B must finish by 7, and start by 3. C feeds E, by 9, and F, by 8. The smaller, 8, governs, so C's late start is 6. A feeds B, by 3, and C, by 6. A must finish by 3, so it can start by 0. A's late start is day 0, exactly where the forward pass began. The two passes agree.

Critical Path

Where Early and Late Dates Coincide

Now read off the critical path: the chain whose early and late dates coincide. A, B, D and G have identical early and late dates, and they join end to end, at days 3, 7 and 12. So the critical path is A, B, D, G. And 3 plus 4 plus 5 plus 2 is 14. C, E and F have late dates later than their early ones. They have room the critical chain doesn't.

Cross-Check

Four Paths and a Wiring Delay

Check against the longest-path idea. The network has four complete paths. A, B, D, G is 14 days. A, B, E, G is 12. A, C, F, G is 11. And A, C, E, G is 10. The longest is the same chain the dates found. If the two ever disagree, look for an arithmetic error. And a delay on that chain moves the finish. Suppose the wiring takes 7 days instead of 5. D now finishes at 14. G can't start until 14, so the project ends at day 16. The finish slips by exactly the two days D slipped. How far an activity off the path can slip is a question of float, in subchapter 9.6.

Quick Check

Early Finish at a Merge Point

Quick check, on a different network. Activity K follows three activities, whose early finishes are day 10, day 8 and day 8. K takes 3 days. What is K's early finish: day 11, day 13, or day 29? Pause and predict. Day 13. K is a merge point, so it waits for the latest predecessor, day 10, then adds its 3 days. Day 11 is the classic slip: taking the smaller finish gives dates that are too early. And early finishes are never added together.

Lags

Screed Drying Between Floor Activities

A lag is a fixed wait between two linked activities. It takes calendar time, but no work and no resources. A crew lays a floor screed, P, in 3 days. It must dry for 2 days before the covering, Q, which takes 2. Then a final clean, R, in 1 day. The drying is a lag on the link from P to Q, not an activity, because nobody works during it. Forward, P runs from 0 to 3. Q starts at 3 plus the 2-day lag, so at 5, and finishes at 7. R runs from 7 to 8. Backward, the lag is subtracted, and every early date equals its late date. The duration, 8, includes the lag, though no activity fills it.

Other Relationships

Start-to-Start and Finish-to-Finish Dates

The other relationship types apply the same idea to the dates they name. Start-to-start plus a lag: the successor's early start is the predecessor's early start, plus the lag. Finish-to-finish plus a lag: the successor's early finish is the predecessor's early finish plus the lag, and its start comes from subtracting its own duration. Where several constraints meet, the most restrictive governs. And label every link that isn't plain finish-to-start, or readers will misread the dates.

Critical Success Factors

Conditions That Must Go Right

A calculated schedule says which activities control the finish date. It doesn't say whether the project will be judged a success. A critical success factor is one of a few conditions that must go right, for the project to reach its intended outcome. If one fails, the project fails, whatever else goes well. It isn't an objective. An objective is a result the project is trying to achieve, like opening the hall by an agreed date, within budget. A factor is a condition that must hold to get there, like the committee approving the layout before materials are ordered. It can be checked while the project runs. And it isn't the critical path. Critical there means calculated. Here it means a judgment of what is decisive, and it may sit on an activity no calculation would flag. Factors are found through a short, structured conversation, not a calculation. First, restate the objectives in the sponsor's own words, and have the sponsor rank them. Second, ask the sponsor and the team, separately: what has to go right, and what would sink the project, whatever else we did? Third, compare the lists and merge duplicates. Fourth, cut to a short list, commonly five or six at most, and drop any factor whose failure alone wouldn't sink the project. The sponsor confirms the list, and it is reviewed whenever the plan is reconsidered.

Measures and Thresholds

Making Each Factor Observable

A factor nobody can observe can't be managed. So each one gets a measure, readable without opinion, and a threshold that says when to act. For the hall, the committee approves the layout. The measure is a signed approval, and the threshold is signed before materials are ordered. Electrical work is passed by a qualified inspector. The measure is the inspector's written pass, obtained before the stage is used. Enough trained volunteers. The measure is confirmed volunteers per work day, with a threshold of at least 6, two days ahead. These are examples, not standards. Morale is good is not a measure. A signed approval is.

Quick Check

Objective, Factor, or Critical Path

Quick check. A clinic's sponsor says: the new booking website must be live by March first, within the approved budget. Is that statement a critical success factor, a project objective, or the critical path? Pause, and decide. A project objective. It names a result, judged at the end: live, on a date, within budget. A factor would be a condition that must hold on the way, like clinic staff signing off the booking rules before the build. And a critical path is calculated, never declared.

Applied Example

Willowmere Festival Path and Safety Factors

Rosa coordinates the Willowmere Arts Festival. The organizers have two priorities: open on the announced day, and keep visitors safe. Her set-up tasks give a duration of 8 days. The critical path is site marking, the main stage, lighting and sound, and the safety walk-through: 1 plus 4 plus 2 plus 1. Training the volunteer marshals wasn't on that path, and her first thought was to treat it as routine. Then she asked what had to go right for safety. First, marshals trained and on the rota before the gates open, measured by a signed roster. Second, the walk-through passed at the first attempt, measured by the inspector's written pass. A walk-through held on time and failed is still a failure. So she watches the stage against its date, and the roster and the inspector's pass against their thresholds. The schedule asks what controls the date. The factors ask what would sink the festival.

Comparison

Precedence Method Versus Arrow Method

One last comparison. Older practice often used the arrow method, with activities on arrows and events in circles. Three differences matter. The arrow method supports only finish-to-start, while the precedence method handles all four relationship types, and lags. The arrow method needs dummy activities, and the precedence method needs none. And scheduling software is commonly built around the precedence method. Given the same logic, both give the same project duration.

Key Takeaways

Passes, Critical Path, and Success Factors

To recap. Forward pass: early start is the largest predecessor finish. Backward pass: late finish is the smallest successor late start. The critical path is where early and late dates match, and a delay on it moves the finish. And a critical success factor is a judged condition, tied to a measure and a threshold.

About Project Management at UPI Study

Project Management (Business 230) is a self-paced online course of 73 video lessons in 12 chapters, from starting and defining a project to planning, budgets, scheduling tools, proposals, contracts, execution, monitoring, closure, teams and certification. It carries a NCCRS credit recommendation for 3 semester credits.

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Why students take Project Management with UPI Study

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Universities that work with NCCRS

Project Management carries a NCCRS credit recommendation. These universities work with NCCRS; some are UPI Study's signed partners. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.

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FAQ

Questions students ask us

About Precedence Diagram Method and Critical Success Factors

How do you calculate early start and early finish in a forward pass?
Start activities with no predecessor at day 0, set early finish to early start plus duration, and give each successor the largest early finish among its predecessors. If activity K follows three activities finishing on days 10, 8, and 8 and takes 3 days, it starts at day 10 and finishes at day 13. Taking the smaller finish is a classic mistake that gives dates too early.
How do you calculate late start and late finish in a backward pass?
Set the last activity's late finish to the project duration, subtract each duration to get late start, and give each predecessor the smallest late start among its successors. If one successor must start by day 9 and another by day 6, the activity must finish by day 6. As a check, when the backward pass starts from the calculated duration, the critical start activity's late start comes back to day 0, where the forward pass began.
How do you identify the critical path using the precedence diagram method?
The critical path is the chain of activities whose early and late dates are identical and that join end to end from start to finish. In a hall refit where A, B, D, and G take 3, 4, 5, and 2 days, those four activities have matching dates and total 14 days. A two-day delay on any of them pushes the project finish two days later.
What is the difference between a critical success factor and a project objective?
A project objective is a result the project aims to achieve, while a critical success factor is a condition that must hold along the way for the project to reach that result. Opening a hall by an agreed date within budget is an objective. Having the committee approve the layout before materials are ordered is a factor, checked with a measure such as a signed approval and a threshold.

About the Project Management course

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Project Management (Business 230) carries a NCCRS credit recommendation for 3 semester credits. ACE and NCCRS have over 2,100 cooperating colleges that will consider accepting credits; the final decision is with the universities.
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$250, paid once, with lifetime access: all 73 video lessons, a practice quiz after each, the graded work and final exam, and an official transcript when you finish. Students who want several courses choose UPI Study PRO instead.
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It is self-paced with no deadlines. The 73 lessons total about 15 hours of video; most students add reading and practice time and finish in a few weeks to a few months, on their own schedule.
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