Scheduling fundamentals · Verbatim sources
The two terms are used as synonyms in most project-management writing. They are not synonyms. One names a drawing of logic; the other names a statistical estimating technique that happens to be drawn on a particular kind of network. This article defines each part of both, labels every field on the diagrams, and shows the arithmetic behind the numbers.
Every definition in the Definitions section is quoted verbatim from the cited source and enclosed in quotation marks. Nothing is paraphrased inside a quotation mark. Full source list at the end.
PMI's Lexicon of Project Management Terms defines a project schedule network
diagram as A graphical representation of the logical relationships among the
project schedule activities.
[1]
It answers one question: what must happen before what? Durations, dates, and float are layered onto it afterward by the critical path method. It carries no probability of any kind.
The same lexicon defines PERT as A technique used to estimate project duration
through a weighted average of optimistic, pessimistic, and most likely activity
durations when there is uncertainty with the individual activity estimates.
[1]
It answers a different question: how confident are we in the duration? It needs a network to run on, but the network is not the technique.
The historical PERT chart was drawn in the activity-on-arrow (event-oriented) style.
Wikipedia records that PERT relies "on arrow and node diagrams of activities
and events: arrows represent the activities or work necessary to reach
the events or nodes that indicate each completed phase of the total project."
[3] Because that arrow-style drawing was for
decades the only network most managers ever saw, "PERT chart" became a loose label for
any schedule network. Today, per the Wikipedia article on the critical path method,
Although the activity-on-arrow diagram (PERT chart) is still used in a few places, it
has generally been superseded by the activity-on-node diagram, where each activity is
shown as a box or node and the arrows represent the logical relationships going from
predecessor to successor.
[4]
One two-step workflow — write a draft, then edit it. The work does not move; the drawing convention moves it. Watch which element holds the duration.
The view is not called a PERT chart. Microsoft's support page states: A Network Diagram
is a graphical way to view tasks, dependencies, and the critical path of your project.
and Boxes (or nodes) represent tasks, and dependencies show up as lines that connect
those boxes.
[8]
Microsoft reserves the word PERT for the estimate, not the drawing:
You can enter the expected duration as part of a PERT analysis calculation, which takes
a weighted average of expected, pessimistic, and optimistic dates and durations, or you
can have Microsoft Office Project calculate it for you.
and By default, the PERT
analysis calculation gives the heaviest weight (4) to the expected information, and the
lightest weight (1 each) to the pessimistic and optimistic information.
[9] That is the same three-point technique the PMI
lexicon defines — carried out in a table of task fields, with no arrows involved.
A number written on an activity-on-node link is therefore never the predecessor's
duration. It is lead or lag: When you add lead time to a task, work on that task
overlaps work on its predecessor. When you add lag time, you delay the start time of the
successor task.
and Lag time creates a delay between two tasks that share a
dependency.
[10] Writing “FS − 5 d” next to a
5-day predecessor mixes the two: as an annotation it would mean a five-day lead, pulling
the successor five days earlier.
Not supported by any source cited here: that Microsoft invented or
flipped the convention, or that it did so because data is hard to print on a
line. None of the Microsoft pages above gives a reason, and the activity-on-node form is
described in the critical-path literature as having generally superseded
the
arrow form [4] without crediting any vendor. Treat
the ergonomic explanation as plausible but unsourced.
Quotations below reproduce the source wording exactly. Bracketed numbers link to the source. Where a term has no definition in PMI's lexicon, the alternative source is named on the row.
A graphical representation of the logical relationships among the project schedule activities. See also node and precedence diagramming method (PDM).
A technique used for constructing a schedule model in which activities are represented by nodes and are graphically linked by one or more logical relationships to show the sequence in which the activities are to be performed. See also node and project schedule network diagram.
A distinct, scheduled portion of work performed during the course of a project.
A significant point or event in a project, program, or portfolio.
The sequence of activities that represents the longest path through a project, which determines the shortest possible duration. See also critical path activity and critical path method.
A method used to estimate the minimum project duration and determine the amount of scheduling flexibility on the logical network paths within the schedule model. See also critical path and critical path activity.
In the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the data date, and any schedule constraints.
In the critical path method, the earliest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the data date, and any schedule constraints.
In the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can start based on the schedule network logic, the project completion date, and any schedule constraints.
In the critical path method, the latest possible point in time when the uncompleted portions of a schedule activity can finish based on the schedule network logic, the project completion date, and any schedule constraints.
A critical path method technique for calculating the early start and early finish dates by working forward through the schedule model from the project start date or a given point in time. See also backward pass.
A critical path method technique for calculating the late start and late finish dates by working backward through the schedule model from the project end date. See also forward pass.
The amount of time that a schedule activity can be delayed or extended from its early start date without delaying the project finish date or violating a schedule constraint.
The amount of time that a schedule activity can be delayed without delaying the early start date of any successor or violating a schedule constraint.
A technique used to estimate cost or duration by applying an average or weighted average of optimistic, pessimistic, and most likely estimates when there is uncertainty with the individual activity estimates.
A technique used to estimate project duration through a weighted average of optimistic, pessimistic, and most likely activity durations when there is uncertainty with the individual activity estimates.
a point that marks the start or completion of one or more activities.
It consumes no time and uses no resources.
When it marks the completion of one or more activities, it is not "reached" (does not occur) until all of the activities leading to that event have been completed.
the best estimate of the time required to accomplish an activity (te) or a path (TE), accounting for the fact that things don't always proceed as normal (the implication being that the expected time is the average time the task would require if the task were repeated on a number of occasions over an extended period of time).
the variability of the time for accomplishing an activity (σte) or a path (σTE)
the longest possible continuous pathway taken from the initial event to the terminal event.
It determines the total calendar time required for the project; and, therefore, any time delays along the critical path will delay the reaching of the terminal event by at least the same amount.
float or slack is a measure of the excess time and resources available to complete a task.
It is the amount of time that a project task can be delayed without causing a delay in any subsequent tasks (free float) or the whole project (total float).
There are two types of network diagrams, activity on arrow (AOA) and activity on node (AON).
A dummy activity is a zero-duration placeholder used in the arrow diagramming method (ADM, also called activity-on-arrow) to show a logical dependency between two activities that cannot be represented with an ordinary arrow. It carries no work and no time — it exists only to keep the network diagram's logic correct.
PERT was originally developed by Charles E. Clark for the United States Navy in 1958;
it is commonly used in conjunction with the Critical Path Method (CPM), which was also
introduced in 1958.
It was developed by the United States Navy Special Projects
Office, Lockheed Aircraft, and Booz Allen Hamilton to support the Navy's Polaris missile
project.
[3] The defense-acquisition
reference adds: PERT was introduced as an event-oriented, probabilistic technique to
increase the Program Manager's control in projects where time was the critical factor and
time estimates were difficult to make with confidence.
[6] Of CPM: The CPM is a project-modeling
technique developed in the late 1950s by Morgan R. Walker of DuPont and James E. Kelley
Jr. of Remington Rand.
[4]
In the precedence diagramming method the activity lives in the box. The six numeric fields below are the standard CPM node; every scheduling tool exposes the same six, whatever it calls them.
PDM links nodes with dependencies. The arrow's meaning changes with the relationship type — this is precisely what an activity-on-arrow PERT chart cannot express.
includes four types of dependencies; the activity-on-node form
where activities are the nodes and the dependencies between them are expressed directly through the four logical relationship types (finish-to-start, start-to-start, finish-to-finish, start-to-finish)[5].
Seven activities from a clinical-trial site-startup sequence. Use the layer buttons to see how the same drawing carries logic first, then the forward pass, then the backward pass, then float.
PMI's CPM primer states the two forward-pass formulas exactly as:
Early Start = Maximum (or Highest) EF value from immediate Predecessor(s)
Early Finish = ES + Duration
And describes the step itself: The first step in the calculation process is known as
the Forward Pass. In the forward pass, the Early Start and Early Finish values for each
activity, along with the overall Project Duration, are calculated.
[2]
F has three predecessors — B (EF 15), D (EF 27), E (EF 13). ESF = max(15, 27, 13) = 27. The merge takes the latest, never the average.
Late Start = LF – Duration
Late Finish = Minimum (or Lowest) LS value from immediate Successor(s)
Total Float = LS – ES (it is also calculated by LF – EF)
Free Float = Lowest ES of successors – EF
The second step in the calculation is comprised of the Backward Pass. Through this
pass, the Late Start and Late Finish values are calculated.
[2]
A has three successors — B (LS 17), C (LS 5), E (LS 19). LFA = min(17, 5, 19) = 5, so LSA = 5 − 5 = 0 and TFA = 0. A is critical because of C alone.
| ID | Activity | Pred. | Dur | ES | EF | LS | LF | Total float | Free float | Critical? |
|---|---|---|---|---|---|---|---|---|---|---|
| A | Protocol feasibility review | — | 5 | 0 | 5 | 0 | 5 | 0 | 0 | Yes |
| B | Budget & contract negotiation | A | 10 | 5 | 15 | 17 | 27 | 12 | 12 | No |
| C | IRB submission packet | A | 7 | 5 | 12 | 5 | 12 | 0 | 0 | Yes |
| D | IRB review & approval | C | 15 | 12 | 27 | 12 | 27 | 0 | 0 | Yes |
| E | Regulatory document collection | A | 8 | 5 | 13 | 19 | 27 | 14 | 14 | No |
| F | Site initiation visit / training | B, D, E | 3 | 27 | 30 | 27 | 30 | 0 | 0 | Yes |
| G | Activation / green light | F | 2 | 30 | 32 | 30 | 32 | 0 | 0 | Yes |
Project duration = 32 working days. Every path: A-B-F-G = 20; A-E-F-G = 18;
A-C-D-F-G = 32. The longest is the critical path, matching the lexicon wording
the longest path through a project, which determines the shortest possible duration.
[1]
Same seven activities, drawn the original PERT way. Here the arrow is the work and the
circle is an event — a point that marks the start or completion of one or more
activities
that consumes no time and uses no resources
[3]. Note what appears that AON never needs: a dummy.
a zero-duration placeholder … it exists only to keep the network diagram's logic correct[5]. An AON diagram of the same logic needs none.
An event or milestone — a state, not work. Numbered so activities can be named by their start-end pair (activity 2-5 is B).
An activity — the work and the time. Length carries no meaning; the label carries the duration.
A dummy activity — logic only, zero duration, zero resources.
Event 1. No predecessors; the origin of the forward pass.
The last event. the longest possible continuous pathway taken from the initial event to the terminal event
defines the critical path [3].
Event 5 here. Not reached
until all of the activities leading to that event have been completed
[3].
Event 2 here — one event, several activities starting from it.
Expected time, not a raw duration. This is the part that makes the chart PERT rather than just a network.
Wikipedia states the two formulas as
te = (o + 4m + p) / 6 and
TE = Σ te, with
σte = (p − o) / 6 and
σTE = √(Σ σte²)
[3]. The defense reference states the same expected
time as (P+4M+O)/6
and notes An expected time is calculated based on a beta
probability distribution for each activity from these estimates.
[6]
| ID | o optimistic |
m most likely |
p pessimistic |
te = (o+4m+p)/6 | σ = (p−o)/6 | σ² | On critical path? |
|---|---|---|---|---|---|---|---|
| A | 3 | 5 | 10 | 5.50 | 1.17 | 1.36 | Yes |
| B | 7 | 10 | 16 | 10.50 | 1.50 | 2.25 | No |
| C | 5 | 7 | 12 | 7.50 | 1.17 | 1.36 | Yes |
| D | 10 | 14 | 30 | 16.00 | 3.33 | 11.11 | Yes |
| E | 5 | 8 | 15 | 8.67 | 1.67 | 2.78 | No |
| F | 2 | 3 | 5 | 3.17 | 0.50 | 0.25 | Yes |
| G | 1 | 2 | 4 | 2.17 | 0.50 | 0.25 | Yes |
| Critical path A-C-D-F-G | TE = 34.33 | σTE = 3.79 | Σσ² = 14.33 | — | |||
Worked: for D, te = (10 + 4·14 + 30) / 6 = 96/6 = 16.00; σ = (30 − 10)/6 = 3.33; σ² = 11.11. D alone contributes 78% of the whole path's variance — the single most useful thing PERT tells you about this schedule, and something the deterministic 32-day network cannot say at all.
z = (target − TE) / σTE, with TE = 34.33 and σTE = 3.79. Drag the target.
35.0days
z = 0.18
57% confidence
Read this before quoting a percentage. The curve assumes the critical path is the only path that can drive the end date and that path durations add to a normal distribution. Here B and E have 12 and 14 days of float against a σ of 1.50 and 1.67, so that assumption holds comfortably. When a near-critical path has float smaller than its own standard deviation, classical PERT understates the project duration and Monte Carlo simulation is the honest tool. The sources quoted above state the formulas; they do not state that the result is unconditionally valid.
| Dimension | Network diagram (activity-on-node / PDM) | PERT chart (activity-on-arrow) |
|---|---|---|
| What it is | A model of schedule logic — a category of drawing | An estimating technique, historically drawn as an event network |
| Boxes / circles mean | Activities (work) | Events (milestones — no work, no time) |
| Arrows mean | Logical relationships (FS, SS, FF, SF), with leads and lags | Activities (the work itself) |
| Duration input | One deterministic number per activity | Three numbers per activity: optimistic, most likely, pessimistic |
| Output | ES, EF, LS, LF, total float, free float, critical path | te, TE, σ, variance, probability of meeting a date |
| Orientation | Activity-oriented | Event-oriented and probabilistic [6] |
| Dummy activities | Never needed | Needed whenever logic cannot be drawn with a real arrow [5] |
| Relationship types | All four, plus lead/lag | Finish-to-start only |
| Answers | "When, and what has slack?" | "How likely is that date?" |
| Current status | The standard form in every modern scheduling tool [4] | The drawing is largely superseded; the estimating math is alive and in the PMI lexicon [1] |
| Our example says | 32 days, four activities with zero float | 34.33 days expected, 27% chance of hitting day 32 |
Nothing stops you from putting PERT expected times into an activity-on-node network: run three-point estimating per activity, use te as the duration, run the forward and backward passes, then attach σTE to the answer. That is the normal modern practice, and it is why the terms drifted together. The precise sentence is: a PERT chart is one historical style of network diagram; PERT estimating is a technique that any network diagram can carry.
PERT analysis calculationon task fields [9].
All quotations above are verbatim from these documents. PMI's lexicon is the authority for the schedule-model vocabulary; the remaining sources supply the formulas and the PERT-specific terms the lexicon does not define.
event-oriented, probabilistic technique, the expected-time formula
(P+4M+O)/6, and the beta-distribution basis.
Boxes (or nodes) represent tasks, and dependencies show up as lines that connect those boxes.
PERT analysis calculation, the
Calculate PERTcommand on the
PERT Analysistoolbar, and the default 4-1-1 weights.
Note on limits: the PMI lexicon contains no entry for "dummy activity", "PERT chart", "network diagram" (unqualified), or "expected time", so those terms are quoted from the non-PMI sources named on each row rather than attributed to PMI. No definition above has been reworded to fill a gap.