Skip to content
Sem 5 Prep
← OperationsProject management: PERT and CPM

Formulas for this chapter

Forward pass

ES = largest EF among the activities feeding this activity's start event EF = ES + duration Project duration = largest EF in the network

First pass through any network. An event occurs only when every activity feeding it is complete, so take the largest.

ES
Earliest start
EF
Earliest finish

Backward pass and slack

LF = smallest LS among this activity's successors LS = LF - duration Slack = LS - ES = LF - EF

Second pass, starting from the project duration. Compute slack both ways as a check.

LS
Latest start without delaying the project
LF
Latest finish without delaying the project
Slack
Zero on the critical path

Path slack

Slack of a path = critical path length - that path's length

Small networks where every path can be listed. The longest path is the critical path and the project duration.

critical path length
Longest total duration from start to finish

PERT expected time and variance

t-e = ( t-o + 4 t-m + t-p ) / 6 sigma^2 = ( ( t-p - t-o ) / 6 )^2

When activity durations are uncertain and three estimates are given. The most likely time does not appear in the variance.

t-o
Optimistic time, under optimal conditions
t-m
Most likely time, the most probable duration
t-p
Pessimistic time, under worst conditions

Probability of on-time completion

Path variance = SUM of variances of activities on the critical path Path sigma = sqrt( path variance ) z = ( target date - expected project length ) / path sigma

After a PERT network is timed. Add variances, never standard deviations, and look z up in a normal table.

target date
The completion date being tested
expected project length
Sum of expected times along the critical path
Step 1 of 26
The ideaTheory

The longest road decides the journey

A house needs foundations, walls, a roof, wiring and paint. Some of those can happen at the same time. Some cannot start until another finishes.

Add up the times along every possible route from start to finish. The longest route is how long the house takes, however fast everything else goes.

That longest route is the critical path, and every activity on it has zero slack: delay one of them by a day and the whole project slips a day.

← BackContinue →