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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 4 of 26
The real wordsTheory

Work breakdown structure

Work breakdown structureA hierarchical decomposition of a project into the activities that must be done.

Three steps, and the exam wants them in order:

  1. Identify the major elements of the project
  2. Identify the major supporting activities for each of the major elements
  3. Break down each major supporting activity into a list of the activities needed to accomplish it

It is step 1 of the six-step PERT and CPM procedure, because you cannot draw a network of activities you have not listed.

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