What does a backward pass find?

The latest event times, taking the smallest value at each event.

What is the minimum project time?

The earliest event time at the finish event.

What is a critical activity?

One with zero total float, so any delay delays the project.

What is the critical path?

The longest path from start to finish.

Formula for total float?

F(i, j) = l(j) − e(i) − duration(i, j).

An activity has float 2 and is delayed by 5 days. What is the effect?

The project is delayed by 3 days.

What is a Gantt (cascade) chart?

A chart of bars against time showing when each activity takes place, with one worker per activity.

Lower bound for the number of workers?

Sum of durations ÷ project time, rounded up.

Critical paths and floatEdexcel A-Level Further Maths: Flashcards

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What does a forward pass find?

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What does a forward pass find?: The earliest event times, taking the largest value at each event.
What does a backward pass find?: The latest event times, taking the smallest value at each event.
What is the minimum project time?: The earliest event time at the finish event.
Earliest finish of an activity?: Earliest start + duration.
Latest start of an activity?: Latest finish − duration.
What is a critical activity?: One with zero total float, so any delay delays the project.
What is the critical path?: The longest path from start to finish.
Formula for total float?: F(i, j) = l(j) − e(i) − duration(i, j).
An activity has float 2 and is delayed by 5 days. What is the effect?: The project is delayed by 3 days.
Can a network have more than one critical path?: Yes.
What is a Gantt (cascade) chart?: A chart of bars against time showing when each activity takes place, with one worker per activity.
Lower bound for the number of workers?: Sum of durations ÷ project time, rounded up.

Exam questions on Critical paths and float

A project has eight activities. Each activity, its duration in days and its immediate predecessors are: A 4 (none); B 6 (none); C 5 (A); D 3 (A, B); E 7 (B); F 4 (C, D); G 2 (D, E); H 3 (F, G). The earliest start time of an activity is the earliest time at which all of its predecessors are complete.
Find the total float of activity C.2 marks
A project has seven activities. Each activity, its duration in days and its immediate predecessors are: A 3 (none); B 5 (none); C 4 (A); D 2 (A); E 6 (B, C); F 3 (D); G 4 (E, F). Each activity needs one worker.
Find the total float of activity D.2 marks
A project has seven activities. Each activity, its duration in days and its immediate predecessors are: A 5 (none); B 3 (none); C 4 (A); D 6 (A, B); E 2 (B); F 5 (C, D); G 4 (D, E). Activities start as soon as they can.
Carry out a forward pass to find the earliest start time of each activity. State the minimum project completion time and the critical activities.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).