Critical Path Method (CPM) is a very widely used technique. Applications include:
Building/construction;
Production planning;
Maintenance planning;
Computer system development;
Launching a new product;
Auditing;
Mobilisation/military planning;
Planning generally.
Critical path methods are a vital tool in all project based activities
Representing a Project as a Network
Design Planning Permission A project involves several activities (or tasks) e.g. to build a house design, get planning permission, find a builder, lay foundations, order materials, build, select paint, select carpet and finish.
We can represent the relationship between the tasks as a network
In the network, nodes represent events (usually the start or completion of a task) and arcs represent activities (usually the tasks to be done)
The arrows on the arcs indicate that an event must be completed before the next i.e.
Representing a Project as a Network
Design Planning Permission 6 weeks 13 weeks More than one event can occur at the same time (concurrent activities) Design Planning Permission 6 13 Find Builder 4 1 2 3 1 2 3 4 We can add times to the arcs, showing how long each activity takes:
Representing a Project as a Network
In the network, 2 or more activities are not allowed to have the same starting and ending node
To model this, we add an extra “Dummy Activity” of duration 0 when one of the 2 activities are finished: Design Planning Permission 6 13 Find Builder
4 1 2 3 4 Dummy 0 Foundations 2 Order Materials 4 5 6
Critical Path Characteristics
There is one and only one starting and one completion (terminal) node
Critical Path networks are directional. Hence we talk about arcs rather than links
There is only one arc between each pair of nodes
There are no circuits
There are no loops
There must be at least one path from start node to completion node
There may be multiple paths from start to completion
There may be more than one critical path
There may be activities with zero duration
Critical Path Objectives
There may be more than one Critical Path Objective.
Objectives may include:
Minimise total project time;
Minimise total project cost;
Minimise cost for a given time;
Minimise time for a given cost;
Minimise idle resources;
Straightforward project management;
Budget control.
CPM methods are used as both
planning tools and
control tools
Critical Path Methods
There are three stages.
First we go through the network from the start working out the earliest possible completion time of each task.
This is known as the forward pass. This will give you a total time for the project.
Then, starting at the final node, we work backwards calculating the latest completion time necessary to complete the preceding task for each activity.
This is known as the backward pass.
Where the forward earliest completion time equals the backward latest completion at a node, that node lies on the critical path.
The Critical Path
There are several paths from start to finish of the project
The longest path is called the critical path
It represents the shortest time that the project can be completed
We can find the critical path by asking the following questions:
What is the earliest time that activities can be completed (or, in other words, each node is reached)?
What is the latest time that we could start the activities from a node and still complete the project in the shortest time?
A Critical Path Problem
1 6 5 4 3 2 3 What is the critical path through this network?
How would we set about computing it? 0 2 3 7 2 2 5 6 3 Finish Start 0 2
Building the Network from a list of the activities
We’ll look at this by example – see handout
The basic ideas are:
Start with the first activity
Subsequent activities start from the completion node of one of its predecessors
If an activity has more than one predecessor, you put in“dummy” arcs from the other predecessors to the starting node of the activity
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