464 lecture 09 cpm revision. scheduling techniques r the scheduling techniques are î to plan,...

464 Lecture 09CPM Revision

Scheduling Techniques The scheduling techniques are

To plan, schedule, budget and control the many activities associated the projects;

Focusing on customer’s desired completion date; Converting project plans into an operating timetable and Providing direction for managing the day-to-day activities of

projects

Critical Path Method (CPM)

Deterministic

Project Evaluation Review Technique (PERT)

Probabilistic

Critical Path 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

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.

DesignPlanning Permission


We can add times to the arcs, showing how long each activity takes:

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


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

65

4

3

2

3

What is the critical path through this network?

How would we set about computing it?

0

2

37

2

2

5

6

3

Finish

Start

0

2

Forward Pass

1

65

4

3

2

3

0

2

37

2

2

5

6

3Finish

Start

0

0

2

Calculating the Earliest Finishing/completion time (EF)

Forward Pass

1

65

4

3

2

32

37

2

2

5

6

3Finish

Start

0

0

2


3

Forward Pass

1

65

4

3

32

37

2

2

5

6

3Finish

Start

0

0

2


3

5?

Forward Pass (Cont.)

65

4

3

32

37

2

2

5

6

3Finish

Start

0

0

2


2

3


65

4

3

32

37

2

2

5

6

3Finish

Start

0

0

2


2

3

6 =max(3+3, 4)


65

4

32

37

2

2

5

6

3Finish

Start

0

0

2


2

3

6

6 =max(3+2, 6+0)


6532

37

2

2

5

6

3Finish

Start

0

0

2


2

3

6

6

13

=max(6+7, 6+3)


632

37

2

2

5

6

3Finish

Start

0

0

2


2

3

6

6

1319

=max(13+6, 11)


32

37

2

2

5

6

3Finish

Start

0

0

2

2

3

6

6

1319

EF

LF

Backward Pass

32

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

Calculating the latest finishing/completion time (LF)

Backward Pass (cont.)

32

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

14?



32

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19


13


6532

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6


=min(13-7, 19-5)


6532

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6


6 =min(6-0, 13-3, 19-2)


6532

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6


6

=min(6-2, 6-3)3


6532

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6


6

3

4


6532

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6


6

3

4

0

=min(3-3, 4-2)

Critical Path

1

65

4

3

2

3

0

2

37

2

2

5

6

3Finish

Start

0

0 3

2 6

2

6

1319

19

13

6

6

3

4

0

Critical Path

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

464 lecture 09 cpm revision. scheduling techniques r the scheduling techniques are î to plan,...

Documents

project r

completion r

network r

r critical path methods

critical path objectives

r objectives

completion node r

circuits r