LECTURE 7

Calculating the Critical Path

Introduction

Critical Path:

• The path through the network that takes the longest total time, and

• Determines the earliest possible time the project can be completed.

All activities on this path have zero float; the early and late start (and early and late finish) are the same.

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What the Critical Path Calculates

Earliest Start (ES) = the earliest time at which the activity can begin.

• Calculated by a forward pass through the network diagram,

• Calculated on the basis of the project’s start time and the duration the preceding activity.

Earliest Finish (EF) = the earliest time by which the activity can be completed

• Calculated by adding the activity’s duration estimate to the earliest start time.

EF= ES + Duration estimate

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Latest Finish (LF) = the latest time that the activity can end and still allow the project to be completed on time.

• Calculated by a backward pass through the network diagram

• Calculated on the basis of the project’s completion time and the duration for the succeeding activities. Generally, the latest finish time of the activity is equal to the earliest of all the lastest start times of all activities emerging directly from that activity.

Latest Start (LS) = the latest time that the activity can begin and still allow the project to be completed on time.

• Calculated by subtracting the activity’s duration from the activity’s latest finish time

LS= LF – Duration estimate

What the Critical Path Calculates

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Total Slack: The time difference between the scheduled completion date and required date to meet critical path

Total Slack = LF- EF or

Total Slack = LS - ES

• If Total Slack >0: some activities can be delayed without jeopardizing completion of the project by its required completion time

• If Total Slack <0: some activities need to be accelerated in order to complete the project by its required completion time

Total Slack / Float

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Slack Identification

C (8,10)

2 (15,17)

EARLIEST START TIME (ES)

EARLIEST FINISH TIME (EF)

LATEST FINISH TIME (LF)

LATEST START TIME (LS)

ACTIVITY

TIME

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Types Of Slack

[ 20, 26 ]

[ 24, 30 ]

[ 30, 36 ]

[ 24, 30 ]

POSITIVE SLACK NEGATIVE SLACK

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Negative Slack

FORWARD PASS

BACKWARD PASS

CUSTOMER’S CUSTOMER’SSTART DATE FINISH DATE

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2

4

1

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Slack Identification

Activity Description

ESEarliest Start

Duration Estimate

Person Responsible

Activitiy Number

EFEarliest Finish

LSLatest Start

LFLatest Finish

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Picnic at the Lake - Activities

Activity Description

Person Responsible

Duration (mins.) Preceding activity

1. Decide on trip Husband & Wife 2 none

2. Get money from bank

Wife 12 1

3. Boil eggs Husband 10 1

4. Make egg sandwiches

Husband 10 3

5. Load car Husband & Wife 5 2,4

6. Drive to lake Husband & Wife 30 5

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Picnic at the Lake

Decide on tripMin: 2 Float:Early Start:Early Finish:Late Start:Late Finish:

Get money from bankMin: 12 Float:Early Start:Early Finish:Late Start:Late Finish:

Boil eggsMin: 10 Float:Early Start:Early Finish:Late Start:Late Finish:

Make egg sandwichesMin: 10 Float:Early Start:Early Finish:Late Start:Late Finish:

Load carMin: 5 Float:Early Start:Early Finish:Late Start:Late Finish:

Drive to lakeMin: 30 Float:Early Start:Early Finish:Late Start:Late Finish:

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Classroom Activity 10a

Picnic at the lake – create planned and preceding activities network diagram.

Determine critical path.

Add early start, late start, early finish, and late finish to each activity.

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Questions?