Gantt Chart

Graph or bar chart with a bar for each project activity that shows passage of time

Provides visual display of project Provides visual display of project scheduleschedule

Slack amount of time an activity can be delayed

without delaying the project

| | | | |Activity

Design house and obtain financing

Lay foundation

Order and receive materials

Build house

Select paint

Select carpet

Finish work

00 22 44 66 88 1010MonthMonth

MonthMonth11 33 55 77 99

Example of Gantt ChartExample of Gantt Chart

The Project NetworkThe Project Network

Use of nodes and arrowsUse of nodes and arrows

ArrowsArrows An arrow leads from tail to head directionally An arrow leads from tail to head directionally Indicate Indicate ACTIVITY, ACTIVITY, a time consuming effort that is required to a time consuming effort that is required to

perform a part of the work.perform a part of the work.

NodesNodes A node is represented by a circle A node is represented by a circle

- Indicate - Indicate EVENT,EVENT, a point in time where one or more activities start a point in time where one or more activities start and/or finish.and/or finish.

CPM/PERTCPM/PERT

Critical Path Method (CPM)Critical Path Method (CPM) DuPont & Remington-Rand (1956)DuPont & Remington-Rand (1956) Deterministic task timesDeterministic task times Activity-on-node network constructionActivity-on-node network construction

Project Evaluation and Review Technique Project Evaluation and Review Technique (PERT)(PERT) US Navy, Booz, Allen & HamiltonUS Navy, Booz, Allen & Hamilton Multiple task time estimatesMultiple task time estimates Activity-on-arrow network constructionActivity-on-arrow network construction

Project NetworkProject Network

Activity-on-node (AON) nodes represent activities,

and arrows show precedence relationships

Activity-on-arrow (AOA) arrows represent activities

and nodes are events for points in time

Event completion or beginning

of an activity in a project

1 32

Branch/ActivityBranch/Activity

NodeNode

AON Network for House Building Project

13

22

43

31 5

1

61

71Start

Design house and obtain financing

Order and receive materials Select paint

Select carpet

Lay foundations Build house

Finish work

13

22

43

31 5

1

61

71Start

Critical Path

Critical pathCritical path Longest path Longest path

through a networkthrough a network Minimum project Minimum project

completion timecompletion time

A:A: 1-2-4-71-2-4-73 + 2 + 3 + 1 = 9 months 3 + 2 + 3 + 1 = 9 months

B:B: 1-2-5-6-71-2-5-6-73 + 2 + 1 + 1 + 1 = 8 months3 + 2 + 1 + 1 + 1 = 8 months

C:C: 1-3-4-71-3-4-73 + 1 + 3 + 1 = 8 months3 + 1 + 3 + 1 = 8 months

D:D: 1-3-5-6-71-3-5-6-73 + 1 + 1 + 1 + 1 = 7 months3 + 1 + 1 + 1 + 1 = 7 months

Activity Start Times

13

22

43

31 5

1

61

71Start

Start at 3 monthsStart at 6 months

Start at 5 months

Finish at 9 months

Finish

Calculation of Required Time (Te)Calculation of Required Time (Te)

tt0 + 0 + 44 ttm + m + ttpp

Te= Te= 66

te=weighted arithmetic average time

to= Optimistic Time

tm= most likely time

tp= pessimistic time

NetworkingNetworking

1

2

3 4

513

12

15

82

2

ActivityActivity optimisticoptimistic Most Most likelylikely

PessimistPessimisticic

AverageAverage

Time (Te)Time (Te)

A 1-2A 1-2 99 1212 2121 1313

B 1-3B 1-3 66 1212 1818 1212

C 2-4C 2-4 11 1.51.5 55 22

D 3-4D 3-4 44 8.58.5 1010 88

E 2-5E 2-5 1010 1414 2424 1515

F 4-5F 4-5 11 22 33 22

Calculation of Required Time (Te)Calculation of Required Time (Te)

Activity SlackActivity Slack

Each event has two important times associated with it :Each event has two important times associated with it :- Earliest timeEarliest time , , Te Te , which is a calendar time when a event can occur , which is a calendar time when a event can occur

when all the predecessor events completed at the earliest possible when all the predecessor events completed at the earliest possible timestimes

- Latest time Latest time , , TL , TL , which is the latest time the event can occur with out which is the latest time the event can occur with out delaying the subsequent events and completion of project.delaying the subsequent events and completion of project.

Difference between the latest time and the earliest time of an event is Difference between the latest time and the earliest time of an event is the the slack timeslack time for that event for that event

Slack=LF-EF, LS-ESSlack=LF-EF, LS-ESPositive slackPositive slack : : Slack is the amount of time an event can be delayed Slack is the amount of time an event can be delayed

without delaying the project completionwithout delaying the project completion

Mode ConfigurationMode Configuration

1 0 3

3 0 3

Activity number

Activity duration

Earliest start

Latest start

Earliest finish

Latest finish

Forward PassForward Pass

Start at the beginning of CPM/PERT network to determine the earliest activity times

Earliest Start Time (ES) earliest time an activity can start ES = maximum EF of immediate predecessors

Earliest finish time (EF) earliest time an activity can finish earliest start time plus activity time

EF= ES + t

Earliest Activity Start and Earliest Activity Start and Finish TimesFinish Times

1 0 3

3

2 3 5

2

3 3 4

1 5 5 6

1

4 5 8

3

6 6 7

1

7 8 9

1

Start

Design house and obtain financing

Select paint

Lay foundations

Select carpet

Build house

Finish work

Order and receive materials

Earliest Activity Start and Earliest Activity Start and Finish TimesFinish Times

1 0 3

3

2 3 5

2

3 3 4

1 5 5 6

1

4 5 8

3

6 6 7

1

7 8 9

1

Start

Design house and obtain financing

Select paint

Lay foundations

Select carpet

Build house

Finish work

Order and receive materials

0+3

3+1

* For forward pass maximum EF time would be taken in calculating ES time

*

Backward PassBackward Pass

Determines latest activity times by starting at the end of CPM/PERT network and working forward

Latest Start Time (LS) Latest time an activity can start without delaying

critical path time

LS= LF - t Latest finish time (LF)

latest time an activity can be completed without delaying critical path time

LS = minimum LS of immediate predecessors

Latest Activity Start and Latest Activity Start and Finish TimesFinish Times

1 0 3

3 0 3

2 3 5

2 3 5

3 3 4

1 4 5 5 5 6

1 6 7

4 5 8

3 5 8

6 6 7

1 7 8

7 8 9

1 8 9

Start

Design house and obtain financing

Select pain

Lay foundations

Select carpet

Build house

Finish work

Order and receive materials

* Critical Path* Critical Path

00009999999988888888*7*7*7*7

111177778888666677776666

111166667777555566665555

00008888888855555555*4*4*4*4

111144445555333344443333

00005555555533333333*2*2*2*2

00003333333300000000*1*1*1*1

Slack SSlack SEFEFLFLFESESLSLSActivityActivity

Activity SlackActivity Slack