PERT & CPM…are the two most widely use techniques for planning and coordinating large-scale projects…

…by using PERT or CPM, managers are able to obtain:

1. A graphical display of projects activities.2. An estimate of how long the project will

take.3. An indication of which activities are the

most critical to timely completion of the project.

4. An indication of how long any activity can be delayed without lengthening the project.

PERT & CPM

The network diagram: • The arrows represent the

project activities• The nodes represent both

beginnings and endings of activities

CPM Terminology

Activity A task or a certain amount of work

required in the project Requires time to complete Represented by an arrow

Dummy Activity Indicates only precedence relationships Does not require any time of effort

CPM Terminology

Event Signals the beginning or ending of an

activity Designates a point in time Represented by a circle (node)

Network Shows the sequential relationships

among activities using nodes and arrows

CPM Terminology

Path A connected sequence of activities

leading from the starting event to the ending event

Critical Path The longest path (time); determines the

project duration Critical Activities

All of the activities that make up the critical path

CPM Terminology

Earliest Start (ES) The earliest that an activity can begin;

assumes all preceding activities have been completed

Earliest Finish (EF) ES + activity time

Latest Finish (LF) The latest that an activity can finish and not

change the project completion time Latest Start (LS)

LF - activity time

Steps in CPM Analysis

Draw the CPM network A graphic view of the relationships among the

required activities Analyze the paths through the network

Determine the length of each path (time required to complete each path)

Starting at the beginning of the network and working toward the end (from left to right), determine the ES and EF for each activity

. . . more

Steps in CPM Analysis

Path analysis (continued) Identify the critical path(s) (the longest

path[s] through the network) The critical path(s) determines how long

the project will take . . . more

Steps in CPM Analysis

Determine the slack for each activity Working from the end of the project

network (from right to left), find the LF and the LS for each activity

Compute the activity’s slack slack = LS - ES = LF - EF

Slack is the maximum amount of time that this activity can be delay in its completion before it becomes a critical activity, i.e., delays completion of the project

PERT Analysis

Critical Path Method…is one of two ways or tools to identify the path through your project…

Critical Path Uses one time estimate

Where as

PERTUses three time estimate

Critical path is for those times when you are pretty sure about the duration of each task.

PERT is used in more uncertain situations.

ES(Early start)

A (Activity)

EF(Early finish)

S(Slack time)

LS(Late start)

D(Duration

)

LF(Late finish)

Details of Critical Path – Example 1Activity Predecessor Duration

A - 5B - 4C A 3D A 4E A 6F B, C 4G D 5H D, E 6I F 6J H, G 4

Path Diagram (For Example 1)

1

2

3

4

5

6

7

8A

B

C

D

E

F

G

H

I

J

Critical Path

Critical PathA C F I : 5 + 3 + 4 + 6 = 18 weeksA D G J : 5 + 4 + 5 + 4 = 18 weeksA D H J : 5 + 4 + 6 + 4 = 19 weeksA E H J : 5 + 6 + 6 + 4 = 21 weeksB F I : 4 + 4 + 6 = 14 weeks

Example 2Activity Precedence

activitiesActivities Duration

(Weeks)1 2 0 Locate

facilities8

1 3 0 Interview 42 4 Locate

facilitiesOrder furniture 6

2 5 Locate facilities

Remodel 11

3 5 Interview Hire/train 94 5 Order furniture Received/set

up furniture3

5 6 Received / set up furniture;

hire/train; remodeling

Move in 1

Network (For Example 2)

1

2

3

4

56

8 weeks

4 weeks

6 weeks

11 weeks

9 weeks

3 weeks

1 weeks

start

end

Critical Path (For Example 2)

Critical Path1 2 4 5 6 : 8 + 6 + 3 + 1 = 18 weeks 1 2 5 6* : 8 + 11 + 1 = 20 weeks*1 3 5 6 : 4 + 9 + 1 = 14 weeks

*Critical path

Slack time (week)1 2 4 5 6 : 20 – 18 = 2 weeks1 2 5 6* : 20 – 20 = 0 week1 3 5 6 : 20 – 14 = 6 weeks

Practicing draw a network

See Example on page 102 – 103 (Notes)

Example 3 (Project Crashing)

Activity Normal Time

Crash time

Cost per day to crash (RM)

Available days

1 2 6 6 - -

2 5 10 8 500 2

1 3 5 4 300 1

3 4 4 1 700 3

4 5 9 7 600 2

4 6 2 1 800 1

Network (For Example 3)

1

2

34

56

6 weeks

5 weeks

10 weeks

4 weeks9 weeks

2 weeks

start

end

Critical Path (For Example 3)

Critical Path1 2 5 6 : 6+ 10 + 2 = 18 weeks 1 3 4 5 6* : 5 + 4 + 9 + 2 = 20 weeks*

*Critical path

Slack time (week)1 2 5 6 : 20 – 18 = 2 weeks1 3 4 5 6* : 20 – 20 = 0 week

Crash time (summary)Length after crashing n days

Path n = 0 1 2 31 2 5 6 18 18 18* 17

1 3 4 5 6* 20* 19* 18* 17

Activity crashed 1 3 4 5 5 6

Cost (crash) RM300 RM600 RM800 Total : RM1,700

TUTORIAL EXERCISE – Q1 Syarikat KukuhSyarikah Kukuh is planning to develop and market a new racing bicycle. The project comprise of the following activities.

Activity Normal cost (RM)

Duration (day) Cost to reduce/day

(RM)

Time can be shorten until

(day)1 2 4000 5 600 21 3 12000 3 1000 21 4 10000 10 1600 72 5 2000 7 800 63 6 8000 8 1800 64 6 12000 7 1200 44 7 6000 4 1000 35 8 14000 6 1400 56 8 16000 5 1400 37 8 4000 6 1200 4

The contract specifies a RM2000 per day penalty for each day the completion of the project extends past 15 days:

Required to:

a)Draw the network diagramb)Determine the critical pathc) Determine the normal time (day)

and cost (RM) to finish the project

d)Determine the optimum time (day) and cost (RM) to finish the project

Solution (a) – Tutorial (Q1 – Syarikat Kukuh)

Please draw the network

Solution (b) – Tutorial (Q1 – Syarikat Kukuh)

Please determine the critical path

Solution (c) – Tutorial (Q1 – Syarikat Kukuh)Activity Normal cost

(RM)Duration (day) Cost to

reduce/day (RM)

Time can be shorten until

(day)1 2 4000 5 600 21 3 12000 3 1000 21 4* 10000 10* 1600 72 5 2000 7 800 63 6 8000 8 1800 64 6* 12000 7* 1200 44 7 6000 4 1000 35 8 14000 6 1400 56 8* 16000 5* 1400 37 8 4000 6 1200 4

Critical1468

Total cost:RM88000

Normal day:22 days

Normal cost (RM): Total cost + Penalty = RM88000 + (7*RM2000) = RM102000

Solution (d) – Tutorial (Q1 – Syarikat Kukuh)Path 0 1 2 3 4 End/

stop

Activity crashedCost crashed

Complete and determine the optimum day and cost to finish the project

Task to completeComplete all Questions in Workbook:

Question 2 – Harmony (F1001 F1023; F1091 F1037 F1042)Question 3 – Syarikat Ramadhani (F1009 F1026; F1010 F1045)Question 4 – Syarikat TT (F1012 F1025; F1013 F1028) Question 5 – Hitech (F1015 F1035; F1017 F1024)Question 6 – A Farm (F1018 F1052; F1039 F1044)Question 7 – Rainbow (F1041 F1047; F1048 F1049; F1050 F1051)