7793250 Cpm Pert Example

5/26/2018 7793250 Cpm Pert Example

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2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 074583-1

Network Planning MethodsExample PERT &CPM : Saint

Pauls Hospital


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Terms Used in Project Management

Activity : A certain amount of work or task required in the

project

Activity duration: In CPM the best estimate of time to

complete an activity . In PERT the expected time or

average time to complete an activity

Critical activity: An activity that has no room for schedule

slippages: if it slips the entire the entire project completion

will slip. An activity with zero slack


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Critical path: The chain of critical activities for the project

.The longest path through the network

Dummy activity:An activity that consumes no time butshows precedence among activities

Earliest finish (EF):The earliest that an activity can finish

from the beginning of the project

Earliest start ( ES):The earliest that an activity can start

from the beginning of the project


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Event :A beginning , a completion point ,or amilestone accomplishment within the project . Anactivity begins and ends with events

Latest finish (LF) : The latest that an activity can finishfrom the beginning of the project

Latest start (LS):The latest that an activity can start fromthe beginning of the project

Most likely time ( t m): The time for completing theactivity that is is the consensus best estimate, used inPERT



Optimistic Time(to): The time for completing an activity ifall goes well : used in PERT

Pessimistic Time(tp): The time for completing an activityif bad luck is encountered : used in PERT

Predecessor activity: An activity that must occur beforeanother activity .

Slack: The amount of time that an activity or group ofactivities can slip without causing a delay in thecompletion of the project

Successor activity: An activity that must occur after

another activity



Conventions used in drawing network diagrams

(Arrows & Circles )

Activity on Arrow (AOA): The activities are denoted byArrows and events are denoted by circles

Activity on Node(AON): Activities are denoted bycircles(or nodes) and the precedence relation ships

between activities are indicated by arrows



Relationship between activities

Project duration

Critical path Slack for noncritical activities

Crashing (cost / time trade-offs)

Resource usage

PERT / CPMNetwork planning methods that generate:



St. Pauls Hospital

ImmediateActivity Description Predecessor(s)

A Select administrative and medical staff.

B Select site and do site survey.

C Select equipment.D Prepare final construction plans and layout.

E Bring utilities to the site.

F Interview applicants and fill positions in nursing,

support staff, maintenance, and security.

G Purchase and take delivery of equipment.H Construct the hospital.

I Develop an information system.

J Install the equipment.

K Train nurses and support staff.

AB

B

A

CD

A

E,G,H

F,I,J



St. Pauls Hospital












AB

B

A

CD

A

E,G,H

F,I,J

AON Network

FinishStart

A

B

C

D

E

F

G

H

I

J

K



St. Pauls Hospital












AB

B

A

CD

A

E,G,H

F,I,J

Completion Time

FinishStart

K

9

I

15

F

10

C

10

D10

E

24

G

35

H40

J4

A

12

B9



St. Pauls Hospital












AB

B

A

CD

A

E,G,H

F,I,J

Completion Time

FinishStart

K

9

I

15

F

10

C

10

D

10

E

24

G

35

H

40

J

4

A

12

B

9

Path Expected Time (wks)

A-I-K 36

A-F-K 31

A-C-G-J-K 70

B-D-H-J-K 72

B-E-J-K 46

Critical

Path



Critical Path

The longest path in the network Defines the shortest time project can be completed

Critical path activity delay project delay



Begin at starting event and work forward

ES is earliest start

ES = 0 for starting activities

ES = Maximum EF of allpredecessors for

non-starting activities

EF is earliest finish EF = ES + Activity time

Earliest Start and Earliest Finish

ES

LS

EF

LF

Activity

Name

Activity

Duration



A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

I

15

F

10

FinishStart

Earliest Start / Earliest Finish


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Earliest Start / Earliest Finish

Finish

Earliest start time Earliest finish time

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

Critical

path

Start


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Begin at ending event and work backward

LF is latest finish

LF = Maximum EF for

ending activities LF = Minimum LS of all

successors for

non-ending activities

LS is latest start

LS = LFActivity time

Latest Start and Latest Finish

ES

LS

EF

LF

Activity

Name

Activity

Duration


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Latest Start / Latest Finish

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63

Latest start time Latest finish time

Critical

path

FinishStart

What do you

notice aboutES/LS & EF/LF?


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Activity Slack Analysis

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63


Critical

path

FinishStartSlackK= 63 63 = 0

or

SlackK= 72 72 = 0

Slack = LS

ES

or

Slack = LFEF


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Activity Slack Analysis

A

12

K

9

C

10

G

35

J

4

H

40

B

9

D

10

E

24

0 12

I

15

F

10

12 27

12 22 63 72

22 57

59 6319 59

9 33

0 9 9 19

12 22

48 63

2 14 53 63 63 72

14 24 24 59

0 9 9 19 19 59

35 59

59 63


Critical

path

FinishStart

Node Duration ES LS Slack

A 12 0 2 2

B 9 0 0 0

C 10 12 14 2

D 10 9 9 0

E 24 9 35 26F 10 12 53 41

G 35 22 24 2

H 40 19 19 0

I 15 12 48 36

J 4 59 59 0K 6 63 63 0

Activity slack = maximum delay time

Critical path activities have zero slack


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Activity Slack

How much would we like to reduce

the time for activity B?

C

15

5 20

10 25

A

5

0 5

0 5 FinishStart

B

20

5 25

5 25D

10

25 35

25 35


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3 activity time estimates

Optimistic times (a)

Most-likely time (m)

Pessimistic time (b)

Follow beta distribution Expected time: t = (a+ 4m+ b) / 6

Variance of times: v= (b- a)2/ 6

Expected project time:T = sum of critical path activity times, t

Project variance:V = sum of critical path activity variances

Activity Times & Project Times


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Completion Time for Noncritical Activities

Variability of times for activities on non-criticalpaths must be considered when determining

the probability of finishing in a specified time.

Variation in non-critical activity may causechange in critical path.


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Cost / Time Trade-offs

Most activities can be done faster if youpay more money

Work overtime / hire more people /

rent extra equipment / incentive contracts

PERT / CPM have the ability to crash

a scheduleto shorten activity time in a network

to reduce project completion time.


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Cost / Time Relationship

8000

7000

6000

5000

4000

3000

0

Directcost(dollars)

Crash cost

Normal cost

| | | | | |

5 6 7 8 9 10 11

Crashtime Normaltime

Activity B

Documents

7793250 Cpm Pert Example