PLANNING ENGINEERING AND

PROJECT MANAGEMENT

By

Lec. Junaid Arshad

1

Lecture#08

DEPARTMENT OF ENGINEERING MANAGEMENT

Topics Covered

CPM Calculations for AOA

and AON Networks Slack Time / Float Critical Path, Critical Activity Practice Problems

CPM Calculations for AON Network

Provides activity information

Early start (ES) & late start (LS) Early finish (EF) & late finish (LF) Slack (S) / Float (FL)

Identifies critical path

Forward and Backward Pass

Forward pass is a technique to move forward through network diagram. Backward pass is its opposite.

Early Start (ES) and Early Finish (EF) use the forward pass technique.

Late Start (LS) and Late Finish (LF) use the backward pass technique.

Note: If the float of the activity is zero, the two starts (ES and LS) and the two finish (EF and LF) are the same. Hence, If float of activity is zero, ES = LS and EF = LF.

Early Start and Early Finish Steps

Begin at starting event and work forward ES = 0 for starting activities

ES is earliest start EF = ES + Activity time

EF is earliest finish ES = Maximum EF of all predecessors for

non- starting activities

Late Start and Late Finish Steps

Begin at ending event and work backward LF = Maximum EF for ending activities

LF is latest finish; EF is earliest finish LS = LF - Activity time

LS is latest start LF = Minimum LS of all successors for

non-ending activities

Latest Finish

ES

LS

EF

LF

Earliest Finish

Latest Start

Earliest Start

Activity Nam

eActivity Duration

AON Network Calculations

Problem 04

Activity Preceding Activity

Duration (days)

A - 10

B - 07

C - 12

D A 18

E B 14

F B 13

G C 16

H D, E 12

I F, G 06CPM Calculations for an AON Network

Slack Time is tis the amount of time an activity may be delayed without affecting the project deadline. This is also referred as float.

Total Slack Time / Total Float:

Time shared among more than one activity.

Free Slack Time /Free Float: Time associated with a single activity.

Slack Time/FloatSlack Time/Float

An activity having zero slack time is called critical activity.

The concept of critical activities is that it draws the attention of the project manager to the activities that needs the closest monitoring.

Any delay of a critical activity leads to an equivalent delay of the total project.

Critical ActivityCritical Activity

A path having longest duration (completion time) in the network is called critical path.

Shortest time project can be completed

Any delay on critical path activities, delays project

Critical path activities have zero slack

Critical PathCritical Path

Total Float is valid for a chain and not for a single activity.

In the under discussion example, C and G have a float of 06 days. This means that the sum of delays for C and G may run up to 06 days without affecting the project finish time.

Analysis of float is a particularly neat tool for calculating consequences of schedule variance.

Explanation of Total FloatExplanation of Total Float

Assume the following data with respect to

schedule (for problem 04)

B will be delayed by 04 days D will be delayed by 01 day E will be delayed by 05 days G will be delayed by 03 days

It is recognized that D is critical, hence a delay of at least one day to the overall project is unavoidable.

Activity G has a float of 06 days. Since no other activity on that chain has a delay, the float will accommodate the 03 day delay of G.

Further, B and E are both on the same chain. The float along the chain is 07 days and the total delay is 4+5=9 days. This means a 02 day delay of the project.

In conclusion, the project will be delayed by 02 days and B-E-H will be the new critical path. A-D will have a float of one, and C-G a float of 04.

CPM calculation for AON Network is same as for AOA network, but the calculation of events is omitted.

CPM Calculations for AON Network

Problem 05: General Hospital’s Activities and Predecessors

Activity

Immediate Predecessors Duration (days)

A - 2

B - 3

C A 2

D A, B 4

E C 4

F C 3

G D, E 5

H F, G 2

AON Network for General Hospital Includes Critical Path

Slack=0

Start

A

B

C

D

F

F

G

HH

1313

2

1515

HG

88

5

1313

HF

410

3

713

HC

22

2

44

HE

44

4

88

HD

34

4

78

HB

01

3

34

HA

00

2

22

H00

0

00

Slack=0 Slack=0

Slack=0

Slack=0

Slack=6

Slack=1Slack=1

Start

Critical Path for General Hospital

Start

A

B

C

D

F

G

HE

Explanation of Free Float

Consider slack time of activity F. Delaying this activity decreases only its slack time and does not impact the slack time of any other activity. This type of slack time is referred as free slack / free float.

Gantt Chart for General Hospital Early Start and Finish

GENERAL HOSPITAL GENERAL HOSPITAL

A Build internal componentsB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution deviceH Inspect and test

1 2 3 4 5 6 7 8 9 10 1112 13 1415 16

Gantt Chart for General Hospital Late Start and Finish

A Build internal componentsB Modify roof and floorC Construct collection stackD Pour concrete and install frameE Build high-temperature burnerF Install pollution control systemG Install air pollution deviceH Inspect and test

1 2 3 4 5 6 7 8 9 10 1112 13 1415 16

GENERAL HOSPITAL

Table for Network Scheduling

Problem 06

Problem 06Solution - AOA Method

Early Event Time (TE)

Finding TE Values

Late Event Time (TL)

Finding TL Values

Critical Path

Activity Scheduling

An activity’s early starting time equals the TE of its beginning event: ES = TE.

An activity’s late finishing time equals the TL for its ending event: LF = TL.

From these, Two times are computed using the expected activity completion time t:

Early finishing time: EF = ES + t.Late starting time: LS = LF t.

Scheduled Times must fall between ES and LF and allow at least time t to complete.

Problem 06Solution - AOA Method

Problem 07

Activity Preceding Activity

Duration (weeks)

A - 10

B - 07

C - 12

D A 18

E B 14

F B 13

G C 16

H D, E 12

I F, G 06CPM Calculations for an AOA Network

 

ActivityPredecessors

(Dependencies)

 

Time (Weeks)

A - 3

B - 5

C - 7

D A 8

E B 5

F C 5

G E 4

H F 5

I D 6

J G - H 4

Table for Network Scheduling

Problem 08

34