LECTURE 08 & 09 LECTURER ENGR

ALI SALMANengineer348@yahoo.com

DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST

DEPARTMENT OF ENGINEERING MANAGEMENTCOLLEGE OF E & ME, NUST

PLANNING ENGINEERING AND

PROJECT MANAGEMENT

Topics Covered

CPM Calculations for AOA

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

Provides activity information

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

Identifies critical path

CPM Calculations for AOA Network

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.

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

Early Start and Early 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

Late Start and Late Finish Steps

Problem 04

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

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 quite interesting. 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

Latest Finish

ES

LS

EF

LF

Earliest Finish

Latest Start

Earliest Start

Activity Nam

eActivity Duration

Problem 05Problem 05AON Network for General AON Network for General

HospitalHospital

Key

AON Network for General AON Network for General Hospital Hospital Includes Critical PathIncludes Critical Path

Slack=0

Start

A

B

C

D

F

F

G

HH

1313

2

1515

HG

88

5

1313

HE

410

3

713

HC

22

2

44

HF

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

E

G

H

Arrows show

precedence

relationships

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 HospitalGeneral HospitalGeneral HospitalGeneral 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

General HospitalGeneral HospitalGeneral HospitalGeneral 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

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 AON 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

Discussion