Project Management

Part 3

Project Scheduling

Topic Outline: Project Scheduling

• Identifying relationships among activities• Project network diagrams• Identifying critical paths and critical activities• Determining activity slack times• Gantt charts• Project scheduling exercise• Other precedence relationships• Management of project schedules

Identifying Activity Relationships

In addition to estimating activity time duration and cost, relationships among activities must also be identified

Relationships:• What task immediately precedes this task?• What task immediately follows this task?• What tasks can be done concurrently?

These are referred to as precedence relationships

The main relationship for scheduling is ‘what task immediately precedes the current task,’ which is referred to as the immediate predecessor task

Project Network Diagrams

• Network diagrams show the precedence relationships among activities

• It’s easier to understand these relationships graphically

• Network diagrams help to understand the flow of work in a project

• Network diagrams are a useful tool for project planning and control, as well as for scheduling

• One (perhaps exaggerated) claim is that the network represents ¾ of the planning process

2 Versions of Network Diagrams

Activity-on-Arrow (AOA) networks

Activity-on-Node (AON) networks

Activities vs. Events

• Activity – a chunk of work that is part of the project; an activity may be broken down into multiple subactivities

• Event – a significant point in time during the project, such as a milestone event; an event could be the time at which an activity is completed or the time at which related concurrent activities have all completed

• Dummy Activity – an artificial activity with zero time duration that only shows a precedence relationship among activities

Activity-on-Arrow (AOA) Networks

bc

d

e

fg

Activity Predecessormnrs

__

m, nn

m r

n s

k

j

k

j

j

k

or

Dashed lines are called dummy activities

1 2Excavate

& pour footings

Pour foundation

Install drains

Project Network for House Construction

(AOA network)

3

6

7

4

8

9

5

10

11

12

16

1813

1715

14

Install roughelectrical & plumbing

Pourbasement

floorInstall

cooling &heating

Erectframe & roof

Laybrickwork

Laystormdrains

Installdrywall

Layflooring

Installfinished

plumbing

Installkitchen

equipmentPaint

Finishroof

Installroof

drainage

Finishgrading

Finishfloors

Pourwalks;

Landscape

Finishelectrical

work

Finishcarpeting

Project Network Example

Task Pred. Dur. Task Pred. Dur.

a -- 4 g c,d 1

b -- 3 h e 4

c a 3 i f 5

d a 2 j e,g 6

e b 6 k h,i 1

f b 4

Draw AOA and AON networks

Activity-on-Arrow (AOA or ADM) Network(Initial Network)

Activity-on-Arrow (AOA or ADM) Network(Final Network)

a

b

d

c

gj

k

i

h

f

e

Activity-on-Node (AON or PDM) Network

A project has the following activities and precedence relationships:

Predecessor Predecessor

Activity Activities Activity Activitiesa -- f c,eb a g bc a h b,dd a i b,de b j f,g,h

Draw AOA and AON networks

Project Network Example

Activity on Arrow(Initial Network)

Activity on Arrow(Final Network)

a

b

c

d

e

f

g

hi

j

Activity on Node

Critical Pathpath – any route along the network from start to

finish

Critical Path – path with the longest total duration

This is the shortest time in which the project can be completed.

Critical Activity – an activity on the critical path

*If a critical activity is delayed, the entire project will be delayed. Close attention must be given to critical activities to prevent project delay. There may be more than one critical path.

Critical Path

Brute force approach to finding critical path:

1. identify all possible paths from start to finish

2. sum up durations for each path

3. largest total indicates critical path

(This approach is inefficient, but is instructive)

1

2 6

4 7

53

b = 2

d = 4

g = 9

h = 9

f = 8c = 5

a = 6

k = 6

j = 7

i = 4

e = 3

Slack Times

• EST—Earliest Start Time– Largest EFT of all predecessors

• EFT—Earliest Finish Time– EST + duration for this task

• LFT—Latest Finish Time– Smallest LST of following tasks

• LST—Latest Start Time– LFT – duration for this task

• Slack—LFT – EFT or LST – EST

Computing Slack Times

Task = duration

slack = xxxx

EST EFT

LST LFT

Slack Times Example

Task Pred. Dur. Task Pred. Dur.

a -- 4 g c,d 1

b -- 3 h e 4

c a 3 i f 5

d a 2 j e,g 6

e b 6 k h,i 1

f b 4

For each task, compute ES, EF, LF, LS, Slack

Start Finish

a=4slack=

b=3slack=

c=3slack=

d=2slack=

e=6slack=

f=4slack=

g=1slack=

h=4slack=

i=5slack=

j=6slack=

k=1slack=

Task=durslack=xxx

EST EFT

LFTLST

Gantt Charts

• The main purpose of a Gantt chart is to display the schedule of activities

• They are easy to understand• They are flexible in that you can also show other

information on the chart, such as resources required, who is responsible, critical activities, percent complete, etc.

• All project management software packages will create Gantt charts

Gantt ChartActivity

a

b

c

d

e

f

g

h

i

Time (weeks)

Project Scheduling Exercise

DynaTech Equipment Corp. case• Divide into small groups• Read case (5 minutes)• Assignment: (40 minutes)

– List the immediate predecessors and WBS number for each activity

– Draw project network diagram (lowest level)– Draw Gantt chart– Determine project completion time

Other Precedence Relationships

• The typical precedence relationship between two activities is that when the first activity has finished, then the second activity can start. In this case the first activity is called the immediate predecessor of the second activity.

• This is referred to as a Finish-to-Start linkage.• Other precedence relationships, or linkages, are

also possible.• Lead and lag times are also possible.

Other Precedence Relationships

Finish-to-StartLinkage (FS)

Start-to-StartLinkage (SS)

Finish-to-FinishLinkage (FF)

Start-to-FinishLinkage (SF)

Activity 1

Activity 2

Activity 1

Activity 2

Activity 1

Activity 2

Activity 1

Activity 2

Lead and Lag Times

Lead (-) and Lag (+) times are expressed as part of the immediate predecessor notation. So 1FS+3 listed for the immediate predecessor of Activity 2 means that Activity 1 is the predecessor with a Finish-to-Start linkage and a 3-day lag time after Activity 1 finishes before Activity 2 can start.

1FS-3 means that Activity 2 can start 3 days before Activity 1 finishes.

1FF+3; 1SF-5; 1SS+4

Management of Project Schedules

• Meeting project deadlines is often the most important goal in project management

• Careful scheduling of project activities is critical to meeting the project due date

• Effective project managers should have a good understanding of the issues involved in activity scheduling