Project Scheduling: Networks, Duration estimation, and Critical Path.

Project Scheduling: Networks, Duration estimation,

and Critical Path

Project Scheduling Terms• Successors

• Predecessors

• Network diagram

• Serial activities

• Concurrent activities

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C

B

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Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-3

Project Scheduling Terms

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• Merge activities

• Burst activities

• Node

• Path

• Critical Path


Network Diagrams

Show interdependence

Facilitate communication

Help schedule resources

Identify critical

activities

Determine project completion

Show start & finish dates

AOA vs. AON

The same mini-project is shown with activities on arrow…

C

ED

B F

E

C

DB F

…and activities on node.

Node Labels

Early Start

Activity Float Activity Descriptor

Late Start

ID Number

Activity Duration

Late Finish

Early Finish

Duration Estimation Methods

• Past experience• Expert opinion• Mathematical derivation – Beta distribution

– Most likely (m)– Most pessimistic (b)– Most optimistic (a)

22 =

6

b aActivity Variance s

4 = TE

6

a m bActivity Duration

Task Predecessor a m b

A -- 7 8 15

B A 13 16 19

C A 14 18 22

D B, C 12 14 16

E D 1 4 13

F D 6 10 14

G F, E 11 14 19

1. Sketch the network described in the table.

2. Determine the expected duration and variance of each activity.


Constructing the Critical Path

• Forward pass – an additive move through the network from start to finish

• Backward pass – a subtractive move through the network from finish to start

• Critical path – the longest path from end to end which determines the shortest project length

Rules for Forward/Backward Pass

Forward Pass Rules (ES & EF)– ES + Duration = EF– EF of predecessor = ES of successor– Largest preceding EF at a merge point becomes EF

for successor

Backward Pass Rules (LS & LF)– LF – Duration = LS– LS of successor = LF of predecessor– Smallest succeeding LS at a burst point becomes LF

for predecessor

Task Predecessor Time

A -- 4

B A 9

C A 11

D B 5

E B 3

F C 7

G D, F 3

H E, G 2

K H 1

1. Sketch the network described in the table.

2. Determine the ES, LS, EF, LF, and slack of each activity

Laddering Activities

Project ABC can be completed more efficiently if subtasks are used

A(3) B(6) C(9) ABC=18 days

Laddered ABC=12 days

A1(1) A2(1) A3(1)

B1(2) B2(2) B3(2)

C1(3) C2(3) C3(3)

Hammock Activities

Used as summaries for subsets of activities

0 A 5

0 5 5

5 B15

5 1015

15 C 18

15 3 18

0 Hammock 18

0 18 18

Useful with a complex project or one that has

a shared budget


Reducing the Critical Path

• Eliminate tasks on the CP• Convert serial paths to parallel when possible• Overlap sequential tasks• Shorten the duration on critical path tasks• Shorten

– early tasks– longest tasks– easiest tasks– tasks that cost the least to speed up

Chapter 10



Lags in Precedence Relationships

The logical relationship between the start and finish of one activity and the start and finish of another activity.

Four logical relationships between tasks

1. Finish to Start

2. Finish to Finish

3. Start to Start

4. Start to Finish

Finish to Start Lag

• Most common type of sequencing

• Shown on the line joining the modes– Added during forward pass– Subtracted during backward pass

0 A 6Spec Design

6

6 B 11Design Check

5

15 C 22Blueprinting

7

Lag 4

This lag is not the same as activity slack


Finish to Finish Lag

Two activities share a similar completion point– The mechanical inspection cannot happen until

wiring, plumbing, and HVAC installation are complete

10 B 16Plumbing

6

16 C 24HVAC

5

24 D 25Inspection

1

15 A 21Wiring

6

Lag 3


Start to Start Lag

Logic must be maintained by both

forward and backward pass

31 B 32Plumbing

1

33 C 36HVAC

5

36 D 37Inspection

1

30 A 36Wiring

6

Lag 3


Start to Finish Lag

• Least common type of lag relationship

• Successor’s finish dependent on predecessor’s start

22 B 28Plumbing

6

28 C 33HVAC

5

33 D 34Inspection

1

30 A 36Wiring

6 Lag 3


Gantt Charts

Establish a time-phased network Can be used as a tracking tool

Benefits of Gantt charts

1. Easy to create and comprehend

2. Identify the schedule baseline network

3. Allow for updating and control

4. Identify resource needs


Create a Gantt chart based on the activities listed in the table.

Task Time Pred

A 8 --

B 5 A

C 8 A

D 4 B,C

E 5 D


Crashing

The process of accelerating a project

Principal methods for crashing

Improving existing resources’ productivity Changing work methods Increasing the quantity of resources


Managerial Considerations

• Determine activity fixed and variable costs

• The crash point is the fully expedited activity

• Optimize time-cost tradeoffs

• Shorten activities on the critical path

• Cease crashing when– the target completion time is reached– the crashing cost exceeds the penalty cost


What is the lowest cost to complete this project in 52 weeks? Times are in weeks and costs in dollars. Plot the AON & AOA networks and the GANTT chart.

Activity Pred Normal Time

Min Time

Normal Cost

Crash Cost

A -- 14 9 500 1500

B A 5 2 1000 1600

C A 10 8 2000 2900

D B, C 8 5 1000 2500

E D 6 6 1600 1600

F D 9 6 1500 3000

G E, F 7 4 600 1800

H G 15 11 1600 3600


Activity on Arrow Networks

Activities represented by arrows

Widely used in construction

Event nodes easy to flag

Forward and backward pass logic similar to AON

Two activities may not begin and end at

common nodes

Dummy activities may be required


1. Use AOA to sketch the network that represents the project as described in the table.

2. Calculate early and late event times for all activities.

Activity Time Pred Activity Time Pred

A 4 -- F 15 E

B 2 A G 4 E

C 10 A H 7 D,F,G

D 3 B I 11 H

E 15 B,C


Activity on Arrow Network

A H

F

D

E

C

B I

G


Controversies in the Use of Networks

Networks can be too complex

Poor network construction creates problems

Networks may be used inappropriately

When employing subcontractors– The master network must be available to them– All sub-networks must use common methods

Positive bias exists in PERT networks

Project Scheduling: Networks, Duration estimation, and Critical Path.

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