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Project Scheduling: Networks, Duration

Estimation, and Critical PathChapter 9

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1. Understand and apply key scheduling terminology. 2. Apply the logic used to create activity networks,

including predecessor and successor tasks. 3. Develop an activity network using Activity-on-Node

(AON) techniques. 4. Perform activity duration estimation based on the use

of probabilistic estimating techniques. 5. Construct the critical path for a project schedule

network using forward and backward passes. 6. Identify activity float and the manner in which it is

determined. 7. Understand the steps that can be employed to reduce

the critical path.

Learning Goals

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Project scheduling requires us to follow some carefully laid-out steps, in order, for the schedule to take shape.

Project planning, as it relates to the scheduling process, has been defined by the PMBoK as:

◦ “The identification of the project objectives and the ordered activity necessary to complete the project including the identification of resource types and quantities required to carry out each activity or task.”

Project Scheduling

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Represents the conversion of project goals into an achievable methodology.

Creates a timetable and reveals the network logic that relates project activities to each other.

A graphical set of sequential relationships between project task which, when performed, result in the completion of the project goals.

Vitally important to obtaining project goals, being on time and on budget.

Project Scheduling

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Allows project teams to use a method for planning and scheduling

There are several advantages when project networks and scheduling are done well

Project Network Diagrams (PND)

Show interdependence

Facilitate communication

Help schedule resources

Identify critical activities

Determine project completion

Show start & finish dates for task

See slide 26 for an example

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Project Scheduling Terms

SuccessorsPredecessorsNetwork diagramSerial activitiesConcurrent

activities

ED

C

B

A F

Merge activitiesBurst activitiesNodePathCritical Path

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Most Common Methods for Constructing Activity Networks

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

C

ED

B F

E

C

DB F

…and activities on node.

AOA vs. AON

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1. Some determination of activity precedence ordering must be done prior to creating the network.

2. Network diagrams usually flow from left to right.3. An activity cannot begin until all preceding connected

activities have been completed.4. Arrows on networks indicate precedence and logical flow.

Arrows can cross over each other, although it is helpful for clarity’s sake to limit this effect when possible.

5. Each activity should have a unique identifier associated with it (number, letter, code, etc.).

6. Looping, or recycling through activities, is not permitted.7. Although not required, it is common to start a project on a

single node. A single node point also is typically used as a project end indicator.

Rules for Developing Activity Networks

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Information for Network Construction Name: Project Delta

Activity Description PredecessorsA Contract signing None

B Questionnaire design A C Target market ID A D Survey sample B, C E Develop presentation B F Analyze results D G Demographic analysis C H Presentation to client E, F, G

Construct a Network Diagram

Example of Creating a Project Activity Network

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Activity Network Example

A Contract

CMarket ID

BDesign

GDemog.

EDev. Present.

DSurvey

F Analysis

H Present

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College research paper example

Project Activities Linked In Series/Parallel (Concurrent)

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Merge/Burst Activities

Activity A

Activity B

Activity C

Activity D Activity C

Activity B

Activity A

Activity D

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Node Labels

Early Start

Activity Float Activity Descriptor

Late Start

ID Number

Activity Duration

Late Finish

Early Finish

11 D 240 Survey11 13 24

ES ID EFSlack Task NameLS Duration LF

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Duration Estimation

Assumptions◦ Based on normal working methods during normal

hours◦ Durations are always somewhat uncertain◦ Timeframes can be from minutes to weeks

Methods◦ Past experience◦ Expert opinion◦ Mathematical derivation based on Beta Distribution

Most optimistic (a) time – better then planned Most likely (m) time – realistic expectation Most pessimistic (b) time – Murphy’s Law kicks in

There are only two types of estimates…lucky and wrong.

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Critical Path Method (CPM) assumes we know a fixed time estimate for each activity and there is no variability in activity times

Program Evaluation and Review Technique (PERT) uses a probability distribution for activity times to allow for variability

Variability in Activity Times

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Where:

 a = Most optimistic time

 m = Most likely time

 b = Most pessimistic time

Activity Duration Estimation – Beta Distribution

22 =

6

b aActivity Variance

4 = TE

6

a m bActivity Duration

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Project variance is computed by summing the variances of activities on the critical path

Project variance = (variances of activities on critical path)

Probability of Project Completion

Project standard deviation = Project Variance

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Task Predecessor a m b mean variance

Z -- 7 8 15 9.00 1.78

Y Z 13 16 19 16.00 1.00

X Z 14 18 22 18.00 1.78

W Y, X 12 14 16 14.00 0.44

V W 1 4 13 5.00 4.00

T W 6 10 14 10.00 1.78

S T, V 11 14 19 14.33 1.78

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

2. Sketch the network described in the table.

3. Determine the expected project time and standard deviation.

Network Example

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Constructing the Network Paths 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

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Activity Description Predecessors Estimated Duration

A Contract signing None 5

 

B Questionnaire design A 5

C Target market ID A 6

 

D Survey sample B, C 13

E Develop presentation B 6

 

F Analyze results D 4

G Demographic analysis C 9

 

H Presentation to client E, F, G 2

Constructing the Critical Path Example

Construct the critical path.

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Activity Network with Task Durations and Critical Path

AContract

5

BDesign

5

CMarket ID

6

DSurvey

13

GDemog.

9

FAnalysis

4

EDev. Present

6

HPresent

2

Critical Path is indicated in bold

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Rules for Forward/Backward PassForward Pass Rules (ES & EF)

◦ ES + Duration = EF◦ EF of predecessor = ES of successor◦ Largest preceding EF at a merge point becomes

ES 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

ES ID EFSlack Task NameLS Duration LF

Calculate the forward/backwards pass.

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Activity Network with Forward Pass Added

0 A 5Contract

5

5 B 10Design

5

5 C 11Market ID

6

11 D 24Survey 13

11 G 20Demograph.

9

24 F 28Analysis

4

10 E 16Dev. Present

6

28 H 30Presentation

2

ES ID EFSlack Task NameLS Duration LF

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Activity Network With Backward Pass Added

0 A 5Contract

0 5 5

5 B 10Design

6 5 11

5 C 11Market ID

5 6 11

11 D 24Survey

11 13 24

11 G 20Demograph.

19 9 28

24 F 28Analysis

24 4 28

10 E 16Dev. Present

22 6 28

28 H 30Presentation

28 2 30

ES ID EFSlack Task NameLS Duration LF

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Informs us of the amount an activity can be delayed without delaying the overall project.

It is determined as a result of performing the forward and backward pass through the network.

Calculated either by◦ LF-EF = Slack◦ LS-ES = Slack

The critical path is the network path with “0” slack.*◦ *This assumes a deadline has not been set for LF that is

within our calculated project time. ◦ *Negative float is a result of the project time being longer

than a set project end time.

Activity Float - Slack Time

Calculate the slack time and determine critical path.

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Completed Activity Network With Critical Path And Activity Slack Times Identified

0 A 50 Contract0 5 5

5 B 101 Design6 5 11

5 C 110 Market ID5 6 11

11 D 240 Survey11 13 24

11 G 208 Demograph.

19 9 28

24 F 280 Analysis

24 4 28

10 E 1612 Dev. Present

22 6 28

28 H 30 0 Presentation

28 2 30

ES ID EFSlack Task NameLS Duration LF

Critical Path is indicated in bold

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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.

3. Determine the critical path.

Example

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Laddering Activities

Project ABC can be completed more efficiently if subtasks are used. Example: A does not need to be completely finished before work

on B starts.

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)

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Hammock Activities

Used as a summary 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

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Eliminate tasks on the critical path◦ remove task with no value

Convert serial paths to parallel when possible Overlap sequential tasks

◦ use laddering when possible Shorten the duration on critical path tasks Shorten

◦ early tasks (have you read “The Goal”)◦ longest tasks◦ easiest tasks◦ tasks that cost the least to speed up – “crashing”

Reducing the Critical Path

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1. Define the following terms: Path, Activity, Early start, Early finish, Late start, Late finish, Forward pass, Backward pass, Node, AON, Float, Critical Path, PERT

2. Distinguish between serial activities and concurrent activities. Why do we seek to use concurrent activities as a way to shorten a project’s length?

3. List three methods for deriving duration estimates for project activities. What are the strengths and weaknesses associated with each method?

Discussion Questions

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4. In your opinion, what are the chief benefits and drawbacks of using beta distribution calculations (based on PERT techniques) to derive activity duration estimates?

5. “The shortest total length of a project is determined by the longest path through the network.” Explain the concept behind this statement. Why does the longest path determine the shortest project length?

6. The float associated with each project task can only be derived following the completion of the forward and backward passes. Explain why this is true.

Discussion Questions

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Now that Joe has agreed to your WBS, he wants to review a schedule and present it to the president. She is a “big picture” thinker and does not usually get involved with the details, so Joe wants to limit the content of the diagram you show her to the basics that concern her.

You have also worked with your team on estimating the durations of each of the work packages in the WBS. Note that in this case, the work packages are the scheduled activities. Here is your current plan for the briefing to the president:

Case Study 5

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Case Study 5

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1. Build a network diagram2. Calculate forward pass, backward pass,

float, and critical path3. Be ready to address—

◦ How long will the project take?◦ When should you begin installing new furniture,

communications equipment, and computers if you want to be in the new office by July 31?

◦ What items are on the critical path?

Case Study 5