Project Management in Practice Fifth Edition

Copyright © 2014 John Wiley & Sons, Inc.

Chapter 5

Scheduling the Project

5-2

Introduction

• Project schedule is the project plan in an altered format

• It is a convenient form for monitoring and controlling project activities

• Can be prepared in several formats

– Gantt charts

– PERT network

– CPM network

5-3

PERT and CPM Networks

• PERT and CPM developed independently in 1950’s

• Program Evaluation and Review Technique (PERT) – U.S. Navy, Booz-Allen Hamilton, and Lockheed

Aircraft

– Probabilistic activity durations

• Critical Path Method (CPM) – Dupont De Nemours Inc.

– Deterministic activity durations

5-4

The Language of PERT/CPM

• Activity – A task or set of tasks

– Uses resources and time

• Event – An identifiable state resulting from completion of one

or more activities

– Consumes no resources or time

– Predecessor activities must be completed

• Milestones – Identifiable and noteworthy events that mark significant

progress

5-5

The Language of PERT/CPM Continued

• Network

– A diagram of nodes (activities or events) and arrows (directional arcs) that illustrate the technological relationships of activities

• Path

– A series of connected activities between two events

• Critical path

– The set of activities on a path that, if delayed, will delay the completion date of the project

• Critical Time

– The time required to complete all activities on the critical path

5-6

Building the Network

• There are two ways of displaying a project network

1. Activities on arrows (AOA) network • The activities are shown as arrows and events as nodes

• Generally more difficult to draw but depicts the technical relationships of the activities well

2. Activities on nodes (AON) network • Each task is shown as a node and the technological

relationship is shown by the arrows

• AON network usually associated with CPM

• AOA network usually associated with PERT

5-7

Sample AON Network

Table 5-1 Figure 5-3

5-8

Sample AOA Network

Table 5-1 Figure 5-6 (a)

5-9

Which to Use?

• Mostly AON used throughout this textbook

• AON used by most of the popular software

• AON networks are easier to draw by hand

– Large (20+ activities) AOA networks are

difficult to draw

• Software to draw AOA networks is

expensive

5-10

Finding the Critical Path and Critical

Time

• ES: Earliest start time

• EF: Earliest finish time

• LS: Latest start time

• LF: Latest finish time

• Displayed on node as shown

• ES + completion = EF

• LS + completion = LF Figure 5-9

5-11

A Sample Problem for Finding the

Critical Path and Critical Time

Table 5-2

5-12

The Complete Network

Table 5-2 and Figure 5-8

5-13

The Critical Path and Completion

Time for Sample Project

Figure 5-10

5-14

Notes on Sample Project

• All activities, and thus all paths, must be

completed to finish the project

• The shortest time for completion of the network is

equal to the longest path through the network

– In this case a-e-h-j

• If any activity on this path

is even slightly delayed,

the project will be delayed

5-15

Calculating Activity Slack

• ES: Earliest start time

• EF: Earliest finish time

• LS: Latest start time

• LF: Latest finish time

• Slack = LS – ES

• Slack = LF – EF

• Either method of calculating slack gives the same

results

5-16

Managerial Implications

• The primary attention of the project

manager must be to activities on the critical

path

• If anything delays one of these activities,

the project will be late

• Projects are easier to manage when there is

project slack

5-17

Doing It the Easy Way—Microsoft

Project (MSP)

• Data is entered using a tab entry table

– Shown on next slide

• MSP automatically numbers each activity

• MSP has numerous options for viewing the

data

• MSP automatically draws an AON network

– Shown on later slide

5-18

A Microsoft Project Version of Data

in Table 5-2

Table 5-3

5-19

A Microsoft Project Version of the

PERT/CPM Network from Table 5-3

Figure 5-11

5-20

Calculating Probabilistic Activity

Times

• Figure below shows distribution of all possible

durations for some task

• Estimate a is such that the actual duration of the

task will be a or lower less than 1 percent of the

time

• Estimate b is such that the actual finish time will

be b or greater less than 1 percent of the time

• Estimate m is the most likely time

Figure 5-13

5-21

Activity Expected Time and

Variance

2

2

E

6

)(Var

6

)4(T

ab

bma

5-22

95 Percent Level

• Task will be a or lower 5 percent of the

time

• Task will be b or greater 5 percent of the

time

3.3

)( ab

5-23

90 Percent Level

• Task will be a or lower 10 percent of the

time

• Task will be b or greater 10 percent of the

time

6.2

)( ab

5-24

The Probabilistic Network

• Expected time (TE) for each activity is calculated

• Variance (σ2) for each activity is calculated

• TE for each activity is used to find the critical path

and critical time for the network

– Slack is calculated in the usual fashion

• The variance (σ2) of a path is the sum of the

activity variances for that path

– Standard deviation (σ) is the square of the variance

5-25

The Probabilistic Network, an

Example

Table 5-4

5-26

Is it Really the Critical path

• Given uncertainty, cannot be sure that any specific path is the critical path

• “Critical” path may take less than expected while another path takes longer

• Only after the fact do we know which path was actually critical

• Managerial implication is the project manager must carefully manage all paths that have a reasonable probability of becoming critical

5-27

Once More the Easy Way

• Microsoft Project can easily handle the

probabilistic network

– However, it does not perform some of the calculations

– These can be done in Excel

• Microsoft Project calculates using a calendar

rather than days

• Uses a real-world calendar including weekends

and holidays

5-28

The Probability of Completing the

Project on Time

• Can the project be completed in X days?

• Can be answered with the information available concerning the level of uncertainty for the various project activities

– Assumes activities are statistically independent

• To complete a project by a specified time requires that all the paths in the network be completed by the specified time

5-29

The Probability of Completing the

Project on Time Continued

• Determining the probability that a project is

completed by a specified time requires calculating

the probability that all paths are finished by the

specified time

• We then calculate the probability that the entire

project is completed within the specified time by

multiplying these probabilities together

– This requires the assumption that the paths are

statistically independent

5-30

Calculating Path Probability

• D = desired project completion time

– 50 in this example

• μ = the sum of the TE activities on the path being investigated

– 47 in this example

• σ2u = the variance of the path

being considered

• A Z of 1.10 yields a probability of 0.8643 or 86 percent

Table 5-4

10.1

00.400.025.078.1

4750

2

D

Z

5-31

The Statistical Distribution of the

Completion Times for Example

Figure 5-18

5-32

Selecting Risk and Finding D

5-33

Simulation

• Simulation is a different approach to managing risk

• Builds on the probabilistic functions already discussed

• Helps to understand the consequences of uncertainty

• Provides insight into the range and distribution of project completion times

5-34

Crystal Ball Chart for Project

Completion Time

Figure 5-19

5-35

Traditional Statistics vs. Simulation

• Both approaches assume that task times are

statistically independent

• Both approaches assume the paths are independent

– A simulation can circumvent the assumption of

statistical independence by including the activity or

path dependencies as part of the model

• Simulation requires less computational effort

5-36

The Gantt Chart

• Henry Gantt developed the Gantt chart

around 1917

• It displays project activities as bars

measured against a horizontal time scale

• Most popular way of exhibiting sets of

related activities in the form of schedules

5-37

The Chart

• Gantt charts are easy to draw

• Problems arise when several tasks begin at the same time and have the same duration

– Can make it hard to find critical path

– Only a problem on hand-drawn charts

• Software shows critical path using some visual method

• Even with software, technical dependencies are harder to see on a Gantt chart

5-38

A Gantt Chart of a Sample Project

Figure 5-21

5-39

A Gantt Chart Showing Critical

Path, Path Connections, Other Data

Figure 5-22

5-40

Extensions to PET/CPM

• Application of fuzzy set theory to aid in

estimating activity durations

• Extensions to precedence diagramming

• Goldratt’s Critical Chain

5-41

Precedence Diagramming

• Finish to start (F to S)

– Finish of Activity A to start of Activity B

• Start to start (S to S)

– Start of Activity A to start of Activity B

• Finish to finish (F to F)

– Finish of Activity A to finish of Activity B

• Start to finish (S to F)

– Start of Activity A to finish of Activity B

5-42

Precedence Diagramming

Conventions

Figure 5-25

5-43

Copyright

Copyright © 2014 John Wiley & Sons, Inc.

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