Project Scheduling

Project Management 517Chapter 8

Prof. M. Anvarihttp://www.anvari.net/project_management.htm

Scheduling Scheduling Defined Gantt Charts Network Techniques: PERT and

CPM Determining Task Durations

Probability and Simulation Some Examples

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Scheduling Defined The conversion of a project action

plan into an operating timetable Serves as the basis for monitoring

and controlling the project A major tool for the management of

projects

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Scheduling A schedule is the conversion of a

project action plan into an operating timetable

It serves as the basis for monitoring and controlling project activity

Taken together with the plan and budget, it is probably the major tool for the management of projects

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Some Benefits of Successful Scheduling Illustrates interdependence of all tasks Identifies times when resources must be

available Facilitates communication throughout

the project Determines critical activities/critical

path Affects client expectations through

establishment of activities, milestones, and completion dates

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A Process for Scheduling 1. Think 2. List activities 3. Arrange activities considering

precedence and relationships 4. Develop Gantt charts and PERT/CPM

networks 5. Determine critical activities/critical

path 6. Crash and adjust as necessary

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Gantt Charts

The Gantt chart shows planned and actual progress for a number of tasks displayed against a horizontal time scale

It is an effective and easy-to-read method of indicating the actual current status for each set of tasks compared to the planned progress for each item of the set

It can be helpful in expediting, sequencing, and reallocating resources among tasks

Gantt charts usually do not show technical dependencies

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Gantt Charts

Advantages Easy to understand Easy to show progress and status Easy to maintain Most popular view to communicate project status

to client and/or senior management Disadvantages

Can be superficial Not always easy to see precedence, relationships

JAN FEB MAR

1 8 15 22 29 5 12 19 26 5 12 19 26

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Network Techniques: PERT and CPM

With the exception of Gantt charts, the most common approach to scheduling is the use of network techniques such as PERT and CPM

The Program Evaluation and Review Technique (PERT) was developed by the U.S. Navy in 1958

The Critical Path Method (CPM) was developed by DuPont, Inc during the same time period

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Scheduling Terminology

Activity - A specific task or set of tasks that are required by the project, use up resources, and take time to complete

Event - The result of completing one or more activities. An identifiable end state occurring at a particular time. Events use no resources.

Network - The combination of all activities and events define the project and the activity precedence relationships

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Scheduling Terminology

Path - The series of connected activities (or intermediate events) between any two events in a network

Critical - Activities, events, or paths which, if delayed, will delay the completion of the project. A project’s critical path is understood to mean that sequence of critical activities that connect the project’s start event to its finish event

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Scheduling Terminology

An activity can be in any of these conditions: It may have a successor(s) but no predecessor(s)

- starts a network It may have a predecessor(s) but no successor(s)

- ends a network It may have both predecessor(s) and successor(s)

- in the middle of a network Interconnections from horizontal links in

vertical WBS

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PERT/CPM Network Charts

Advantages Allows visualization of task relationships Facilitates calculation of critical path Clarifies impact of decisions on downstream

activities Disadvantages

Complex, not easy to comprehend at a glance Charts don’t readily depict durations, dates,

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Look at a Simple Network, for a Simple Project

Activity

A

B

C

D

E

F

Duration (weeks)

14

3

3

7

4

10

Predecessor

Start

Start

A,B

B

C,D

E

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Drawing Networks

Activity-on-Arrow (AOA) networks use arrows to represent activities while nodes stand for events

Activity-on-Node (AON) networks use nodes to represent activities with arrows to show precedence relationships

The choice between AOA and AON representation is largely a matter of personal preference

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AOA Network Building Blocks

8079Install software

EventActivity

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Activity-on-Node Network Fundamentals

X

Y

Z

Y and Z are preceded by X

Y and Z can begin at thesame time, if you wish

(B)

A B C

A is preceded by nothingB is preceded by AC is preceded by B

(A)

J

K

L

M

J, K, & L can all begin atthe same time, if you wish(they need not occursimultaneously)

All (J, K, L) must becompleted before M canbegin

but

X Z

AAY

(C)

(D)

Z is preceded by X and Y

AA is preceded by X and Y

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A Simple Network (AON) (cont’d)

Start

A 14 C 3

E 4 F 10

B 3 D 7 Finish

Calculate:

Critical Path

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The Critical Path

Start

A 14 C 3

E 4 F 10

B 3 D 7 Finish

ES = 0EF = 14

ES = 14EF = 17

ES = 17EF = 21

ES = 21EF = 31

ES = 0EF = 3

ES = 3EF = 10

= Critical Path

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ES = Early StartEF = Early Finish

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Determining Slack How much slack is there Where is it? How do you know? Why might you care?

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Determining Slack (cont’d)

Start

A 14 C 3

E 4 F 10

B 3 D 7 Finish

ES = 0EF = 14LS = 0LF = 14

ES = 14EF = 17LS = 14LF = 17

ES = 17EF = 21LS = 17LF = 21

ES = 21EF = 31LS = 21LF = 31

ES = 0EF = 3LS = 7LF = 10

ES = 3EF = 10LS = 10LF = 17

Work Back . . .

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ES = Early StartEF = Early FinishLS = Late StartLF = Late Finish

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Determining Slack (cont’d)

Start

A 14 C 3

E 4 F 10

B 3 D 7 Finish

ES = 0EF = 14LS = 0LF = 14

ES = 14EF = 17LS = 14LF = 17

ES = 17EF = 21LS = 17LF = 21

ES = 21EF = 31LS = 21LF = 31

ES = 0EF = 3LS = 7LF = 10

ES = 3EF = 10LS = 10LF = 17 Slack = LS - ES

CP = 0 Slack, where ES = LS

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Three Sequential Activities, AON Format

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Activity Network, AON Format

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Activity Network, AOA Format

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Sample of Network Construction, Figure 8-5

AONAON AOAAOA

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Sample of Network Construction, Figure 8-6

AONAON AOAAOA

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Sample of Network Construction, Figure 8-7

AONAON AOAAOA

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Networking Concurrent Activities, Figure 8-8

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Activity c Not Required for e, Figure 8-9

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Showing Precedents, Figure 8-10

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MSP Gantt Chart, Figure 8-11

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MSP AON Network, Figure8-12

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An AON Network for a 10-Activity Project, Figure 8-13

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Distribution of Possible Activity Times, Figure 8-14

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AON Network with Durations and Variances, Figure 8-15

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AON Network with Earliest/Latest Start/Finish Times, Figure 8-16

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Gantt Chart of Table 8-4, Figure 8-17

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AON Network of Table 8-4, Figure 8-18

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MSP Gantt Chart of Table 8-4, Figure 8-19

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MSP Gantt Chart, Video Project, Figure 8-20

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MSP AON Network, Video Project, Figure 8-21

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MSP Calendar, Video Project, Figure 8-22

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MSP Calendar, Video Project, Figure 8-22 (continued)

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MSP Gantt Chart, Video Project, Figure 8-23

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Probability Distribution,Figure 8-24

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a, m, and b Estimates,Figure 8-25

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Crystal Ball®

Spreadsheet, Figure 8-26

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CB Frequency Chart, Figure 8-27

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CB Summary Statistics,Figure 8-28

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CB Percentile Probabilities, Figure 8-29

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CB Cumulative Probability Chart, Figure 8-30

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Precedence Diagramming Conventions, Figure 8-31

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Sample GERT Network,Figure 8-33

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Apartment Complex Network, Figure 8-35

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Hypothetical Network

2 5 61

4

3

5

16

620

13

30

TE=64

Calculate t(e) and Z for this network……

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Activity and Project Frequency Distributions

ACTIVITY PROJECT

a m b TE

(A) (B)

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PERT Activity Calculation

t(e) = a + 4m + b a = Most Optimistic (MO)

6 m = Most Likely (ML)

b = Most Pessimistic (MP)

t(e) = Activity Duration

When a single estimate for activity time is not sufficient!

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PERT Schedule Probability

Z is derived from a table of predetermined probabilities

Z = T(S) – T(E) Z = Probability of SD(T[E])2 Meeting Schedule

T(S) = Scheduled Duration

T(E) = Critical Path Duration

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PERT Activity Times & Variances

Activity a m b t(e)

1-2 17 29 47

2-3 6 12 24

2-4 16 19 28

3-5 13 16 19

4-5 2 5 14

5-6 2 5 8

Variance of Activity Estimates

Activity a m b t(e) [(b-a)/6]2

Var

1-2 17 29 47 30

2-3 6 12 24 13

2-4 16 19 28 20

3-5 13 16 19 16

4-5 2 5 14 6

5-6 2 5 8 6

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Possible Project Durations

TE=64

TS=67

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Z Table

Z Value Probability Z Value Probability

-2.0 0.02 +2.0 0.98

-1.5 0.07 +1.5 0.93

-1.0 0.16 +1.0 0.84

-0.7 0.24 +0.7 0.76

-0.5 0.31 +0.5 0.69

-0.3 0.38 +0.3 0.62

-0.1 0.36 +0.1 0.54