11

Project Management: Project Management: A Managerial A Managerial

ApproachApproach

Chapter 8 – SchedulingChapter 8 – Scheduling

22

OverviewOverview

• WBS to Schedule ProcessWBS to Schedule Process

• PERTPERT

• Schedule TypesSchedule Types

• CPMCPM

33

SchedulingScheduling• A schedule is the conversion of a A schedule is the conversion of a

project action plan into an project action plan into an operating timetableoperating timetable

• It serves as the basis for monitoring It serves as the basis for monitoring and controlling project activityand controlling project activity

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

99

Simple Schedule – Gantt Simple Schedule – Gantt ChartChart

1010

Network Techniques: PERT and Network Techniques: PERT and CPMCPM

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

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

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

1212

Scheduling TerminologyScheduling Terminology• ActivityActivity - A specific task or set of tasks - A specific task or set of tasks

that are required by the project, use up that are required by the project, use up resources, and take time to completeresources, and take time to complete

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

• NetworkNetwork - The combination of all - The combination of all activities and events define the project activities and events define the project and the activity precedence relationshipsand the activity precedence relationships

1313

Scheduling TerminologyScheduling Terminology

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

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

1414

Scheduling TerminologyScheduling Terminology

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

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

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

successor(s) - in the middle of a networksuccessor(s) - in the middle of a network

• Interconnections from horizontal links Interconnections from horizontal links in vertical WBSin vertical WBS

1515

Hypothetical NetworkHypothetical Network

2 5 61

4

3

5

16

620

13

30

TE=64

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

1616

Activity and Project Frequency Activity and Project Frequency DistributionsDistributions

ACTIVITY PROJECT

a m b TE

(A) (B)

1717

PERT Activity CalculationPERT 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!

1818

PERT Schedule ProbabilityPERT 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

Z = T(S) – T(E) T(S) = Scheduled Duration √ΣVar(T[E])

T(E) = Critical Path Duration

1919

PERT Activity Times & VariancesPERT Activity Times & Variances

ActivityActivity aa mm bb t(e)t(e)

1-21-2 1717 2929 4747 3030

2-32-3 66 1212 2424 1313

2-42-4 1616 1919 2828 2020

3-53-5 1313 1616 1919 1616

4-54-5 22 55 1414 66

5-65-6 22 55 88 55

2020

Variance of Activity Variance of Activity EstimatesEstimatesActivitActivit

yyaa mm bb t(e)t(e) [(b-a)/6][(b-a)/6]22

VarVar

1-21-2 1717 2929 4747 3030 2525

2-32-3 66 1212 2424 1313 99

2-42-4 1616 1919 2828 2020 44

3-53-5 1313 1616 1919 1616 11

4-54-5 22 55 1414 66 44

5-65-6 22 55 88 55 11

2121

Critical PathCritical Path

620

13

5

16

3062

3

4

51

TE = 30 + 13 + 16 + 5 = 64

Var(TE) = 25 + 9 + 1 + 1 = 36

2222

Possible Project DurationsPossible Project Durations

TE=64

TS=67

Z = (67 – 64) / √(25 + 9 + 1 + 1) = 0.5

Hence, the probability of meeting the target schedule (Ts) is 0.69 (69%)

2323

Z TableZ TableZ ValueZ Value ProbabilitProbabilit

yyZ ValueZ Value ProbabilitProbabilit

yy-2.0-2.0 0.020.02 +2.0+2.0 0.980.98

-1.5-1.5 0.070.07 +1.5+1.5 0.930.93

-1.0-1.0 0.160.16 +1.0+1.0 0.840.84

-0.7-0.7 0.240.24 +0.7+0.7 0.760.76

-0.5-0.5 0.310.31 +0.5+0.5 0.690.69

-0.3-0.3 0.380.38 +0.3+0.3 0.620.62

-0.1-0.1 0.360.36 +0.1+0.1 0.540.54

2525

Gantt ChartsGantt Charts

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

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

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

• Gantt charts usually do not show technical Gantt charts usually do not show technical dependenciesdependencies

2727

Drawing NetworksDrawing Networks

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

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

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

2929

Hypothetical NetworkHypothetical Network

2 5 61

4

3

3030

AOA Network Building BlocksAOA Network Building Blocks

8079Install software

EventActivity

3131

Partial Koll Business Center - Partial Koll Business Center - AOAAOA

4

5

1 32AApplication

approval

DService

availabilitycheck

CTrafficstudy

BConstruction

plans

3232

Partial AOA NetworkPartial AOA Network

2

3

1 4A

X

C

B

E

(A)

2

3

1 4A

B

C

X

E

(B)

2 31

4

A

B

XC

E

(C)

3333

Partial AOA NetworkPartial AOA Network

2 31

4

A

B

CX

E

(D) 5D

2 31

4

A

B

CX

E

(E)

5

D

F?

3434

Full AOA NetworkFull AOA Network

KOLL BUSINESS CENTERCounty Engineers Design Department

2 31

4

A5

B

C10

X

5

150

6 7 8

0Y

F10

G170

H35

E15

D5

ActivityDuration

Legend

3535

Activity-on-Node Network Activity-on-Node Network FundamentalsFundamentals

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