engm91- unit 2b- critical path method

7/25/2019 ENGM91- Unit 2b- Critical Path Method

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MSc PROJECT MANAGEMENT

MODULE: ENGM91: PROJECT MANAGEMENT & CONTROL.

Unit 2b: THE CRITICAL PATH METHOD.



2b.1 INTRODUCTION

In the previous lesson you have learned how to subdivide a project into smaller

manageable tasks or activities via a Work Breakdown Structure (WBS). You alsolearned how to construct a Network Diagram which shows the logical relationships

between and general se!uence o" activities which make up a project. What we

didn#t consider in the previous lesson was the time dimension o" activities within the

network diagram.

By way o" e$planation each activity will have a known or estimated duration. Some

activities will need to be carried out in series while others can be carried out in

parallel. %his almost always leads to some degree o" "le$ibility in the scheduling o"

activities. In turn this can a""ect the duration o" the whole project. &or e$amplesuppose a project comprised ' activities. %he time taken to complete the project is

rarely the sum o" the durations o" the ' individual activities because parallel

activities can be carried out at the same time provided you have su""icient resources

to allow this.

*ecisions on when to schedule activities (in terms o" their start and "inish dates) is

largely a "unction o" (i) network logic and (ii) individual activity durations. +pplying

this type o" analysis leads us to one o" the most important techni!ues available to the

project manager namely that o" the ,ritical -ath ethod (,-). %hat is the major

topic we will consider in this lesson.

2b.2 YOUR AIMS.

/n completion o" this lesson you should be able to0

• ,alculate the start and "inish dates "or individual activities within a network

diagram.

• -resent this data within the network diagram in a style according to an

appropriate convention.

• Identi"y the ,ritical -ath through thy network o" activities and calculate the overall

project duration.

2b.3 STUDY ADICE.

%his lesson relates to ,hapter ' (,ritical -ath ethod) o" the module te$t. You have

already studied Sections ' to 1 o" this chapter in the previous lesson. In this lesson

we will consider the remainder o" ,hapter '. When studying ,hapter ' take care

to become "amiliar with the terminology used and work through and understand the

worked e$amples provided.



You should also re"er to the supporting -ower-oint presentations which contain a

number o" worked e$amples o" (i) network diagram development and (ii) critical path

indenti"ications2calculations.

!You should now read Sections 8 to16 of Chapter 10 of the module tet .

2b." ACTIITY #O$ES.

3aving identi"ied activity relationships and durations it is possible to establish the

start and "inish dates "or each activity and "or the project as a whole.

ost projects involve a large number o" related activities. %he logic network diagram

enables the project planner to understand the order in which activities can take

place. eeting the target completion date "or a project normally re!uires that some

activities are started as soon as the preceding ones are completed. In other cases

there is likely to be some "le$ibility about when activities can be started and

completed. It is in understanding and planning these issues o" timing that network

diagrams and critical path analysis assist the project planner.

%o assist us in this task it is normal to add critical in"ormation other than the activity

identity to each activity bo$. %he layout o" in"ormation inside the activity bo$ may

vary but the one given below is typical. +ctivity bo$es such as the one shown below

(also see &igure '.4 in the module te$t) are the basic building blocks o" the network

diagram (i.e. at the 5nodes6). %hey contain vital in"ormation derived as a result o" theanalysis o" the network. *etails o" the activity number description and duration are

available prior to the analysis. Speci"ically in"ormation on activity start date finish

date and float are the result o" the analysis. Start dates and "inish dates can be

termed 5earl! 6 or 5late6. %he signi"icance o" these terms will become clear as we

work through a number o" e$amples.

E%'( St%t E%'( )ini*+

)',%t Acti-it( I/ntit(N0b/

D0%ti,n

L%t/ St%t L%t/ )ini*+

Network Diagram "cti#it! Bo $a!out%



2b. )ORARD PASS

%he forward pass relates to a 5pass6 through the network diagram and is the "irst

step in calculating the in"ormation needed to "ill the activity bo$es (Burke deals withthis topic in Section 7 ,hapter '). It allows us to "ill in the earl! start and earl!

finish dates in each bo$.

,onsider a simple hypothetical 8 activity in series project as de"ined in the table

below0

Acti-it( P/c/in4 Acti-it( D0%ti,n 5D%(*6

+ 9 8

B + :

, B 4

%his leads to a very simple network diagram as shown below0

%here are two main conventions by which start and "inish dates are !uoted and you

should be able to do network diagram calculations according to each o" these

conventions.

2b..1 Di*c/t/ St%t %n )ini*+ D%t/*

%he "irst convention is that adopted by Burke (see Section 7 ,hapter '). +ssume

we are working in units o" days. ;ach day is treated as a discrete entity in the

project timetable. %his convention makes it easy to map the schedule onto a

calendar.

• +ctivity + has a duration o" 8 days and would there"ore start on *ay '

and "inish on *ay 8 (i.e. occupying *ays ' < and 8).

• +ctivity B has a duration o" : days and would there"ore start on *ay :

(a"ter + has "inished) and "inish on *ay 1 (i.e. occupying *ays : 4 =

and 1).

C # "

A 3



• +ctivity , has a duration o" 4 days and would there"ore start on *ay >

(a"ter B has "inished) and "inish on *ay '< (i.e. occupying *ays > 7 '

'' and '<).

• 3ence the project has a minimum duration o" '< days.

Burke shows this type o" in"ormation on a ?antt ,hart (&igure '.1) which helps to

"urther clari"y the convention.

%he early starts and early "inishes are there"ore as "ollows0

Acti-it( E%'( St%t E%'( )ini*+

A 1 3

# " 7

C 8 12

%his in"ormation may be trans"erred to the network diagram0

2b..2 C,ntin0,0* St%t %n )ini*+ D%t/ Ti/'in/

In the other convention time is treated as a continuous variable such as would be

encountered on a time a$is on a graph. %he main advantage o" this convention is

that we avoid all o" the @ ' day terms in start and "inish date calculations we see in

Sections 7 and ' o" Burke ,hapter ' In accordance with this convention we

could represent the se!uence o" activities on a graph with a continuous time a$is0

8 12

C

" 7

# "

1 3

A 3



3ence0

• + takes place "rom time t A to t A 8.

• B takes place "rom time t A 8 to t A 1.

• , takes place "rom time t A 1 to t A '<.

ote the project still has a minimum duration o" '< days we can#t make a project

duration shrink just by adopting a di""erent time conventionC %he in"ormation may betrans"erred to the network diagram again0

ote that this convention only changes the early start dates by choosing to measure

"rom t A rather than de"ining the start point as *ay '. &or all e$ercises on critical

path in this lesson and later it would be worth doing each e$ercise according to both

conventions just to rein"orce the di""erences and similarities. Beyond that adopt the

convention you "eel most com"ortable with.

2b. #ACARD PASS

CBA

7 12

C

3 7

# "

; 3

A 3



%he backward pass is very similar but allows us to calculate the late start and late

"inish dates. %he late "inish date o" the "inal activity may be given2assigned but i" not

we simply use the early "inish date o" the "inal activity as its late "inish date.

We can now subtract activity durations "rom this late "inish date as we pass

backwards through the network diagram. With a little thought here it should be

clear that i" we do this e$ercise on our simple 89activity diagram we#re going toend up with all o" our late starts and "inishes being identical to our early starts and

"inishes. %his is true but it won#t be true "or other network diagrams we look at.

3owever "or the sake o" completeness we will complete the 89activity diagram

with late start D late "inish data and also in accordance with each convention.

Discrete Dates& Start and 'inish Dates following 'orward and Backward

(asses

Continuous )imeline& Start and 'inish Dates following 'orward and Backward

(asses

7 12

C

12

8 12

C

8 12

" 7

# "

" 7

1 3

A 3

1 3

7 12

C

7 12

3 7

# "

3 7

; 3

A 3

; 3



2b.7 ACTIITY )LOAT AND CRITICAL PATH

+n important reason "or analysing a network is to determine what "le$ibility there is in

precisely when each activity must be started and completed. +ctivity "loat or slack is

a measure o" the e$tent to which an activity can be delayed or e$tended be"ore

having any e""ect on subse!uent activities or the project as a whole. I" an activity has

no "loat there is no "le$ibility "or it to be delayed or e$tended.

%he "loat or slack "or each activity may be calculated a"ter having completed the

backward pass. +ctivity &loat may be calculated as "ollows0

)',%t < L%t/ St%t = E%'( St%t or

)',%t < L%t/ )ini*+ = E%'( )ini*+

With re"erence to our 89activity diagram the above calculations result in >/, "loat"or all 8 activities. %his is as would be e$pected in a simple series project where the

late "inish was de"ined as the early "inish.



%he above network diagram could be completed by speci"ying Eero "lat in each "loat

bo$.

Discrete Dates& 'loat* Start and 'inish Dates

Continuous )imeline& 'loat* Start and 'inish Dates

%he se!uence o" activities in which there is no "loat is re"erred to as the Citic%' P%t+through the network and determines the overall duration o" the project. I" le"t

unattended a delay in any activity on the critical path will inevitably lead to a delay in

the project as a whole. %he progress o" items on the critical path should there"ore be

closely monitored. %he critical path is also important i" we need to accelerate a

project#s progress.

In our simple 89activity project all 8 activities are on the ,ritical -ath. We now need

to look at more realistic network diagrams to appreciate the ,ritical -ath ethod in

action.

2b.8 ORED CRITICAL PATH METHOD E$AMPLE

/n the basis o" an activity logic table (which includes activity durations) you should

be able to0

construct the network diagram

per"orm a "orward pass to identi"y early start and early "inish dates

per"orm a backward pass to identi"y late start and late "inish dates

8 12

; C

8 12

" 7

; # "

" 7

1 3

; A 3

1 3

7 12

; C

7 12

3 7

; # "

3 7

; 3

; A 3

; 3



• calculate activity "loats

• determine minimum project duration

• identi"y the ,ritical -ath through the activity network

%he best way to achieve this is to work through some e$amples step9by9step. We

present one such e$ample here but also ensure that you work through those

e$amples given in Burke. Burke gives such e$amples in ,hapter ' but also in

+ppendi$ '.

SA? 1:

%he table below shows the logical relationship between activities table "or aparticular project.

Acti-it( P//c/**,5*6 D0%ti,n 5D%(*6

+ 9 8

B + 1

, + 4

* , 8

; B <

& B , :

? * ; & =

$ogic ta+le for pro,ect acti#ities " through -%

5i6 ,onstruct a etwork *iagram showing the various logical activity relationships"rom this in"ormation.

5ii6 -er"orm a "orward and backward pass to complete activity bo$es . +rrange datawithin activity bo$es as outlined below.

E%'( St%t E%'( )ini*+

)',%t Acti-it( I/ntit(N0b/

D0%ti,n

L%t/ St%t L%t/ )ini*+

$a!out of "cti#it! Bo information%

5iii6 3ighlight the critical path on your diagram and state the earliest projectcompletion time.



SA? 1: S,'0ti,n:

5i6 %he "irst step is to draw up a network diagram that obeys the logical rules o" the

given table. Satis"y yoursel" that the "ollowing network diagram depicts the correct

logical relationships.



5ii6 It is now necessary to conduct a "orward pass to determine early start and "inish dates. %he result o" the "orward pass is shown

below. ote that we#ve used the discrete date convention as does Burke.



Some o" these "igures may need some e$planation. Fook "or e$ample at this portion o" the diagram0

• ; must "ollow B. B has its early "inish on *ay '. %here"ore ; cannot begin until *ay ''. Its early start is there"ore *ay ''.

• & cannot begin until both B and , have been completed. ,#s earliest "inish is *ay > but B#s earliest "inish is *ay '.

%here"ore & cannot begin until *ay '' at the earliest (since B needs to be complete).

• %his leads to a general principle that in the "orward pass it is the latest2highest early "inish date (i.e. B#s ' rather than ,#s >

in the e$ample above) which determines the late start "or an immediate succeeding activity.

+pply the same logic to the rest o" the diagram and satis"y yoursel" that the "orward pass data is correct. We now conduct a

backward pass to determine late starts and late "inishes.



%he main complication in the backward pass process is where < activities with different late starts "eed back into another activity.

3ow do we then decide on the latest "inish date "or that activityG %he logic behind these "igures can be seen by considering the

same portion o" the network diagram as earlier.

• %he backward pass through ; and & leads into B.

• ; has its latest start on *ay '8. & has its latest start on *ay ''.

• I" the latest that & can start is *ay '' then +FF predecessors HS% be "inished by *ay '.

• 3ence the latest B can "inish is *ay ' since it is a predecessor "or & (and & must begin on *ay '' at the latest).

• %his leads to a general principle that in the backward pass it is the lowest2earliest late start date (i.e. &#s '' rather than ;#s

'8 in the e$ample above) which determines the late "inish "or an immediate predecessor.

We can now calculate activity "loats and determine the critical path through the network. emember that activity "loat is calculated

"rom either o" the "ollowing e$pressions0



)',%t < L%t/ St%t = E%'( St%t or

)',%t < L%t/ )ini*+ = E%'( )ini*+



5iii6 %he completed network diagram is as shown below with the critical path highlighted in red.0

+ctivities + B & and ? have Eero "loat and are there"ore on the critical path.

%he earliest project completion time is < days.



N.#. )he supporting (owerpoint presentation gi#es further eamples of network anal!sis .deri#ed from /antel /eredith

see reading list2* where +oth the 3discrete4 and 3continuous4 time con#entions with respect to start dates and finish

dates are illustrated% "gain* it is emphasised that !ou must +e familiar with +oth techni5ues and a+le to switch freel! from

one to the other%



2b.9 LOGICAL ERRORS

With more comple$ networks care must be taken to validate the integrity o" the

network#s logic since logical errors can creep in. ead Section '8 o" ,hapter ' in

the module te$t and then answer the "ollowing !uestion.

SA? 2 An*@/:

%he 8 types o" logic error mentioned are0

• Fogical Foop0

%his is an impossible situation. +ctivities ' and < are predecessors "or +ctivity

8. %here"ore +ctivity 8 can#t be a predecessor "or +ctivity ' as implied.

• Fogical *angle0

SA? 2: Identi"y the 8 types o" logical error described by Burke anddiscuss their nature.

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+ logical dangle is simply where an activity is le"t 5dangling6 or hanging. It either

comes "rom nowhere or goes nowhere. /nly the "irst and "inal activities have single

5connections6.

• edundant -recedence elationship0

In a network diagram only I;*I+%; predecessors need to be made e$plicit with

connecting arrows. In the above diagram ' is a predecessor "ro < and < is a

predecessor "ro 8. %here"ore ' is also a predecessor "or 8 but this does not

need to be shown on the network diagram. %he connecting arrow shown between

' and 8 is unnecessary or redundant.

2b.1; ACTIITY )LOAT = REISITED

Burke deals with some e$tensions to the concept o" activity "loat in Section '= o"

,hapter '. We encountered one such concept (o" "loat being shared by a number

o" activities) earlier in this lesson. ead Section '= o" ,hapter ' and then answer

the "ollowing !uestion.

SA? 3: Identi"y the 8 types o" "loat described by Burke and comment ontheir signi"icance.

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SA? 3 An*@/:

T,t%' )',%t. &loat is shared with all other activities. I" the "loat is used by one activity

"loat available "or other activities will be reduced. ,are must be taken to avoid

assuming that the apparent "loat is available "or all activities independently.

)// )',%t. %his is a measure the amount o" "loat an activity can use up without

a""ecting the early start o" other activities.

N/4%ti-/ )',%t. %his is an indication that an activity must start be"ore the preceding

activities are "inished. /" course there cannot be negative "loat in a real9li"e

situation. It is however a use"ul academic tool when conducting e$ercises in project

acceleration (sometimes called 5crashing6).

2b.11 LESSON SUMMARY

We have built on our knowledge o" activity se!uencing "rom the previous lesson and

incorporated a time dimension into our network diagrams. In doing so we have

analysed networks through (i) "orward passes (ii) backward passes and (ii) activity

"loat calculations. Beyond that we have identi"ied the critical path through the

network as the path through activities with Eero "loat. %he critical path is important in

that it determines the overall duration o" the project. *elay in any activity on the

critical path leads to a delay in the project as a whole.

&inally we have looked at some o" the rami"ications o" the critical path method interms o" (i) the nature o" any "loat identi"ied and (ii) possible errors in the logic o"

networks.

%his leaves us in a good position to begin considering later topics such as project

acceleration and resource planning and control.

engm91- unit 2b- critical path method

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