MSc PROJECT MANAGEMENT MODULE: ENGM91: PROJECT MA NAGEMENT & CONTROL. Unit 2b: THE CRITICAL PATH METHOD.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 1/20
MSc PROJECT MANAGEMENT
MODULE: ENGM91: PROJECT MANAGEMENT & CONTROL.
Unit 2b: THE CRITICAL PATH METHOD.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 2/20
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$amples provided.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 3/20
You should also re"er to the supporting -ower-oint presentations which contain a
number o" worked e$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 $a!out%
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 4/20
2b. )ORARD PASS
%he forward pass relates to a 5pass6 through the network diagram and is the "irst
step in calculating the in"ormation needed to "ill the activity bo$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$.
,onsider a simple hypothetical 8 activity in series project as de"ined in the table
below0
Acti-it( P/c/in4 Acti-it( D0%ti,n 5D%(*6
+ 9 8
B + :
, B 4
%his leads to a very simple network diagram as shown below0
%here are two main conventions by which start and "inish dates are !uoted and you
should be able to do network diagram calculations according to each o" these
conventions.
2b..1 Di*c/t/ St%t %n )ini*+ D%t/*
%he "irst convention is that adopted by Burke (see Section 7 ,hapter '). +ssume
we are working in units o" days. ;ach day is treated as a discrete entity in the
project timetable. %his convention makes it easy to map the schedule onto a
calendar.
• +ctivity + has a duration o" 8 days and would there"ore start on *ay '
and "inish on *ay 8 (i.e. occupying *ays ' < and 8).
• +ctivity B has a duration o" : days and would there"ore start on *ay :
(a"ter + has "inished) and "inish on *ay 1 (i.e. occupying *ays : 4 =
and 1).
C # "
A 3
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 5/20
• +ctivity , has a duration o" 4 days and would there"ore start on *ay >
(a"ter B has "inished) and "inish on *ay '< (i.e. occupying *ays > 7 '
'' and '<).
• 3ence the project has a minimum duration o" '< days.
Burke shows this type o" in"ormation on a ?antt ,hart (&igure '.1) which helps to
"urther clari"y the convention.
%he early starts and early "inishes are there"ore as "ollows0
Acti-it( E%'( St%t E%'( )ini*+
A 1 3
# " 7
C 8 12
%his in"ormation may be trans"erred to the network diagram0
2b..2 C,ntin0,0* St%t %n )ini*+ D%t/ Ti/'in/
In the other convention time is treated as a continuous variable such as would be
encountered on a time a$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$is0
8 12
C
" 7
# "
1 3
A 3
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 6/20
3ence0
• + takes place "rom time t A to t A 8.
• B takes place "rom time t A 8 to t A 1.
• , takes place "rom time t A 1 to t A '<.
ote the project still has a minimum duration o" '< days we can#t make a project
duration shrink just by adopting a di""erent time conventionC %he in"ormation may betrans"erred to the network diagram again0
ote that this convention only changes the early start dates by choosing to measure
"rom t A rather than de"ining the start point as *ay '. &or all e$ercises on critical
path in this lesson and later it would be worth doing each e$ercise according to both
conventions just to rein"orce the di""erences and similarities. Beyond that adopt the
convention you "eel most com"ortable with.
2b. #ACARD PASS
CBA
7 12
C
3 7
# "
; 3
A 3
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 7/20
%he backward pass is very similar but allows us to calculate the late start and late
"inish dates. %he late "inish date o" the "inal activity may be given2assigned but i" not
we simply use the early "inish date o" the "inal activity as its late "inish date.
We can now subtract activity durations "rom this late "inish date as we pass
backwards through the network diagram. With a little thought here it should be
clear that i" we do this e$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
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 8/20
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.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 9/20
%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
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 10/20
• 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*+
$a!out of "cti#it! Bo information%
5iii6 3ighlight the critical path on your diagram and state the earliest projectcompletion time.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 11/20
SA? 1: S,'0ti,n:
5i6 %he "irst step is to draw up a network diagram that obeys the logical rules o" the
given table. Satis"y yoursel" that the "ollowing network diagram depicts the correct
logical relationships.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 12/20
5ii6 It is now necessary to conduct a "orward pass to determine early start and "inish dates. %he result o" the "orward pass is shown
below. ote that we#ve used the discrete date convention as does Burke.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 13/20
Some o" these "igures may need some e$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.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 14/20
%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
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 15/20
)',%t < L%t/ St%t = E%'( St%t or
)',%t < L%t/ )ini*+ = E%'( )ini*+
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 16/20
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.
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 17/20
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%
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 18/20
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$t and then answer the "ollowing !uestion.
SA? 2 An*@/:
%he 8 types o" logic error mentioned are0
• Fogical Foop0
%his is an impossible situation. +ctivities ' and < are predecessors "or +ctivity
8. %here"ore +ctivity 8 can#t be a predecessor "or +ctivity ' as implied.
• Fogical *angle0
SA? 2: Identi"y the 8 types o" logical error described by Burke anddiscuss their nature.
JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 19/20
+ logical dangle is simply where an activity is le"t 5dangling6 or hanging. It either
comes "rom nowhere or goes nowhere. /nly the "irst and "inal activities have single
5connections6.
• edundant -recedence elationship0
In a network diagram only I;*I+%; predecessors need to be made e$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$tensions to the concept o" activity "loat in Section '= o"
,hapter '. We encountered one such concept (o" "loat being shared by a number
o" activities) earlier in this lesson. ead Section '= o" ,hapter ' and then answer
the "ollowing !uestion.
SA? 3: Identi"y the 8 types o" "loat described by Burke and comment ontheir signi"icance.
JJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJJ
7/25/2019 ENGM91- Unit 2b- Critical Path Method
http://slidepdf.com/reader/full/engm91-unit-2b-critical-path-method 20/20
SA? 3 An*@/:
T,t%' )',%t. &loat is shared with all other activities. I" the "loat is used by one activity
"loat available "or other activities will be reduced. ,are must be taken to avoid
assuming that the apparent "loat is available "or all activities independently.
)// )',%t. %his is a measure the amount o" "loat an activity can use up without
a""ecting the early start o" other activities.
N/4%ti-/ )',%t. %his is an indication that an activity must start be"ore the preceding
activities are "inished. /" course there cannot be negative "loat in a real9li"e
situation. It is however a use"ul academic tool when conducting e$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.