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Critical Path Analysis Handout
CRITICAL PATH ANALYSIS Example 1: To toast 3 pieces of bread A, B, C with a single toaster. Mr. : !tep & ( 3 ) Acti"ity Toast one side of A and B. Toast the other side of A and B Toast one side of C Toast the other side of C Total ti#e Ti#e $s% 3' 3' 3' 3' 120
Mr. *: !tep & ( 3 Acti"ity Toast one side of A and B. Toast the other side of A and one side of C Toast the other side of B and C Total ti#e Ti#e $s% 3' 3' 3' 90
This is a si#ple e+a#ple of how proper planning sa"es ti#e $and #oney%. Critical Path Analysis is a techni,ue to enable us to plan, execute, monitor co#ple+ pro-ects to the #a+i#u# e icienc!.
"#at i$ Critical Pat# Anal!$i$% Critical Path Analysis can be defined as the logical se,uencing of a series of e"ents necessary for a successful research pro-ect in such a #anner that the #ost efficient route to so#e cul#ination point can be calculated. Critical Path Analysis is an e+tre#ely effecti"e #ethod of analysing a co#ple+ pro-ect. .t helps you to calculate the #ini#u# length of ti#e in which the pro-ect can be co#pleted, and which acti"ities should be prioritised to co#plete by that date. /here a -ob has to be co#pleted on ti#e, critical path analysis helps you to focus on the essential acti"ities to which attention and resources should be de"oted. .t gi"es an effecti"e basis for the scheduling and #onitoring of progress. Se&uential an' parallel acti(itie$ The essential concept behind Critical Path Analysis is that so#e plan acti"ities are dependent on other acti"ities being co#pleted first. 0or e+a#ple, you should not start building a bridge unless you ha"e designed it first1 These dependent acti"ities need to be co#pleted in a se,uence, with each acti"ity being #ore2 or2less co#pleted before the ne+t acti"ity can begin. 3ependent acti"ities are also called 4se,uential4 acti"ities. 5ther acti"ities are not dependent on co#pletion of any other tas6s, or #ay be done at any ti#e before or after a particular stage is reached. These are non2dependent or 4parallel4 tas6s.
th6oo78un (''97gaya
&
Critical Path Analysis Handout
Example 2) 8enny has a date with her boyfriend at 9*00 pm. The ti#e now is :*10 pm and she is "ery worried she couldn;t #a6e it on ti#e. <et us now list down the acti"ities and access whether =elly and <e"y could help her #a6e it or not to #eet her bf. >ow so#e acti"ities can ta6e place concurrently$at the sa#e ti#e% while others cannot begin until others are co#pleted. 0or e+a#ple, while ironing her dress, the car can be got ready. 5n the other hand, 8ane cannot get dress until her dress is iron? she cannot blow her hair until she has ta6en her bath. Before drawing the acti"ity networ6, there are so#e element$ +rules, sy#bols and definitions% we need to 6now. ACTI,ITY An acti(it! is a tas6 which consu#es both ti#e and resources $#anpower, #achinery,%. E,ENT An e(ent is a point in ti#e. .t does not consu#e ti#e or resources and is used only to #ar6 the -e.innin. or the en' of an acti"ity. An e"ent at the start of a pro-ect is called a $tart e(ent or $ource* An acti"ity at the end of a pro-ect is called an en' e(ent or $in/* 0EY E,ENTS An e"ent which has been no#inated bya #anager to be of particular importance is called a /e! e(ent or mile$tone* The #anager is usually to be infor#ed when this e"ent occurs. 1233IES A 'umm! is a non2e+istent acti"ity which does not consu#e ti#e or resources. .ts #ain purpose is #ainly to represent a constraint or a logical connection in a pro-ect. 3u##ies are used to @forceA a correct logic. SY345LS The British standard: Acti(it! 3escription$3uration% 3BMM*
E(ent$)
!tart C"ent
5rdinary C"ent
=ey C"ent
Cnd C"ent
th6oo78un (''97gaya
(
Critical Path Analysis Handout
The following is the acti"ity table: Acti"ity A B C 3 C 0 shower blow hair fetch car iron dress dress and #a6e2up dri"e there Ti#e $#ins% 3 : D &( &' (' .##ediate Preceding Acti"ities 2 A 2 2 B, 3 C, C
The following is the acti"ity networ6:
Example 6) Try to draw the acti"ity networ6 diagra# for this e+a#ple. Acti"ity A B C 3 C 0 E H .##ediate Preceding Acti"ities 2 2 A A, B C, 3 C, 3 3 C, 0
th6oo78un (''97gaya
3
Critical Path Analysis Handout
I'enti ! a critical pat# The duration$total ti#e% of the whole operation is that of the longest path through the networ6. An! 'ela! in the acti"ities will increase the duration of the whole operation7pro-ect. This path is called the critical path and the acti"ities are called the critical activities. !o a critical path is a se,uence of acti"ities for which there is no scheduling fle+ibility, no float$spare ti#e%. Earlie$t e(ent time$ &. T#e earlie$t e(ent time i$ t#e earlie$t time !ou can lea(e an e(ent The earliest e"ent ti#e for the start event is set to 7ero* .n this case the ti#e is :.&' p#. (. 3raw a double bo+ beside each e"ent: <H!Fearliest e"ent ti#e, GH!Flatest e"ent ti#e. 3. Cg, the earliest e"ent ti#e for Hdry hair; is 3 I after shower? the earliest e"ent ti#e for Hdressing; si &( after Hiron dress;: /hen an acti"ity depend on other acti"ities, then we ha"e to ta6e the longest ti#e to ensure that all the other dependent acti"ities are co#pleted before the start of this acti"ity. Late$t e(ent time$ &. T#e late$t e(ent time i$ t#e late$t time !ou can lea(e an e(ent if the operation is to be co#pleted within its #ini#u# co#pletion ti#e. The latest e"ent ti#e for the drive there event is 22 as 8ane cannot start dri"ing there later than (( otherwise there will be a delay in the operation. Try to co#plete the figure below:
3 iron dress &( #in A !hower & ' ' C fetch car D #in 3 #in B 3ry Hair : #in C dress7#a6eup &' #in (' #in
The -ol' ace' line is the line with the critical activities. Ha"ing added the earliest and latest e"ent ti#e, let us now consider the following: Critical activities are those acti"ities that must start and finish on ti#e if the operation is not to be delayed. .t is clear that ironing dress, dress J #a6eup and dri"e there are critical acti"ities. Any delay in any of these 3 acti"ities will e+tend the operation ti#e and cause a delay in co#pletion of the operation $K)( #ins%. .n general, the acti"ity is critical if the difference between the earliest and latest e"ent ti#e is e,ual to the duration of that acti"ity. 0etch car on the other hand is not a critical acti"ity as you can delay the start ti#e up to &L #ins. *ou do not need the car until 8ane has dressed2up and done her #a6eup. There is a : #ins spare ti#e. <oo6s li6e 8ane can actually reach there on ti#e and if e"erything goes well with : #ins to spare. 8loat The EST$earliest start ti#e% is the earliest possible start ti#e of an e"ent. The LST$latest start ti#e% is the latest possible start ti#e of an e"ent$without delay%. The difference between these two is called the ‘float’, #eaning the float of an acti"ity is the delay allowed on the co#pletion of that acti"ity. 0or e+a#ple, there is a & #in spare ti#e between shower and dry hair. .n this case the float i$ 1 min* .n the acti"ity of fetch car, there is a spare ti#e of &L #ins in itself$-ust this acti"ity%. This is an independent float.
th6oo78un (''97gaya
)
Critical Path Analysis Handout
Total loat is the delay allowed without affecting the latest finish ti#e of the pro-ect. Total loat 9 Late$t 8ini$# Time : Earlie$t Start Time ; 1uration* 9 +latest e"ent ti#e for e"ent -% I $earliest e"ent ti#e for e"ent i% 2 $duration of acti"ity%. In'epen'ent loat 9 Earlie$t 8ini$# Time ; Late$t Start Time ; 1uration $earliest e"ent ti#e for e"ent -%2+latest e"ent ti#e for e"ent i% 2 $duration of acti"ity% Inter erin. loat 9 total loat ; in'epen'ent loat . 8urt#er rea'in.) Plea$e re er t#e a''itional rea'in. material$ CPA<2* T#en tr! Ex* =A* >ue$tion 1:= Re erin. to CPA<2 cour$e #an'out pa.e 1 Example 1* Acti(it! A 4 C 1 E 8 @ H 1e$cription 5-tain 'i..er 1i. trenc# In$pect trenc# La! pipe 5-tain pipe Te$t pipe Prepare $ite 5-tain .ra(el 1uration +Hour$? 1*0 2*0 2*0 1*0 2*0 =*0 =*0 6*0 Imme'iate Prece'in. Acti(itie$ : Con$traint$ : A 4, E C, 8, H : E,@ : @
Acti"ity C has been no#inated to be a /e! e"ent* Con$truct a netAor/ 'ia.ram* The float calculation for this pro-ect are gi"en in Ta-le 2*
Acti(it! 1uration
1:= 2:B 6:C =:D C:B C:E B:D B:E D:E E:9
1 2 = 2 0 6 0 = 2 1
Earlie$t Start 0 0 0 1 = = = = = E
Late$t Start
Earlie$t 8ini$#
Late$t 8ini$#
Total 8loat
In' 8loat
Inter loat
Critical Pat#
Ta-le 2
B$(% A$&% C$(%
D(1)
C$(%
0$)%
E$)%
H$3%.'
th6oo78un (''97gaya
L
CRITICAL PATH ANALYSIS Example 1: To toast 3 pieces of bread A, B, C with a single toaster. Mr. : !tep & ( 3 ) Acti"ity Toast one side of A and B. Toast the other side of A and B Toast one side of C Toast the other side of C Total ti#e Ti#e $s% 3' 3' 3' 3' 120
Mr. *: !tep & ( 3 Acti"ity Toast one side of A and B. Toast the other side of A and one side of C Toast the other side of B and C Total ti#e Ti#e $s% 3' 3' 3' 90
This is a si#ple e+a#ple of how proper planning sa"es ti#e $and #oney%. Critical Path Analysis is a techni,ue to enable us to plan, execute, monitor co#ple+ pro-ects to the #a+i#u# e icienc!.
"#at i$ Critical Pat# Anal!$i$% Critical Path Analysis can be defined as the logical se,uencing of a series of e"ents necessary for a successful research pro-ect in such a #anner that the #ost efficient route to so#e cul#ination point can be calculated. Critical Path Analysis is an e+tre#ely effecti"e #ethod of analysing a co#ple+ pro-ect. .t helps you to calculate the #ini#u# length of ti#e in which the pro-ect can be co#pleted, and which acti"ities should be prioritised to co#plete by that date. /here a -ob has to be co#pleted on ti#e, critical path analysis helps you to focus on the essential acti"ities to which attention and resources should be de"oted. .t gi"es an effecti"e basis for the scheduling and #onitoring of progress. Se&uential an' parallel acti(itie$ The essential concept behind Critical Path Analysis is that so#e plan acti"ities are dependent on other acti"ities being co#pleted first. 0or e+a#ple, you should not start building a bridge unless you ha"e designed it first1 These dependent acti"ities need to be co#pleted in a se,uence, with each acti"ity being #ore2 or2less co#pleted before the ne+t acti"ity can begin. 3ependent acti"ities are also called 4se,uential4 acti"ities. 5ther acti"ities are not dependent on co#pletion of any other tas6s, or #ay be done at any ti#e before or after a particular stage is reached. These are non2dependent or 4parallel4 tas6s.
th6oo78un (''97gaya
&
Critical Path Analysis Handout
Example 2) 8enny has a date with her boyfriend at 9*00 pm. The ti#e now is :*10 pm and she is "ery worried she couldn;t #a6e it on ti#e. <et us now list down the acti"ities and access whether =elly and <e"y could help her #a6e it or not to #eet her bf. >ow so#e acti"ities can ta6e place concurrently$at the sa#e ti#e% while others cannot begin until others are co#pleted. 0or e+a#ple, while ironing her dress, the car can be got ready. 5n the other hand, 8ane cannot get dress until her dress is iron? she cannot blow her hair until she has ta6en her bath. Before drawing the acti"ity networ6, there are so#e element$ +rules, sy#bols and definitions% we need to 6now. ACTI,ITY An acti(it! is a tas6 which consu#es both ti#e and resources $#anpower, #achinery,%. E,ENT An e(ent is a point in ti#e. .t does not consu#e ti#e or resources and is used only to #ar6 the -e.innin. or the en' of an acti"ity. An e"ent at the start of a pro-ect is called a $tart e(ent or $ource* An acti"ity at the end of a pro-ect is called an en' e(ent or $in/* 0EY E,ENTS An e"ent which has been no#inated bya #anager to be of particular importance is called a /e! e(ent or mile$tone* The #anager is usually to be infor#ed when this e"ent occurs. 1233IES A 'umm! is a non2e+istent acti"ity which does not consu#e ti#e or resources. .ts #ain purpose is #ainly to represent a constraint or a logical connection in a pro-ect. 3u##ies are used to @forceA a correct logic. SY345LS The British standard: Acti(it! 3escription$3uration% 3BMM*
E(ent$)
!tart C"ent
5rdinary C"ent
=ey C"ent
Cnd C"ent
th6oo78un (''97gaya
(
Critical Path Analysis Handout
The following is the acti"ity table: Acti"ity A B C 3 C 0 shower blow hair fetch car iron dress dress and #a6e2up dri"e there Ti#e $#ins% 3 : D &( &' (' .##ediate Preceding Acti"ities 2 A 2 2 B, 3 C, C
The following is the acti"ity networ6:
Example 6) Try to draw the acti"ity networ6 diagra# for this e+a#ple. Acti"ity A B C 3 C 0 E H .##ediate Preceding Acti"ities 2 2 A A, B C, 3 C, 3 3 C, 0
th6oo78un (''97gaya
3
Critical Path Analysis Handout
I'enti ! a critical pat# The duration$total ti#e% of the whole operation is that of the longest path through the networ6. An! 'ela! in the acti"ities will increase the duration of the whole operation7pro-ect. This path is called the critical path and the acti"ities are called the critical activities. !o a critical path is a se,uence of acti"ities for which there is no scheduling fle+ibility, no float$spare ti#e%. Earlie$t e(ent time$ &. T#e earlie$t e(ent time i$ t#e earlie$t time !ou can lea(e an e(ent The earliest e"ent ti#e for the start event is set to 7ero* .n this case the ti#e is :.&' p#. (. 3raw a double bo+ beside each e"ent: <H!Fearliest e"ent ti#e, GH!Flatest e"ent ti#e. 3. Cg, the earliest e"ent ti#e for Hdry hair; is 3 I after shower? the earliest e"ent ti#e for Hdressing; si &( after Hiron dress;: /hen an acti"ity depend on other acti"ities, then we ha"e to ta6e the longest ti#e to ensure that all the other dependent acti"ities are co#pleted before the start of this acti"ity. Late$t e(ent time$ &. T#e late$t e(ent time i$ t#e late$t time !ou can lea(e an e(ent if the operation is to be co#pleted within its #ini#u# co#pletion ti#e. The latest e"ent ti#e for the drive there event is 22 as 8ane cannot start dri"ing there later than (( otherwise there will be a delay in the operation. Try to co#plete the figure below:
3 iron dress &( #in A !hower & ' ' C fetch car D #in 3 #in B 3ry Hair : #in C dress7#a6eup &' #in (' #in
The -ol' ace' line is the line with the critical activities. Ha"ing added the earliest and latest e"ent ti#e, let us now consider the following: Critical activities are those acti"ities that must start and finish on ti#e if the operation is not to be delayed. .t is clear that ironing dress, dress J #a6eup and dri"e there are critical acti"ities. Any delay in any of these 3 acti"ities will e+tend the operation ti#e and cause a delay in co#pletion of the operation $K)( #ins%. .n general, the acti"ity is critical if the difference between the earliest and latest e"ent ti#e is e,ual to the duration of that acti"ity. 0etch car on the other hand is not a critical acti"ity as you can delay the start ti#e up to &L #ins. *ou do not need the car until 8ane has dressed2up and done her #a6eup. There is a : #ins spare ti#e. <oo6s li6e 8ane can actually reach there on ti#e and if e"erything goes well with : #ins to spare. 8loat The EST$earliest start ti#e% is the earliest possible start ti#e of an e"ent. The LST$latest start ti#e% is the latest possible start ti#e of an e"ent$without delay%. The difference between these two is called the ‘float’, #eaning the float of an acti"ity is the delay allowed on the co#pletion of that acti"ity. 0or e+a#ple, there is a & #in spare ti#e between shower and dry hair. .n this case the float i$ 1 min* .n the acti"ity of fetch car, there is a spare ti#e of &L #ins in itself$-ust this acti"ity%. This is an independent float.
th6oo78un (''97gaya
)
Critical Path Analysis Handout
Total loat is the delay allowed without affecting the latest finish ti#e of the pro-ect. Total loat 9 Late$t 8ini$# Time : Earlie$t Start Time ; 1uration* 9 +latest e"ent ti#e for e"ent -% I $earliest e"ent ti#e for e"ent i% 2 $duration of acti"ity%. In'epen'ent loat 9 Earlie$t 8ini$# Time ; Late$t Start Time ; 1uration $earliest e"ent ti#e for e"ent -%2+latest e"ent ti#e for e"ent i% 2 $duration of acti"ity% Inter erin. loat 9 total loat ; in'epen'ent loat . 8urt#er rea'in.) Plea$e re er t#e a''itional rea'in. material$ CPA<2* T#en tr! Ex* =A* >ue$tion 1:= Re erin. to CPA<2 cour$e #an'out pa.e 1 Example 1* Acti(it! A 4 C 1 E 8 @ H 1e$cription 5-tain 'i..er 1i. trenc# In$pect trenc# La! pipe 5-tain pipe Te$t pipe Prepare $ite 5-tain .ra(el 1uration +Hour$? 1*0 2*0 2*0 1*0 2*0 =*0 =*0 6*0 Imme'iate Prece'in. Acti(itie$ : Con$traint$ : A 4, E C, 8, H : E,@ : @
Acti"ity C has been no#inated to be a /e! e"ent* Con$truct a netAor/ 'ia.ram* The float calculation for this pro-ect are gi"en in Ta-le 2*
Acti(it! 1uration
1:= 2:B 6:C =:D C:B C:E B:D B:E D:E E:9
1 2 = 2 0 6 0 = 2 1
Earlie$t Start 0 0 0 1 = = = = = E
Late$t Start
Earlie$t 8ini$#
Late$t 8ini$#
Total 8loat
In' 8loat
Inter loat
Critical Pat#
Ta-le 2
B$(% A$&% C$(%
D(1)
C$(%
0$)%
E$)%
H$3%.'
th6oo78un (''97gaya
L
