Project Management
CHAPTER 13
TRUE/FALSE
13.1
PERT PERT and and CPM are quant quantitat itative ive analysis analysis tool toolss d desi esign gned ed to sche schedul dulee and control control large large proj projects ects.. AN!ER" TR#E
13.$
PERT PERT is a deter% deter%ini inisti sticc analys analysis is tool tool allo&in allo&ing g 'or 'or precis precisee ti%e ti%ess o o'' activit activities ies &ithin &ithin a project. project. AN!ER" (A)E
13.3 13.3
PERT PERT had had its its *egi *eginn nnin ings gs in a %ili %ilitar tary y depar depart% t%en entt o' the the #ni #nite ted d tate tates. s. AN!ER" TR#E
13.+ 13.+
CPM CPM is a pro* pro*a* a*il ilis isti ticc aana naly lysi siss o o'' %an %anag agin ing g a proj projec ect. t. AN!ER" (A)E
13.,
An event event is a poin pointt in ti%e ti%e that that %ar-s %ar-s the *egin *eginnin ning g or end ending ing o' an an activi activity ty.. AN!ER" TR#E
13.
A net&or net&or- is a graphica graphicall displ display ay o' a projec projectt that that contai contains ns *oth activiti activities es and events events.. AN!ER" TR#E
13./
The opti opti%is %istic tic ti%e ti%e is the great greatest est a%oun a%ountt o' ti%e ti%e that could could *e requi required red to co%p co%plet letee an activ activity ity.. AN!ER" (A)E
13.0 13.0
PERT PERT is a net&o net&orr- tec techn hniq ique ue si%i si%ilar lar to to CPM CPM *ut PERT PERT allo& allo&ss 'or 'or proje project ct cras crashi hing ng.. AN!ER" (A)E
13.2
The %ost %ost li-e li-ely ly co%ple co%pletio tion n ti%e ti%e o' an activ activity ity is used used to represen representt that that activit activity yss ti%e ti%e &ithin &ithin a project. AN!ER" (A)E
13.14
The e5pe e5pecte cted d co%p co%plet letion ion ti%e ti%e and variance variance o' o' an activity activity is appro5i% appro5i%ated ated *y the the nor%a nor%all distri*ution in a PERT analysis. AN!ER" (A)E
13.11 13.11
PERT PERT &as &as devel develope oped d 'or 'or a project project 'or 'or &hich &hich activity activity or tas- ti%e ti%ess &ere &ere uncer uncertain tain.. AN!ER" TR#E
13.1$
CPM &as deve develop loped ed 'or use use in %anag %anaging ing projects projects &hic &hich h are repeat repeated ed and and a*out a*out &hich &hich &e &e have have good in'or%ation as to activity or tas- co%pletion ti%es. AN!ER" TR#E
1+0
Project Management
13.13
CHAPTER 13
!ith !ith PERT PERT &e are a*le a*le to to calculate calculate the the pro*a* pro*a*ilit ility y o' 'ini 'inishi shing ng the project project on a particular particular day. day. AN!ER" TR#E
13.1+
!ith !ith CPM &e are a*le to calcula calculate te the the pro*a*i pro*a*ility lity o' 'inis 'inishin hing g the the projec projectt on a particul particular ar day. day. AN!ER" (A)E
13.1,
A PERT PERT or or CPM net& net&oror- sho sho&s &s activitie activitiess and and activ activity ity sequen sequences ces.. AN!ER" TR#E
13.1
6ne o' o' the %ost %ost di''i di''icult cult aspec aspects ts o' using using PERT PERT is de'in de'inin ing g the the activiti activities es so that that they have have %easura*le7o*serva*le starts and 'inishes. AN!ER" TR#E
13.1/
8e'ore 8e'ore dra&i dra&ing ng a PERT PERT or CPM net&o net&or- r- &e &e %ust %ust identi identi'y 'y each each activ activity ity and and their their prede predeces cessors sors.. AN!ER" TR#E
13.10
The three ti%e esti%ates esti%ates e%ploye e%ployed d in PERT are" opti% opti%istic istic ti%e average ti%e and pessi%istic pessi%istic ti%e. AN!ER" (A)E
13.12
9n the the PERT PERT proces process s i' an activi activity ty has :ero :ero varian variance ce it it %ust %ust *e on the the critical critical path. path. AN!ER" (A)E
13.$4
;iven the varia*ility varia*ility o' o' the the activity activity co%pletio co%pletion n ti%e the original original critical critical path &e identi'y identi'y in our PERT analysis %ay not al&ays *e the actual critical path as the project ta-es place. AN!ER" TR#E
13.$1
9n PERT PERT the activ activity ity co%ple co%pletio tion n ti%es ti%es are %ode %odeled led using using the *eta distri distri*uti *ution. on. AN!ER" TR#E
13.$$
9n PERT PERT the earliest 'inish ti%e in one activity &ill al&ays *e the the earliest earliest start ti%e o' the the 'ollo&ing activity. AN!ER" (A)E
13.$3
9n PERT PERT the earli earliest est start start ti%e ti%e 'or an activ activity ity is equal equal to the the latest latest o' the the earli earliest est 'inis 'inish h ti%es ti%es o' all o' its i%%ediate predecessors. AN!ER" TR#E
13.$+
6ne o' the the li%iti li%iting ng assu% assu%ptio ptions ns o' PERT PERT is that 'or 'or any activi activity ty to start start all o' its its i%%e i%%edia diate te predecessors predecessors %ust %ust *e co%plete. co%plete. AN!ER" TR#E
1+2
Project Management
13.13
CHAPTER 13
!ith !ith PERT PERT &e are a*le a*le to to calculate calculate the the pro*a* pro*a*ilit ility y o' 'ini 'inishi shing ng the project project on a particular particular day. day. AN!ER" TR#E
13.1+
!ith !ith CPM &e are a*le to calcula calculate te the the pro*a*i pro*a*ility lity o' 'inis 'inishin hing g the the projec projectt on a particul particular ar day. day. AN!ER" (A)E
13.1,
A PERT PERT or or CPM net& net&oror- sho sho&s &s activitie activitiess and and activ activity ity sequen sequences ces.. AN!ER" TR#E
13.1
6ne o' o' the %ost %ost di''i di''icult cult aspec aspects ts o' using using PERT PERT is de'in de'inin ing g the the activiti activities es so that that they have have %easura*le7o*serva*le starts and 'inishes. AN!ER" TR#E
13.1/
8e'ore 8e'ore dra&i dra&ing ng a PERT PERT or CPM net&o net&or- r- &e &e %ust %ust identi identi'y 'y each each activ activity ity and and their their prede predeces cessors sors.. AN!ER" TR#E
13.10
The three ti%e esti%ates esti%ates e%ploye e%ployed d in PERT are" opti% opti%istic istic ti%e average ti%e and pessi%istic pessi%istic ti%e. AN!ER" (A)E
13.12
9n the the PERT PERT proces process s i' an activi activity ty has :ero :ero varian variance ce it it %ust %ust *e on the the critical critical path. path. AN!ER" (A)E
13.$4
;iven the varia*ility varia*ility o' o' the the activity activity co%pletio co%pletion n ti%e the original original critical critical path &e identi'y identi'y in our PERT analysis %ay not al&ays *e the actual critical path as the project ta-es place. AN!ER" TR#E
13.$1
9n PERT PERT the activ activity ity co%ple co%pletio tion n ti%es ti%es are %ode %odeled led using using the *eta distri distri*uti *ution. on. AN!ER" TR#E
13.$$
9n PERT PERT the earliest 'inish ti%e in one activity &ill al&ays *e the the earliest earliest start ti%e o' the the 'ollo&ing activity. AN!ER" (A)E
13.$3
9n PERT PERT the earli earliest est start start ti%e ti%e 'or an activ activity ity is equal equal to the the latest latest o' the the earli earliest est 'inis 'inish h ti%es ti%es o' all o' its i%%ediate predecessors. AN!ER" TR#E
13.$+
6ne o' the the li%iti li%iting ng assu% assu%ptio ptions ns o' PERT PERT is that 'or 'or any activi activity ty to start start all o' its its i%%e i%%edia diate te predecessors predecessors %ust %ust *e co%plete. co%plete. AN!ER" TR#E
1+2
Project Management
13.$,
CHAPTER 13
6ne o' o' the li% li%iti iting ng assu%p assu%ptio tions ns o' PERT PERT is is that all activ activiti ities es %ust %ust *e co%ple co%pleted ted at so%e so%e ti%e ti%e during the project. AN!ER" TR#E
13.$
6ne o' o' the %ost %ost signi signi'ic 'icant ant *ene' *ene'its its o' o' PERT is that it 'orces 'orces the the projec projectt %anager %anager to sit sit do&n do&n and plan the project project in great detail < and thus co%e co%e to an understandin understanding g o' relationsh relationships ips *et&een *et&een the activities. AN!ER" TR#E
13.$/
lac- is the ti%e an activity activity can *e delayed delayed &ithou &ithoutt i%pacting i%pacting the co%pletio co%pletion n ti%e ti%e o' the the project. project. AN!ER" TR#E
13.$0
9t is never never possi* possi*le le to delay delay an activity activity &ithou &ithoutt i%pacti i%pacting ng the the project project co%p co%plet letion ion ti%e. ti%e. AN!ER" (A)E
13.$2
The varian variance ce o' the the proje project ct co%p co%plet letion ion ti%e ti%e is equal equal to to the su% su% o' the the varian variances ces o' o' all the the activities. AN!ER" (A)E
13.34
9n PERT PERT &e assu%e that the project co%pletio co%pletion n ti%e can *e %od %odeled eled *y the the nor%al nor%al distri*ution. distri*ution. AN!ER" TR#E
13.31
6ne PERT7C6 PERT7C6T T assu%pt assu%ption ion is that that %oney %oney is spent spent at at a constant constant rate rate over over the the ti%e ti%e ta-en ta-en to co%plete an activity. AN!ER" TR#E
13.3$
PERT PERT helps helps the the project project %anag %anager er understa understand nd *oth *oth &hich &hich activit activities ies %us %ustt ta-e place place and &hic &hich h 'unds %ust *e e5pended. AN!ER" (A)E
13.33
A li%itat li%itation ion o' PERT7C PERT7C6T 6T is the the assu%pt assu%ption ion that %one %oney y is spen spentt at a constant constant rate over over the the ti%e ta-en to co%plete the project. AN!ER" (A)E
13.3+
9n CPM &e assu% assu%ee that the the cost cost to co%pl co%plete ete the tastas- is a linea linearr 'unctio 'unction n o' the the ti% ti%ee to co%pl co%plete ete the tas-. AN!ER" TR#E
13.3,
9n CPM CPM crashing crashing an activ activity ity &hich &hich is not not on the critical critical path incre increases ases the cost o' the the projec project. t. AN!ER" TR#E
1,4
Project Management
13.3
CHAPTER 13
9n CPM i' &e are going to crash an activity &e should crash it to the %a5i%u% e5tent possi*le. AN!ER" (A)E
=13.3/
9n CPM crashing an activity &hich is not on the critical path reduces the cost o' the project just as %uch as crashing one on the critical path. AN!ER" (A)E
=13.30
6ne o' the dra&*ac-s to using either CPM or PERT to %anage an actual project is the a%ount o' data that %ust *e collected over the li'e o' the project to i%ple%ent either %ethod. AN!ER" TR#E
=13.32
9n PERT the variance in co%pletion ti%e is equal to the variance o' the %ost ti%e consu%ing activity on the critical path. AN!ER" (A)E
=13.+4
;iven the assu%ptions in PERT the pro*a*ility that a project &ill *e co%pleted in less ti%e than required *y the activities on the critical path is appro5i%ately ,4>. AN!ER" TR#E
=13.+1
6ne should al&ays &ait until an activitys latest start ti%e *e'ore co%%encing the activity. AN!ER" (A)E
=13.+$
#sing PERT7C6T one is a*le to co%plete the project 'or less %oney than using PERT alone. AN!ER" (A)E
1,1
Project Management
=13.+3
CHAPTER 13
9' an activity has + days o' slac- and &e delay it $ days the project &ill also *e delayed t&o days. AN!ER" (A)E
=13.++
;antt and PERT charts provide the sa%e in'or%ation just in di''erent 'or%ats. AN!ER" (A)E
=13.+,
;antt charts contain in'or%ation as to the ti%e ta-en *y each activity *ut not the sequential dependencies o' the activities. AN!ER" TR#E
=13.+
#sing PERT7C6T as a %anage%ent tool it is al&ays possi*le to *ring a project in under *udget. AN!ER" (A)E
MULTIPLE CHOICE
13.+/
The critical path o' a net&or- is the ?a@ ?*@ ?c@ ?d@ ?e@
shortest ti%e path through the net&or-. path &ith the 'e&est activities. path &ith the %ost activities. longest ti%e path through the net&or-. none o' the a*ove
AN!ER" d 13.+0
9n a PERT net&or- the earliest ?activity@ start ti%e is the ?a@ ?*@ ?c@ ?d@ ?e@
earliest ti%e that an activity can *e 'inished &ithout delaying the entire project. latest ti%e that an activity can *e started &ithout delaying the entire project. earliest ti%e that an activity can start &ithout violation o' precedence require%ents. latest ti%e that an activity can *e 'inished &ithout delaying the entire project. none o' the a*ove
AN!ER" c
1,$
Project Management
13.+2
CHAPTER 13
lac- ti%e in a net&or- is the ?a@ ?*@ ?c@ ?d@ ?e@
ti%e consu%ing jo* or tas- that is a -ey su*part o' the total project. shortest a%ount o' ti%e that could *e required to co%plete the activity. a%ount o' ti%e that you &ould e5pect it &ould ta-e to co%plete the activity. a%ount o' ti%e that an activity can *e delayed &ithout delaying the entire project. none o' the a*ove
AN!ER" d 13.,4
A net&or- activity is a ?a@ ?*@ ?c@ ?d@ ?e@
point in ti%e that %ar-s the *eginning or ending o' an activity. ti%e consu%ing jo* that is a su*part o' the total project. graphical display o' a project. net&or- technique that allo&s three ti%e esti%ates 'or each activity in a project. the longest ti%e path through the net&or-.
AN!ER" * 13.,1
!hich o' the 'ollo&ing is not a concept associated &ith CPM ?a@ ?*@ ?c@ ?d@ ?e@
nor%al ti%e pro*a*ility nor%al cost crash cost deter%inistic net&or-
AN!ER" * 13.,$
PERT ?a@ ?*@ ?c@ ?d@ ?e@
assu%es &e do not -no& ahead o' ti%e &hat activities %ust *e co%pleted. allo&s co%putation o' the progra%s evaluation. is a net&or- technique that uses three ti%e esti%ates 'or each activity in a project. is a deter%inistic net&or- technique that allo&s 'or project crashing. none o' the a*ove
AN!ER" c 13.,3
CPM ?a@ ?*@ ?c@ ?d@ ?e@
assu%es &e do not -no& ahead o' ti%e &hat activities %ust *e co%pleted. is opposite to that o' PERT as it does not consider the net&or- activities. is a net&or- technique that allo&s three ti%e esti%ates 'or each activity in a project. is a deter%inistic net&or- technique that allo&s 'or project crashing. none o' the a*ove
AN!ER" d 13.,+
Managers use the net&or- analysis o' PERT and CPM to help the% ?a@ derive 'le5i*ility *y identi'ying noncritical activities.
1,3
Project Management
CHAPTER 13
?*@ replan reschedule and reallocate resources such as %anpo&er and 'inances. ?c@ plan schedule %onitor and control large and co%ple5 projects. ?d@ all o' the a*ove AN!ER" d 13.,,
9n contrast to PERT or PERT7cost CPM ?a@ ?*@ ?c@ ?d@ ?e@
is a deter%inistic net&or- %odel. uses crash ti%es and costs. allo&s 'or calculating the least additional cost 'or shortening the project ti%e. assu%es that the activity ti%es and costs are -no&n &ith certainty. all o' the a*ove
AN!ER" e 13.,
The e5pected ti%e in PERT is ?a@ a &eighted average o' the %ost opti%istic ti%e %ost pessi%istic ti%e and 'our ti%es the %ost li-ely ti%e. ?*@ the %odal ti%e o' a *eta distri*ution. ?c@ a si%ple average o' the %ost opti%istic %ost li-ely and %ost pessi%istic ti%es. ?d@ the square root o' the su% o' the variances o' the activities on the critical path. ?e@ none o' the a*ove AN!ER" a
13.,/
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' + , and 1$ days respectively co%pute the PERT ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
, / 1$ none o' the a*ove
AN!ER" *
1,+
Project Management
13.,0
CHAPTER 13
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 3 3 and 2 days respectively co%pute the PERT ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
3 + , 2 none o' the a*ove
AN!ER" * 13.,2
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' + 0 and 10 days respectively co%pute the PERT ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
+ 0 2 10 none o' the a*ove
AN!ER" c 13.4
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' $ 14 and $4 days respectively co%pute the PERT variance 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
3 2 10 none o' the a*ove
AN!ER" e 13.1
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' + 1$ and 10 days respectively co%pute the PERT variance 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
$.33 ,.++ 0.44 +.44 none o' the a*ove
AN!ER" *
1,,
Project Management
13.$
;iven an activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 3 , and 1, days respectively co%pute the PERT standard deviation 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
$ + , 1, none o' the a*ove
AN!ER" a 13.3
;iven the 'ollo&ing s%all project the critical path is BBBBBBB days. Activity A 8 C ?a@ ?*@ ?c@ ?d@ ?e@
9%%ediate Ti%e Predecessor ?days@ 14 + A 8
14 1+ 1 $4 none o' the a*ove
AN!ER" c 13.+
CHAPTER 13
;iven the 'ollo&ing s%all project the critical path is BBBBBBB days. Activity A 8 C ?a@ ?*@ ?c@ ?d@ ?e@
9%%ediate Ti%e Predecessor ?days@ 0 A + 14
+ 14 1$ $$ none o' the a*ove
AN!ER" c
1,
Project Management
CHAPTER 13
The 'ollo&ing ta*le provides in'or%ation 'or questions 13., to 13.0. Ta*le 131 The 'ollo&ing represents a project &ith -no&n activity ti%es. All ti%es are in &ee-s. Activity 9%%ediateTi%e Predecessor A + 8 3 C A $ D 8 / E C D + ( 8 , 13.,
#sing the data in Ta*le 131 &hat is the %ini%u% possi*le ti%e required 'or co%pleting the project ?a@ ?*@ ?c@ ?d@ ?e@
0 1+ $, 14 none o' the a*ove
AN!ER" * 13.
#sing the data in Ta*le 131 &hat is the latest possi*le ti%e that C %ay *e started &ithout delaying co%pletion o' the project ?a@ ?*@ ?c@ ?d@ ?e@
4 + 0 14 none o' the a*ove
AN!ER" c 13./
According to Ta*le 131 co%pute the slac- ti%e 'or activity D. ?a@ ?*@ ?c@ ?d@ ?e@
4 , 3 none o' the a*ove
AN!ER" a
1,/
Project Management
13.0
CHAPTER 13
#sing the data in Ta*le 131 co%pute the latest 'inish ti%e 'or activity E. ?a@ ?*@ ?c@ ?d@ ?e@
+ 14 1+ $, none o' the a*ove
AN!ER" c The 'ollo&ing ta*le provides in'or%ation 'or questions 13.2 to 13./$. Ta*le 13$ The 'ollo&ing represents a project &ith 'our activities. All ti%es are in &ee-s. Activity 9%%ediate 6pti%istic Most Pessi%istic Predecessor Ti%e )i-ely Ti%e Ti%e A $ 0 1+ 8 0 0 0 C A 2 10 D 8 , 11 1/ 13.2
According to the data in Ta*le 13$ &hat is the critical path ?a@ ?*@ ?c@ ?d@ ?e@
A 8 A C 8 D A 8 C D none o' the a*ove
AN!ER" c 13./4
According to the data in Ta*le 13$ &hat is the %ini%u% e5pected co%pletion ti%e 'or the project ?a@ ?*@ ?c@ ?d@ ?e@
10 12 3/ 11 none o' the a*ove
AN!ER" *
1,0
Project Management
13./1
CHAPTER 13
According to Ta*le 13$ there are 'our activities in the project. Assu%e the nor%al distri*ution is appropriate to use to deter%ine the pro*a*ility o' 'inishing *y a particular ti%e. 9' you &ished to 'ind the pro*a*ility o' 'inishing the project in $4 &ee-s or less it &ould *e necessary to 'ind the variance and then the standard deviation to *e used &ith the nor%al distri*ution. !hat variance &ould *e used ?a@ ?*@ ?c@ ?d@ ?e@
$ + 0 1$ none o' the a*ove
AN!ER" * 13./$
According to Ta*le 13$ there are 'our activities in the project. Assu%e the nor%al distri*ution is appropriate to use to deter%ine the pro*a*ility o' 'inishing *y a particular ti%e. !hat is the pro*a*ility that the project is 'inished in 1 &ee-s or less ?round to t&o deci%als@ ?a@ ?*@ ?c@ ?d@ ?e@
4.4/ 4.23 4.+3 4.// none o' the a*ove
AN!ER" a 13./3
Consider a project that has an e5pected co%pletion ti%e o' 4 &ee-s and a standard deviation o' 'ive &ee-s. !hat is the pro*a*ility that the project is 'inished in /4 &ee-s or less ?round to t&o deci%als@ ?a@ ?*@ ?c@ ?d@ ?e@
4.20 4.+0 4.,4 4.4$ none o' the a*ove
AN!ER" a
1,2
Project Management
13./+
CHAPTER 13
our co%pany is considering su*%itting a *id on a %ajor project. ou deter%ine that the e5pected co%pletion ti%e is 144 &ee-s and the standard deviation is 14 &ee-s. 9t is assu%ed that the nor%al distri*ution applies. ou &ish to set the due date 'or the project such that there is an 0, percent chance that the project &ill *e 'inished *y this ti%e. !hat due date should *e set ?a@ ?*@ ?c@ ?d@ ?e@
140.4 114.+ 02. 0,.4 none o' the a*ove
AN!ER" * The 'ollo&ing ta*le provides in'or%ation 'or questions 13./, to 13./. Ta*le 133 Activity A 8 C D E ( ; F 13./,
9%%ediate Ti%e E E( ) )( Predecessor + 4 + 14 , 4 , 4 , A 3 + / 14 13 8 0 , 13 , 13 8 3 , 0 1+ 1/ C D $ 13 1, 1, 1/ C D 13 12 13 12 E ( $ 1, 1/ 1/ 12
According to Ta*le 133 there are eight activities to *e co%pleted in a project &ith -no&n activity ti%es. Fo& long could activity E *e delayed &ithout delaying the co%pletion o' the project ?a@ ?*@ ?c@ ?d@ ?e@
3 2 1+ 1/ none o' the a*ove
AN!ER" * 13./
According to Ta*le 133 there are eight activities to *e co%pleted in a project &ith -no&n activity ti%es. !hat is the %ini%u% possi*le ti%e required 'or co%pleting the project ?a@ ?*@ ?c@ ?d@ ?e@
13 1, 1/ 12 33
AN!ER" d The 'ollo&ing ta*le provides in'or%ation 'or questions 13.// to 13./2. Ta*le 13+
14
Project Management
Activity A 8 C D E 13.//
CHAPTER 13
9%%ediate Predecessor A A 8 C
6pti%istic + $ $ ,
Most )i-ely , , 0 , /
Pessi%istic 0 1+ , 0
Average , , 0 , /
tandard Deviation 4.333 1.444 $.444 4.444 4.333
Gariance 4.111 1.444 +.444 4.444 4.111
According to Ta*le 13+ there are 'ive activities in a PERT project. !hich activities are on the critical path ?a@ ?*@ ?c@ ?d@ ?e@
A8CDE ACE 8D A8CD none o' the a*ove
AN!ER" * 13./0
According to Ta*le 13+ there are 'ive activities in a PERT project. !hat is the variance o' the critical path ?a@ ?*@ ?c@ ?d@ ?e@
,.$$$ +.$$$ 1.$$$ 4 none o' the a*ove
AN!ER" * 13./2
According to Ta*le 13+ there are 'ive activities in a PERT project. 9' the nor%al distri*ution &ere used to 'ind the pro*a*ility o' 'inishing this project in $+ &ee-s or less &hat %ean and variance &ould *e used ?a@ ?*@ ?c@ ?d@ ?e@
$4 and +.$$$ 34 and ,.$$$ $4 and ,.$$$ 34 and +.$$$ none o' the a*ove
AN!ER" a
11
Project Management
13.04
CHAPTER 13
The critical path o' a net&or- is the ?a@ ?*@ ?c@ ?d@ ?e@
path &ith the least variance. path &ith :ero slac-. path &ith the %ost activities. path &ith the largest variance. none o' the a*ove
AN!ER" * 13.01
9n a PERT net&or- the latest ?activity@ start ti%e is the ?a@ ?*@ ?c@ ?d@ ?e@
earliest ti%e that an activity can *e 'inished &ithout delaying the entire project. latest ti%e that an activity can *e started &ithout delaying the entire project. earliest ti%e that an activity can start &ithout violation o' precedence require%ents. latest ti%e that an activity can *e 'inished &ithout delaying the entire project. none o' the a*ove
AN!ER" * 13.0$
lac- ti%e in a net&or- is the ?a@ ?*@ ?c@ ?d@ ?e@
ti%e consu%ing jo* or tas- that is a -ey su*part o' the total project. shortest a%ount o' ti%e that could *e required to co%plete the activity. a%ount o' ti%e that you &ould e5pect it &ould ta-e to co%plete the activity. a%ount o' ti%e that an activity can *e delayed &ithout delaying the project. none o' the a*ove
AN!ER" d 13.03
To do a PERT analysis o' a project ?a@ ?*@ ?c@ ?d@ ?e@
&e %ust -no& the sequence in &hich tas-s are to *e per'or%ed. &e %ust -no& the nu%*er o' tas-s in the project. &e %ust -no& the ti%e esti%ates 'or each activity. &e %ust co%pute an e5pected ti%e 'or each activity. all o' the a*ove
AN!ER" e 13.0+
(or &hich o' the 'ollo&ing projects are &e %ore li-ely to use PERT than CPM as a %anage%ent tool ?a@ ?*@ ?c@ ?d@ ?e@
per'or%ing %aintenance in a che%ical plant *uilding a ne& hotel co%ple5 developing a ne& space vehicle constructing a ne& 'actory *uilding a ne& high&ay
AN!ER" c
1$
Project Management
13.0,
CHAPTER 13
PERT ?a@ ?*@ ?c@ ?d@ ?e@
assu%es &e do not -no& ahead o' ti%e the speci'ic a%ount o' ti%e an activity &ill require. allo&s ti%e7cost tradeo''s. is a pro*a*ilistic net&or- technique that allo&s 'or project crashing. is a deter%inistic net&or- technique that allo&s 'or project crashing. none o' the a*ove
AN!ER" a 13.0
9n PERT ?a@ an activity %ay not start until all activities scheduled 'or an earlier ti%e have 'inished. ?*@ &e can have no %ore than t&o activities ta-ing place si%ultaneously. ?c@ a'ter the project has *egun it is possi*le 'or a path other than the original critical path to *eco%e critical. ?d@ &e assu%e that the ti%e to co%plete an activity is descri*ed *y the nor%al distri*ution. ?e@ none o' the a*ove AN!ER" c
13.0/
!hich o' the 'ollo&ing is incorrect 9n PERT ?a@ ?*@ ?c@ ?d@ ?e@
&e assu%e that all activities are co%pleted. an activity %ay not start until all activities scheduled 'or an earlier ti%e have 'inished. &e assu%e that all activities have de'ina*le start and end points. &e assu%e that the ti%e to co%plete an activity is descri*ed *y the *eta distri*ution. none o' the a*ove
AN!ER" * 13.00
9n PERT &e assu%e that ?a@ ?*@ ?c@ ?d@
the ti%es to co%plete individual activities are -no&n &ith certainty. all activities are carried out *y sta'' 'ro% our o&n organi:ation. the total cost o' a project is independent o' the ti%e to co%plete the project. the total ti%e to co%plete all activities on the critical path is descri*ed *y a nor%al distri*ution. ?e@ none o' the a*ove AN!ER" d
13
Project Management
13.02
CHAPTER 13
CPM ?a@ assu%es that &e -no& ahead o' ti%e all activities &hich %ust *e co%pleted. ?*@ assu%es that &e %ay o*tain additional resources or %ove e5isting resources 'ro% one activity to another. ?c@ is an i%portant technique &hen &e are planning a project si%ilar to projects &e have co%pleted in the past. ?d@ is a deter%inistic net&or- technique that allo&s 'or ti%e7cost tradeo''s. ?e@ all o' the a*ove AN!ER" e
13.24
9n CPM ?a@ ?*@ ?c@ ?d@ ?e@
an activity %ay start *e'ore its i%%ediate predecessors have 'inished. no %ore than t&o activities %ay *e per'or%ed si%ultaneously. the total cost o' co%pleting an activity in the crash ti%e is higher than the nor%al cost. &hen &e crash an activity &e co%plete the activity in the %ini%u% possi*le ti%e. none o' the a*ove
AN!ER" c 13.21
Managers use the net&or- analysis o' PERT and CPM to help the% ?a@ ?*@ ?c@ ?d@ ?e@
identi'y the need 'or contingency plans *y identi'ying critical activities. learn %ore a*out the actual ti%es required to co%plete the activities. understand the relationship *et&een the various activities. all o' the a*ove ?a@ H ?c@ only
AN!ER" d 13.2$
9n contrast to CPM PERT ?a@ ?*@ ?c@ ?d@ ?e@
is a deter%inistic net&or- %odel. requires all activities to *e co%pleted. assu%es that activity costs are un-no&n. can identi'y activities &hich %ay *ut do not necessarily lie on the critical path. all o' the a*ove
AN!ER" d
1+
Project Management
13.23
CHAPTER 13
The e5pected ti%e in PERT is ?a@ ?*@ ?c@ ?d@ ?e@
greater than the %ost li-ely ti%e. equal to the %ost li-ely ti%e. less than the %ost li-ely ti%e. could *e any o' the a*ove. none o' the a*ove
AN!ER" d 13.2+
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 3 / and 11 days respectively co%pute the e5pected ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
, / 1$ none o' the a*ove
AN!ER" c 13.2,
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 3 , and 13 days respectively co%pute the e5pected ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
3 + , none o' the a*ove
AN!ER" d 13.2
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 1 2 and 1/ days respectively co%pute the PERT ti%e 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
+ 0 2 10 none o' the a*ove
AN!ER" c
1,
Project Management
13.2/
CHAPTER 13
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates 3 and 2 days respectively co%pute the PERT variance 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
3 1 2 none o' the a*ove
AN!ER" * 13.20
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' 3 , and 13 days respectively co%pute the PERT variance 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
$., ,.+ 0.4 $.0 none o' the a*ove
AN!ER" d 13.22
;iven the 'ollo&ing activitys opti%istic %ost li-ely and pessi%istic ti%e esti%ates o' / 2 and 1, days respectively co%pute the PERT variance 'or this activity. ?a@ ?*@ ?c@ ?d@ ?e@
.4 $./ 0.4 1.0 none o' the a*ove
AN!ER" d 13.144
The project descri*ed *y" Activity A 8 C D E
9%%ediate Predecessor A A 8 C D
1
Ti%e ?days@ 14 + / ,
Project Management
CHAPTER 13
is *est represented *y &hich o' the 'ollo&ing net&or-s ?a@
?*@ 8
tart
8
D (inish
A
C
tart
E
E
(inish
?d@ 8
8
D tart
(inish
A
C
The project descri*ed *y" Activity A 8 C D E
9%%ediate Ti%e Predecessor ?days@ A A 8 C C
has a critical path o' length" ?a@ ?*@ ?c@ ?d@ ?e@
$1 days 1+ days $3 days 3$ days none o' the a*ove
AN!ER" c
1/
14 + / ,
D (inish
A
C
E
AN!ER" * 13.141
D
C
?c@
tart
A
E
Project Management
13.14$
CHAPTER 13
The project descri*ed *y Activity A 8 C D E
9%%ediate Ti%e Predecessor ?days@ A 8 C D
$ 0 , /
has a critical path o' length ?a@ ?*@ ?c@ ?d@ ?e@
1, days $4 days 1/ days 10 days none o' the a*ove
AN!ER" * The 'ollo&ing ta*le provides in'or%ation 'or questions 13.143 to 13.140. Ta*le 13, The 'ollo&ing represents a project &ith -no&n activity ti%es. All ti%es are in &ee-s. Activity 9%%ediate Ti%e Predecessor A + 8 3 C A $ D 8 / E C D + ( 8 , ; E ( + 13.143
#sing the data in Ta*le 13, &hat is the %ini%u% possi*le ti%e required 'or co%pleting the project ?a@ ?*@ ?c@ ?d@ ?e@
0 1$ 10 14 none o' the a*ove
AN!ER" c
10
Project Management
13.14+
CHAPTER 13
#sing the data in Ta*le 13, &hat is the latest possi*le ti%e that C %ay *e started &ithout delaying co%pletion o' the project ?a@ ?*@ ?c@ ?d@ ?e@
4 + 0 14 none o' the a*ove
AN!ER" c 13.14,
#sing the data in Ta*le 13, co%pute the slac- ti%e 'or activity D. ?a@ ?*@ ?c@ ?d@ ?e@
4 , 3 none o' the a*ove
AN!ER" a 13.14
#sing the data in Ta*le 13, co%pute the latest 'inish ti%e 'or activity E. ?a@ ?*@ ?c@ ?d@ ?e@
+ 14 1+ $, none o' the a*ove
AN!ER" c 13.14/
#sing the data in Ta*le 13., deter%ine the latest ti%e activity A can *e started &ithout delaying the project co%pletion. ?a@ ?*@ ?c@ ?d@ ?e@
+ 3 0 none o' the a*ove
AN!ER" a
12
Project Management
13.140
CHAPTER 13
#sing the data in Ta*le 13., deter%ine the latest ti%e activity A can *e 'inished and not delay any activity ?a@ ?*@ ?c@ ?d@ ?e@
+ 4 0 , none o' the a*ove
AN!ER" c The 'ollo&ing ta*le provides data 'or questions 13.142 to 13.11$. Ta*le 13 Activity A 8 C D E ( 13.142
All activity ti%es are in &ee-s. 9%%ediate 6pti%istic Most )i-ely Predecessor Ti%e Ti%e $ 0 0 0 A 2 8 , 11 C D 3 3 8 ,
Pessi%istic Ti%e 1+ 0 10 1/ 2 /
According to the data in Ta*le 13 &hat is the critical path ?a@ ?*@ ?c@ ?d@ ?e@
A C E 8( 8 D E A 8 C D ( none o' the a*ove
AN!ER" c 13.114
According to the data in Ta*le 13 &hat is the %ini%u% e5pected co%pletion ti%e 'or the project ?a@ ?*@ ?c@ ?d@ ?e@
10 12 3/ 11 none o' the a*ove
AN!ER" e
1/4
Project Management
13.111
CHAPTER 13
According to Ta*le 13 there are si5 activities in the project. Assu%e the nor%al distri*ution is appropriate to use to deter%ine the pro*a*ility o' 'inishing *y a particular ti%e. 9' you &ished to 'ind the pro*a*ility o' 'inishing the project in $1 &ee-s or less it &ould *e necessary to 'ind the variance and then the standard deviation to *e used &ith the nor%al distri*ution. !hat variance &ould *e used ?a@ , ?*@ + ?c@ 0 ?d@ 1$ ?e@ none o' the a*ove AN!ER" a
13.11$
According to Ta*le 13 there are si5 activities in the project. Assu%e the nor%al distri*ution is appropriate to use to deter%ine the pro*a*ility o' 'inishing *y a particular ti%e. !hat is the pro*a*ility that the project is 'inished in $4 &ee-s or less ?round to t&o deci%als@ ?a@ ?*@ ?c@ ?d@ ?e@
4.+1 4.21 4.13 4.42 none o' the a*ove
AN!ER" d 13.113
Consider a project that has an e5pected co%pletion ti%e o' ,4 &ee-s and a standard deviation o' 2 &ee-s. !hat is the pro*a*ility that the project is 'inished in ,/ &ee-s or less ?round to t&o deci%als@ ?a@ ?*@ ?c@ ?d@ ?e@
4.0 4./0 4.$$ 4.3$ none o' the a*ove
AN!ER" *
1/1
Project Management
13.11+
our co%pany is considering su*%itting a *id on a %ajor project. ou deter%ine that the e5pected co%pletion ti%e is 1,4 &ee-s and the standard deviation is 14 &ee-s. 9t is assu%ed that the nor%al distri*ution applies. ou &ish to set the due date 'or the project such that there is a 2, percent chance that the project &ill *e 'inished *y this ti%e. !hat due date should *e set ?a@ ?*@ ?c@ ?d@ ?e@
140.4 14.+ 1., 13,.4 none o' the a*ove
AN!ER" c The 'ollo&ing ta*le provides in'or%ation 'or questions 13.11, to 13.11/. Ta*le 13/ Activity A 8 C D E ( ; F 13.11,
9%%ediate Ti%e Predecessor + , A 3 8 0 8 $ C D 3 C D / E ( $
E
E(
)
)(
4 4 + , , 13 13 1
+ , / 13 / 1 $4 10
/ 4 14 , 1 1, 13 10
14 , 13 13 10 10 $4 $4
Fo& long could activity E *e delayed &ithout delaying the co%pletion o' the project ?a@ ?*@ ?c@ ?d@ ?e@
/ 1 11 10 none o' the a*ove
AN!ER" c 13.11
CHAPTER 13
Fo& long could activity ( *e delayed &ithout delaying the project ?a@ ?*@ ?c@ ?d@ ?e@
$ 3 1+ 1 none o' the a*ove
AN!ER" a
1/$
Project Management
13.11/
CHAPTER 13
!hat is the %ini%u% possi*le ti%e required 'or co%pleting the project ?a@ ?*@ ?c@ ?d@ ?e@
1+ $4 1/ $4 none o' the a*ove
AN!ER" d The 'ollo&ing ta*le provides in'or%ation 'or questions 13.110 to 13.1$4. Ta*le 130 Activity 9%%ediate Predecessor A 8 C D E ( ; F 13.110
A A 8 C 8 D E ; (
6pti%istic $ $ 1 , 1$ 1 1
Most )i-ely 3 , $ , / 1$ , +
+ 0 2 , 0 1$ 2 0
!hich activities are part o' the critical path ?a@ ?*@ ?c@ ?d@ ?e@
A 8 E ; F A C E ; F A D ; F 8 ( F none o' the a*ove
AN!ER" * 13.112
!hat is the variance o' the critical path ?a@ ?*@ ?c@ ?d@ ?e@
Pessi%istic
,.$$$ +.3+ 1.3$ ,.1++ none o' the a*ove
AN!ER" d
1/3
Average 3 , 3 , / 1$ +
4.333 1.444 1.334 4.444 4.333 4.444 1.333 1.1/
σ
σ
4.111 1.444 1./04 4.444 4.111 4.444 1./04 1.3$
$
Project Management
13.1$4
CHAPTER 13
9' the nor%al distri*ution &ere used to 'ind the pro*a*ility o' 'inishing this project in $+ &ee-s or less &hat %ean and variance &ould *e used ?a@ ?*@ ?c@ ?d@ ?e@
$4 and ,.1++ $3 and ,.1++ $3 and ,.$$$ $4 and +.$$$ none o' the a*ove
AN!ER" * =13.1$1 !hich o' the 'ollo&ing *est presents the project de'ined *elo&
?a@
Activity A 8 C D E ( ; ?*@ A
Predecessor A 8 DHC 8 E A
C
C E
E tart
A
?c@
C
D
; (
8
?e@
?d @
A
(inish
(
8
E
tart
;
D
(inish
(
8
tart
;
D
C E
tart
;
(inish 8
(
none o' the a*ove AN!ER" c
=13.1$$ Assu%e a particular activity has an opti%istic ti%e o' 14 &ee-s a %ost li-ely ti%e o' 1$ &ee-s and an e5pected ti%e o' 1+ &ee-s. !hat is its pessi%istic ti%e ?a@ ?*@ ?c@ ?d@ ?e@
1$ &ee-s 10 &ee-s $ &ee-s 34 &ee-s none o' the a*ove
AN!ER" c =13.1$3 Assu%e a particular activity has an e5pected ti%e o' $+ &ee-s a pessi%istic ti%e o' 34 &ee-s and a %ost li-ely ti%e o' $/ &ee-s. !hat is the opti%istic ti%e
1/+
(inish
Project Management
?a@ ?*@ ?c@ ?d@ ?e@
CHAPTER 13
14 &ee-s 0 &ee-s / &ee-s 1$ &ee-s none o' the a*ove
AN!ER" e =13.1$+ Assu%e an activity has the 'ollo&ing ti%es" opti%istic I 14 &ee-s %ost li-ely I $, &ee-s pessi%istic I +4 &ee-s. !hat is the e5pected ti%e ?a@ ?*@ ?c@ ?d@ ?e@
14 &ee-s $, &ee-s +4 &ee-s 34 &ee-s none o' the a*ove
AN!ER" * The 'ollo&ing 'igure ?(ig 13.1@ is to *e used as data 'or pro*le%s 13.1$2 < 13.13,. (igure 131 A TI3
C TI
tart
( TI+
F TI/
E TI, 8 TI,
D TI+
; TI
=13.1$, ;iven the net&or- in (igure 13.1 the critical path is ?a@ ?*@ ?c@ ?d@ ?e@
AC(F 8DE(F ACE;F 8D;E(F none o' the a*ove
AN!ER" *
1/,
tart
Project Management
CHAPTER 13
=13.1$ ;iven the net&or- in (igure 13.1 the ti%e to co%plete those activities on the critical path is e5pected to *e ?a@ ?*@ ?c@ ?d@ ?e@
$4 $$ $, $ none o' the a*ove
AN!ER" c =13.1$/ ;iven the net&or- sho&n in (igure 13.1 assu%e that co%pletion o' A is delayed *y t&o days. !hat other activities are i%pacted ?a@ ?*@ ?c@ ?d@ ?e@
8 D E C none o' the a*ove
AN!ER" d =13.1$0 ;iven the net&or- sho&n in (igure 13.1 assu%e that co%pletion o' 8 is delayed *y t&o days. !hat happens to the project ?a@ ?*@ ?c@ ?d@ ?e@
The critical path is e5tended *y t&o days. The start o' activity ( is delayed *y t&o days. The start o' activity E is delayed *y t&o days. all o' the a*ove none o' the a*ove
AN!ER" d =13.1$2 ;iven the net&or- sho&n in (igure 13.1 assu%e that the co%pletion o' activity C is delayed *y 'our days. !hat changes &ill ta-e place ?a@ ?*@ ?c@ ?d@ ?e@
The critical path &ill change to" A C 8 D E ( F. Activity ( &ill *e delayed *y 'our days. Activity E &ill *e delayed *y 'our days. Activity ; &ill *e delayed *y 'our days. none o' the a*ove
AN!ER" e
1/
Project Management
CHAPTER 13
=13.134 ;iven the net&or- sho&n in (igure 13.1 and the 'ollo&ing in'or%ation &hat is the variance o' the critical path Activity A 8 C D E ( ; F
E5pected ti%e 3 , + + + /
Gariance $ 3 3 1 1 $ $ $
?a@ 1 ?*@ / ?c@ 2 ?d@ 0 ?e@ none o' the a*ove AN!ER" c =13.131 ;iven the net&or- sho&n in (igure 13.1 and the e5pected ti%es and variance given a*ove &hat is the pro*a*ility that the project &ill *e co%pleted in $, or 'e&er &ee-s ?a@ 144> ?*@ ,4> ?c@ > ?d@ $,> ?e@ none o' the a*ove AN!ER" *
PROBLEMS
13.13$
Dra& the PERT net&or- associated &ith the 'ollo&ing activities.
9%%ediate Predecessor A A 8 8 C D E (
1//
Project Management
CHAPTER 13
AN!ER" 8
D ; tart
E A
tart
F
C
13.133
(
;iven" Activity
6pti%istic
A 8 C D E ( ;
3 $ 4., + 1
8
Most )i-ely
Pessi%istic
+ / 3 1 2 , 3
, 1+ 14 1., 1$ 1$ 11
E ; tart
D tart
(
A
C
Deter%ine" ?a@ the critical path ?*@ the pro*a*ility that the project &ill *e co%pleted in $$ &ee-s
AN!ER" ?a@ Critical path is 8E;. E5pected ti%e is $1. ?*@ Gariance 'or critical path is ,., so standard deviation is $.$. P?J
1/0
≤
$$@ I 4..3
Project Management
13.13+
CHAPTER 13
The 'ollo&ing represent activities in a %ajor construction project. Dra& the net&or- to represent this situation. Activity A 8 C D E ( ; F AN!ER"
8
9%%ediate Predecessor A 8 8 C D E ( ; E ; tart
D tart
(
A
13.13,
C
A s%all so't&are develop%ent project has 'ive %ajor activities. The ti%es are esti%ated and provided in the ta*le *elo&. (ind the e5pected ti%e 'or co%pleting this project. Activity A 8 C D E
9%%ediate a Predecessor $ − 3 − A + 8 $ C 3
%
*
, / , 3
0 2 14 1+ 3
?a@ !hat is the e5pected co%pletion ti%e 'or this project ?*@ !hat variance &ould *e used in 'inding pro*a*ilities o' 'inishing *y a certain ti%e
1/2
Project Management
CHAPTER 13
AN!ER" ?a@ e5pected co%pletion ti%e I 1, ?Activities ACE@ ?*@ variance I 1 K 1 K 4 I $ A
C E
tart
tart
D
B
13.13
A project has an e5pected co%pletion ti%e o' +4 &ee-s and a standard deviation o' , &ee-s. 9t is assu%ed that the project co%pletion ti%e is nor%ally distri*uted. ?a@ !hat is the pro*a*ility o' 'inishing the project in ,4 &ee-s or less ?*@ !hat is the pro*a*ility o' 'inishing the project in 30 &ee-s or less ?c@ The due date 'or the project is set so that there is a 24 percent chance that the project &ill *e 'inished *y this date. !hat is the due date AN!ER"
13.13/
?a@ P?J ≤ ,4@ I P?L ≤ $@ I 4.2//$, ?*@ P?J ≤ 30@ I P?L ≤ −4.+@ I 4.3++,0 ?c@ Lvalue I 1.$0 Due date I +4 K 1.$0?,@ I +.+
Develop%ent o' a ne& delu5e version o' a particular so't&are product is *eing considered. The activities necessary 'or the co%pletion o' this are listed in the ta*le *elo&. Activity A 8 C D E ( ;
Nor%al Ti%e + $ 3 0 3 +
3 1 3 + 3 $ $
Crash Nor%al Crash Ti%e Cost Cost $444 $44 $$44 $044 ,44 ,44 $344 $44 244 1$44 3444 +$44 1+44 $444
9%%ediate Predecessor A 8 C DE
?a@ !hat is the project co%pletion date ?*@ !hat is the total cost required 'or co%pleting this project on nor%al ti%e ?c@ 9' you &ish to reduce the ti%e required to co%plete this project *y one &ee- &hich activity should *e crashed and ho& %uch &ill this increase the total cost
104
Project Management
CHAPTER 13
AN!ER" ?a@ Project co%pletion ti%e I 1 ?Activities AD;@ ?*@ Total cost I 1$344 ?c@ Crash D one &ee- at an additional cost o' /,
tart
A
D
8
E
C
(
;
101
tart
Project Management
13.130
CHAPTER 13
Dra& the PERT net&or- associated &ith the 'ollo&ing activities. 9%%ediate Predecessor A A 8 8 C E A D ( ( ; F 9
AN!ER" ;
D
8 tart
F
E
A
(
C
10$
9
(inish
Project Management
13.132
CHAPTER 13
;iven" Activity
6pti%istic 3 $ + 1 1 $ 1
A 8 C D E ( ; F 9 A
C
Most )i-ely + / 3 2 , 3 $ , +
Pessi%istic , 1+ 14 1$ 1$ 11 2 0 /
F
(
tart
8
9
(inish
E
D
;
Deter%ine" ?a@ the critical path ?*@ the pro*a*ility that the project &ill *e co%pleted in $$ &ee-s
AN!ER" ?a@ Critical path is 8E;9. ?*@ Gariance 'or critical path is .33O standard deviation is $.,1. P?J
103
≤
$$@ I 4.,
Project Management
13.1+4
CHAPTER 13
The 'ollo&ing ta*le represents activities in a %ajor construction project. Dra& the net&or- to represent this situation. Activity
9%%ediate Predecessor 8 8 A C D E ( 8 ; F
A 8 C D E ( ; F 9 AN!ER" A
E
; C
D
(
tart 8
9
tart
F
13.1+1
A s%all so't&are develop%ent project has 'our %ajor activities. The ti%es are esti%ated and provided in the ta*le *elo&. (ind the e5pected ti%e 'or co%pleting this project. Activity A 8 C D E ( ; F 9
9%%ediatea Predecessor $ − 3 Α A + 8 $ D 3 C E ( 1 C ; F 3
%
*
, / , 3 0 1 14 +
0 2 14 1+ 3 14 1 1+ ,
?a@ !hat is the e5pected co%pletion ti%e 'or this project ?*@ !hat variance &ould *e used in 'inding pro*a*ilities o' 'inishing *y a certain ti%e
10+
Project Management
CHAPTER 13
AN!ER" ?a@ e5pected co%pletion ti%e I $ ?*@ variance I 3.00
?Activities ACF9@
8
D E ;
tart
A 9
(inish
(
C F
13.1+$
A project has an e5pected co%pletion ti%e o' ,4 &ee-s and a standard deviation o' / &ee-s. 9t is assu%ed that the project co%pletion ti%e is nor%ally distri*uted. ?a@ ?*@ ?c@ ?d@
!hat is the pro*a*ility o' 'inishing the project in ,4 &ee-s or less !hat is the pro*a*ility o' 'inishing the project in ,, &ee-s or %ore !hat is the pro*a*ility o' 'inishing the project in ++ &ee-s or less The due date 'or the project is set so that there is a 24 percent chance that the project &ill *e 'inished *y this date. !hat is the due date
AN!ER"
?a@ ?*@ ?c@ ?d@
P?J ≤ ,4@ I P?L ≤ 4@ I 4.,444 P?J ≥ ,,@ I P?L ≥ 4./1@ ≅ 1 4./1 I 4.$32 P?J ≤ ++@ I P?L ≤ −4.0,/@ ≅ 1 4.04+ I 4.12 Lvalue I 1.$0 Due date I ,4 K 1.$0?/@ ≅ ,2 days
13.1+3
Develop%ent o' a ne& delu5e version o' a particular so't&are product is *eing considered. The activities necessary 'or the co%pletion o' this are listed in the ta*le *elo&. Activity
A 8 C D E ( ;
Nor%al Ti%e + , 3 0 3 +
Crash Ti%e 3 3 3 + 3 $ $
Nor%al Cost
$444 $$44 ,44 $+44 244 3444 1/44
Crash Cost
$44 $044 ,44 $44 1$44 +$44 $444
9%%ediate Predecessor A 8 C DE
?a@ 9' you &ish to reduce the ti%e required to co%plete this project *y t&o &ee-s &hich activity?ies@ should *e crashed and ho& %uch &ill this increase the total cost ?*@ !hat &ould *e the added cost i' you &anted to co%plete the project in the %ini%u% ti%e possi*le
10,
