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CE 2353 . CONSTRUCTION PLANNING At{D SCHEDULINGSCHEDULING PROCEDURES AND TECHNTQUES

TINIT IIRelevanie of construction schedules-Bar charts (week wise and Fortnights wiseprogramme)- PERT - The critical path method-Calculations for critical pathscheduling-Activity float and scheduies-presenUng project schedules-critical pathscheduling for Activity-on-node and with leads, Lags and windows-calculations forscheduling with leads, lags and windows-Resource oriented scheduling-schedulingwith resource constraints and prefedences -Use of Advanced SchedulingTechnlques-schedullng wlth uncertain durations-ctrashlng and time/cost trade offs -Improving the Scheduling process..

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43. Mention the three phases of proiect management.Project management involves the following three phases:1. Project planning2. Project scheduling3. Project controlling

44. Write any two tools or techniques of proiect manadement in a proiect scheduling,Following are some of the tools of project management:1. Bar charts and Milestone charts2. Network Diagrams

45, Mention the types of planning in network construction,1. Forward planning2. Backward planning3. Combined planning

46. Differentiate Bar chart and Milestone chart.

SL.NO BAR CHART MILESTONE CHART1. Construction schedules are usually

in the form bar chart onlv.Milestone chart is a modification of thebar chart.

2. Bar charts were introduced byHenry Gantt around 1900 AD.

Milestones are key events of a mainactivltv reoresented bv a bar.

3. It consists oF two co-ordinato Jxcsusually horizon[irl dxis & vet ticalaxes.

The specinc points in time in whichmark the complctlon of certainDortions of the main activitv.

(ay' o"ttn" Arrow diagram.Xlso called: activity network diagram, network diagram. activity chart, node diagram, CpM (criticalpath method) chart. The arrow diagram shows the required order of tasks in a project or process, thebest schedule for the entire project, and potential scheduling and resource problems and thelrsolutions. The arrow diagram lets you calculate the "critical path" of the project. This is the flow ofcritical steps where delays will affect the timing of the entire project and where addltion of resourcescan speed up the project.48. When to use an Arrow diagram?

. When sqheduling and monitoring tasks within a complex project or process with interrelatedtasks and resources,

r When you know the steps of the project or process, their sequence and how long each steptakes, and.

. When project schedule is critical, with serious consequences for completing the project late orsignificant advantage to completing the project early.

49. When the CPM method was developed?In 1957, DuPont developed a project management method designed to address the challerE ofshutting down chemical plants for maintenance and then restarting the plants once the mairtenarchad been completed. Given the complexity of the process, they developed the critcal PatnMethod (CPM) for managing such projects,

66')writ. the benefits of cPM method.' o Provides a graphical view of the project.

o Predicts the time required to complete the project.. Shows which activities are critical to maintaining the schedule and which are not.

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51. Write the steps involved in CpM project planning.1. Specify the individual acHvities,2. Determine the sequence of those activities.3. Draw a network diagram.4. Estimate the completion time for each activity.5. Identify the critical path (longest path through the network)6. Update the CPM diagram as the project progresses.

52. Write thb limitations of CpM method.

CPM was developed for complex but fairly routine projects with rninimal uncertainty in the projectcompletion times. For less routine projects there is more uncertainty in the compleuon times, and thisuncertalnty limits the usefulness of the deterministic CpM model. An aiternative to CpM isthe PERT project planning model, which a ows a range of durations to be specifi;rroi eait, iitirity

Define the term predecessor Evant,an event that immediatery comes before another event without any intervening events.

(84. oefine the term successor Evnt.ff-is an event that immediately follows another event without any intervening event.

85, Define the term predecessor activity.Ifis the activlty that immediatery comes befbre another activity without any intervening activity.j Dfine the term Successor activity.3 the activity that immediatery fo ows'before another activity without any intervening activity.

57. Define the term Network or Arrow diagramThls is a basic document of management syitem in whrch a[ activities and events of projectconnected logically and

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SIXTEEN MARKS QUESTIONS1, Explain Critical path method with neat sketches, (Nov/Dec 2oo8)The most widely used scheduling technique is the critical path method (CPM) for scheduling, oftenreferred to as critical path scheduling. This method calculates the minimum completion time for aproject along with the possible start and finish times for the project activities. Indeed, many texts andmanagers regard critical path scheduling as the only usable and practical scheduling procedure.Computer programs and algorithms For critical path scheduling are widely available and can efficientlyhandle projects with thousands of activities.The critical path itself represents the set or sequence of predecessor/successor activities whlch willtake the longest time to complete. The duration of the critical path is the sum of the activities'durations alonq the path. Thus, the critical path can be defined as the lonqest possible path throughthe "network" of project activities. The duration of the critical path represents the minimum timerequired to complete a project. Any delays along the critical path would imply that addltional timewould be required to complete the project.There may be more than one critical path among all the project activities, so completion of the entireproject could be delayed by delaylng activitles along any one of the critical paths. For example, aproject consisting of two activities performed in parallel that each requires three days would have eachactivity critical for a completion in three days.

Formally, critical path scheduling assumes that a project has been dlvided into activities of fixedduration and well defined predecessor retationships. A predecessor relationship implis that oneactivity must come before another in the schedule. No resource constraints other than those impliedby precedence relationships are recognized in the simplest form of critical Path scheduling'An Activity-on-Branch Network for Crltical Path SchedulingAn Activity-on-Node Network for Critical Path Scheduling

2. Explain Activity float and schedules.A number of different activity schedules can be developed from the critlcal path scheduling proceduredescribed in the previous section. An earliest time schedule would be developed by starting eachactivity as soon as possible, at Es(i,j). similarly, a latest time schedule would delay the start of eachactivity as long as posslble Uut stiti iinisn the pioject in the minimum possible time. This late schedulecan be developed by setting each activity's start time to LS(i,j).Activities that have different early and late start times (i.e'. ES(i,i) < LS(i,i)) can. be scheduled to startanytime between ES(i,j) and LS(i,j). The concept of float is to use part or all of this a.llowable range toschedule an activiry;lthout deiaying tt'e completion of the project. An activity that has the earliesttime for its predecessor and succiss-or nodes dlffering by more than its duration possesses a windowin which it can be scheduled. That is, if E(i) + Dij I r-1;1, tnen some float is available in which toschedulethis activity.

Float is a very valuable concept since it represents the scheduling flexibility or "maneuv-ering room"available to cjmplete particular tasks. Activities on the critical path do not provide. any flexibility forscheduling nor leeway in case of problems. For activities with some float, the actual starting timemight be chosen to balance work loads over time, to correspond with materlal deliveries, Or tOimprove the project's cash flow.3, Describe various methods of Presenting Proiect schedules' (MaylJune 2oo9)

communicating the project schedule is a vital ingredient in successful proiect management._A goodfieieniation *'itr gr"itti ease the minager's probiem of understanding the multitude of activities andiheir inter-relationships, ttoreOver, nrri.orr' individuats and parties are involved in any project, andiniy nave to understand theii assignments. GraPhical presentations of project schedules areparticularly usefut since it is mucn eiier to cohprehend a graphical display.of .nu.merous pieces ofinfoimatioh than to sift through a large table of numbers. Early computer scheduling systems werefarttcutarty poor in this regarJ since t"tl"v produced pages and pages.of "yTP"':.*lt3::. aids to the,"nag", ior understandirig tnem.-fi ii Lxt.emety tidious to iead a table of activity numbers,

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arations, schedure times, and froats and thereby gain an understanding and appreciation of a Fojectschedule'.In practicg, producing diagrams ,r",,,-iriy tras been a common prescription to the rack ofartdrurted draft ing facilities.Inded' it has been common to use computer programs to perform critical path scheduling and then toproduce bar charts of detailed activity scneauLi ini- l"ror.." assignments manually. with theayailabilitv of compurer graphrcs, the cost and;ffil;; producing g."pir."i p.".;nia1ion, na, oe"nsrgnificantly reduced and the production of presentation-aiis can be automated.Network diagrams for projects have already been introduced. These diagrams provide a powerfulvisualization of the precedences and rerationshipi

"ronf-tl," various projtct u.[riti".. they are abasic means of communicating. a project pran among the ;articipat,ng pranners and project inonitors.Project planning is often conducigo- uy ir.oorcin! 'r"liJ* ."p."."ntations of greater and greaterrefinement until the plan is satisfactory.An Exampte Bar Chart for a Nine Activity projectBar. charts are particularly helpful for commirniiaung the current state and schedule of activities on aproJect' As such, they have

-found wioe acceptinie"ui i p-.oi"a representation tool in the field. Forplanning purposes, bar charts_are not as useful.sincl in"v [o not indicate the precedence relationshipsamong activrties. Thus, a ordrnner must remember o, ,"alrd- ,"pu."tery that a change in one activity,sschedule may require changes to successor activiuei.-rnere have been various schemes formechanically linking activitv bars to_ represent pr".aJ"ni"i, but it is now easier to use computer basedtools to represent such relationsntps.

5. Explain Scheduring with R6source Constraints and precedence. (Nov,/Dec 2otl)Two problems arise in developing a resource constrained project schedule. First, it is not necessarilythe case that a criticar path

"ih;ure;; r;;;il#;; 5i" o. .o." resources might be needed bynumerous activities, it can easiry be the case tt'ii-tt'" It ort"r, pro;".t du;aaio; j;;;ftied by thecritical path scheduling calculation is impossibte. T;;;#d;iy arises because crticar path scheduringassumes that no resource availability p.our".11r uoiti"""?. *ilr arise. Finding a feasrble or possibreschedule is the first probrem in resource constrained sctreouiing. oF course, there may be a numerouspossible schedures which conform "itn iio," ,"i i"Io"r"ii!"ilnr,.",n,r. As a second probrem,.it is arsodesirabre to determine schedures *r'i.n nrr" i,ii" ii.i""lil iil"rv, the rowest cosr.

Numerous heuristic methods have been suggested for resource constrained scheduling.Many begin from criticat Dath schedules ;i;;;;;;;j;;;ii'r,gn, or,n" resource constraints. othersbegin in the opposite fishron .ov int-Jr.ing- r"r"Jl"'i#""'rts and then imposing precedenceconstraints on the activities. stirr 'our".s u"liri*;il;;;iiil

". crassification of activirie; into priority3jH:l;J[#.":'i'r.$iJ:-::;l-::h"a,ri,g] b,;''i#"oi"ieeuristic may be better than another ror

mieht be r;i;;;;;;';i;fi:hii:i,.!.,,,:"ip:il.:d:,J,il ff.ffji?lJ:.#L:#tff[tT,,trnumerous important resource constraints ,ignt 6"'u"ii .1-r,idured by considering criircar -resourcesllliJ,j,,Tjl"o approach woutd be t" pio.."i .irrtffi;r.;; considering precedence and resource

A simpre modification to criticar, path scheduring has been shown to be effective for a number ofscheduling problems and is simple to impremenl.'rolirr", i"r'.i.,i. procedure, criticar paah .Jn"autingrs apptied initialv. The resurt is the rumrri"i sei or p"os;;;L';:;y and rate sra* times for each activity.

:"T,",'.:#3 ;::X.X#'..Ln.X?in at its earriesi p;J;i;';i;;?;" may resu^ in more than one activityneuristic proceeds by ioentifviit ll: :ame time Hence, the initial ritrearre rnav -noi'uJ'i"""riu,". ,t"activity ro p..""0.-inJ.i"'ilii:*"ii,|:.-ffili::,:,1:if""Iffff"f;"nJl*::lt,H=iT,,lLT?

ff1,{-:*lttfik"'ffi #fr:';,i!I+i'trt-!ffi [:::::;

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6. Define the procedure for Arrow diagram'

Materials needed: sticky notes or cards, marking pens, large writing surface (newsprint or flipchart

pages)

Drawing the Network -^n,,anianr method is to write each1. List all the necessary tasks in the project or process'..One convenient method is to wr

task on the top hatf of J?i";; ;;".fi;k;;;t". 'A.ror. ttre rnioole of the card, draw a horizontalarrow pointing right.

--r,,^^ lh,aa ^,,ecrinn< for each task:2. Determine the correct sequence of the tasks. Do this by asking three questions for eaclo Which tasks must'happen before this one can begin?o Which tasks can be done at the same time- as this one?; which tasks shoJd nappen immediately after this one?

Itcanbeusefultocreateatablewithfourcolumns-priortasks'thistask'slmultaneoustasks, following tasks.

3. Diagram the network of tasks' If you are llsing !oje: or cards' arrange them in sequence on alargepieceofpaper.rii"lno'lo-no*frorilentorightandconcurrenttasksshouldbe,uii.itrv aligned. Leave space between the cards'

4. Between each two tasks, draw circles for "events"' An event marks the beginning or end of atask. Thus, events are nodes that separate taslG'

5. Look for three common problem situations and redraw them usinq "dummies" or extra events'A dummy is an arrow JJ#;',;,iil;H;i ii"J, ,*o to separat; tasks that would otherwisesiart and stop with th" ;;;

";;;; ;io snotn rogicat s"ouence' Dummles are not real tasks'

6.Whenthenetworkiscorrect,labelalleventsinsequence.witheventnumbersinthecircles.ltcan be useful to label all tasks in sequence' using letters'

Scheduling: Critical Path Method (CPM)7. Determine tasr tlmes-in-e uLii "'1it"t" of the time-that

each task should require'measuring unit lnours, iJvl;; ;;;k;J tht'shout' for consistenci' write the timetask's arrow.

8. Determine the "critical path," the longest path from th.e"beoinninq to the end of the project'Mark the critical path with a heavy line or color' Calculate tie ten-gth of the crltical path: thesum of all the task times on the path'

9. Calculate the earliest times each task can stbrt and.finis!'-based on how long precedinq taskstake. rhese are caled

""rriili"ri"ri' iii)-ind earriest finish (EF)' Start with the first task,

where ES = o, and *o.r. to#"j'iiuil tq'ut" divided into ioui quadrants' as in Figure 4'rrv-iit" tt" es ii itre top left box and the EF in the top right'For each task:

o Earliest start (ES) = the largest EF of the-tasks leading into this oneo E"tti"tt finish iEF) = ES + task time for this task '

10. calculate the latest times SJcn i;:i;;; ;i"'t ";d finish without upsetting the project

schedute, based on trow tong;er iirlr *irr take. These are called latest start (L5) and latestfinish (LF). start from ,h" i:J;;'i, il# tit" r3L"tt 11ish is the project deadline' and workbacklvards. Write the r-s,tt t-tt" rolt"i ieft Oox ana the LF in the lower right box'

o Latest finish furl ='tni tir"ireii'r-s or a tasks immediatelv followinq this oneo Gi"tt start (Lsi = LF - task time for this task

11. calculate slack times for each task and for the entire project'rotal slack is the time

"

j.oL;;i;"#;lipJ'ilJ*lin"tt ielavine the project schedule'I:i:';,':.1 ; hs;,uf"="T";*tlourd ue postponed without arrectine the earlv start or anv

job

i?'111"??,]t: the earliest Es of all tasks immediatelv followins this one - EF

Use oneon each

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7. Differentiate CPM and PERT. (Nov/Dec 2ooa)CPMTie critical Path Method, sometimes referred to as critical Path Analysis (CpA) was developed inthe 1950's by DuPont Corporation and Remington Rand Corporation. tt wai specifically developedto manage power plant maintenance projects. They wanted to develop a management tool thatwould help in the scheduling of chemicai plant shul downs for maintenance anJ then restartingthem once maintenance was complete. The CPM methods saved the company one millio; dollarsin the first year of use.PERTSeparate but simllar work was also being conducted in the mid 1950's by the united States Navy.The us government discovered the Rusiians were deveroping their own missile technotty, and!::1r::-"1,j911]

-s:cur[y_yvas at. stake the Navy immediatity taunched tneri own ir6!1am tocrose rhe missire gap. 8 The project was enormous, and so.it was important for tire -Navy toconduct research on Planning and controlling complicated projects. The research was referred toas the Program Evaluation Research t_ask (co-de-niine eenil. in February of 1958, or-. c-.E-. Oark,from the PERT team, introduced the first ;rrow diagram. pLnt, iater reierred to as the programEvaluation and Review Technique, was applied to ihe rleet Ballistic Missile program later thatyear. with over 3,o00 contraciors, vend6rs,. and other teams invorved, it wis of siiategrcIpf,I?:.:-f-TT_{ete lhe project quickty and efflcientty. PERT proved its worth, and was givencreolr ror taklng two years off the estimated time needed to develop the Polaris missile, and isstill the standard for all Navy projects today.

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t. NormaL dunaabn dirtcl @tE = Sooo * Sooo=

lSooo

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Total caAL

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i t4ayltutte tY'/ NOv lDEC uooT:- (prrec a.ao,ttg))dccaih q o nett or4 Ato Siurn hloco wlere 4At. dutailon

time.

(b) Tite

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lt.sz

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| 5.ro

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'{CPs

Critical Path Analysis

2,

3:

2.

.r.

4.

'5_

9*

Murphy-pcStamp

Murphy-pcStamp

11.

(il

(ii)

./Question 1

lO Explain the following inthe conlext ol a networkft'l Critical Path

nehiork using dlmmies, if necessary'

(iil DunnY activltY3$w9r(i) Critical Path:

critlcal Path is a chain of activities.hat begin liith the starting event and ends with

ending event or u prrri.,rt,'prolt't' ri i1 0'tt mtt' f"!l1t-llt,"*h a network wihthe maximum tengtn ot time

"oiii indicates the maximum possible time required for

complelion of a proiect ctlu*i putft indicates the minimum time that will be

required to complete a pt"itti"fiit o**mined after identifying clitical events'Critical path goes through criticalvents'

(ii) Oummy Activities:Dummy Activity is that ac$vity which does 1:!. t:"t:T-uiT" or

resources' lt is

used shen tuYo or more tJ;il'J;t same initial and terminal evenB' As a resultof using dummy utti'ttlt', itt"'

"*JitlJt tun t" identified by unique end events'

it it. it" usuillv snown by anows with dashed lines'

,i

Murphy-pcStamp

l$ .,/Question e

The followlng netwuk gives the dwation in days for each aetjviry:

(t You are rcquircd to tist the critica! paths.(ii) Giuen that each activtty c.an be aashed by a naxinun of one day. choose to uashany four activities so that the prcject turition ii-riiiiri oy z auy,An swer

Critical Pafts:All are critical patrs:(') 1-2-s-6(ii) ,t

-3-5-6(iii) I -4-s_6(iv) , -3-4-5-6

2 + I + 5 = 15

3+/+$ :154+$+$ .: lg

' 3+1+$+$=lg0 Choose i

- 6, common pah;

Crash by 1 dayO Choose: I

-2, 1-3, 1-4

(iiD Choose: 1-2, 3- 5, 4_siiv) Choose: 2- 5, 3-5,4_5(v)

. Choose; 1 -3, 1 - 4,2 -s

Or

0r0r

Murphy-pcStamp

ao) r/Question 3 (uov tDeC &ood) r"r,12-,i,f ' .A company is launching a new producl and has made estimates of lhe time fu the variousactivities associated with the launch as follows:

Required:

0 Draw the nelwotk diagram.(ii) Catculale the expected me and variance of each aclivily'(ti| Find out he expected length of critical path and its standard deviaton'(iv) Find the prcbabitity that the launching will be completed in 27 days'(v) Find the du ation, which has 95% pro;bability of comPletion'Answer

(i) Network Diagram

Predecessot

Tines (Days)--- Optimistic ' 'Most likety Bessimistic

A

B.

LD

EFG

HI

NoneNoneA,B

B

Ae

E,FD,FG,H

1

3I

1

2

'2210

J-:>'l 4

3

./ 2,/jr

3

210

E

511

I3144

210

Gritical Path A )B ) C ) F ) G > Z

Murphy-pcStamp

(ii) calculation of Expected rime, standard oeviation and variance of ActiuitiesActivity Expecled Tine Standard Deviation Variance a2

_

to+41, +t, ..

tr-to Im-P^.p.066

A ( 1-2)

B ( 1-3)

c (3-4)

D (3-5)

E ( (2-6)

F (+7)

G(&8)

H( ($e)

r ( 8-10)

1+12+5 ^

--6-- ='3+16+ 5-- 6-= 41+12+11--l-l=43+ 12+ I--6 =41+8+3 ^-l--='

2+20+14 ^

--;-- = o2+12+4

^l-=J2+8+2

^6-1er#+=10

a_{-

' = 0.67.

6

T=oo1i-1

=t.n6

f=r.oo3-1=

o.ae6

1l-2 =zoo6

T=o*2-2

=o6

10-10_o6

0.44

0. 1,

2.78

1.00

0.1.1

4.00

0. 11

0'

0

(iir) S.D. of Crificat path=m= {O.11+278+ 4+ 0.11+ 0= Ji = 2.645(iv) Probabilities of completion ofjob in 27 days.y

= 27 Days

z=27-27 - o2645

Forz= 0 fie prcbability is 0.5 from the table of area under normal curve or 50026

Murphy-pcStamp

(v) For 95016 of area the corresponding Z value is 1.64 (ftom the table),Therefore,

1.64 =

x'272646

[ = lJ + r[.t! = 31.33 Days,r/'Question 4 toff copYl"oL

consido the schedure of acriviries and retared infwmation as given below,construction of a Plant:

Activity Varlance

for the

Expecled Tine Expected Cost(Millions of Rs)

53

4

I212

207

14

4

Assuming lhat the cost and time required for one activity is tndependent of the tine andcost of any othq activrty and variations are expected to foltow normal distribution.Draw a netwwk based on the above data and calculate:

0 *rtical path(ti) Expected cost of construction ol the plant(iil Expected time rcquted to buitd the ptant(iv) The standard deviation of he expected time.

1

'11

21

1

qB

16

1

1-2

2.33.6

2-4

1.5

s-o

4-6

5-7

7-8

6-8

4

2J

62

JI7

10

1

4o

Murphy-pcStamp

Answer

The required network is dranrn below:

ifr?oL. ear- .3 t' 'r!

From $e'above network, itcan be noted thatthe critical pathisl-2-4-6-8.Expected cost of construction of the plant

= (S + 3 + 4 + 9 + Z + 12 + 20 + I + 14 +

4) millions of Rs. = Rs.80 millionExpected timo required to build the plant

= 4 r 6 + g + 1 = 20 months.It is given that ihe time required for one activity is independent of the time and costof any other activity and variations are expected to follow normal distribution, thes.D.

Hence, he variance offlre expected time is determined by summing the vafiance ofcritical activities and is

= I +2+E +1=9.Standard Deviation ofthe expected time = {9 = 3 months.

('(iD

(iiD(iv)

Cotf @L)ftoL.

Activity1-2

2-3

2-4

2-5

Nornal Tine (days)3

3

7

9

Nomal cost5A

57A

120

o./ Question 5A product comprised of 10 acriviiles whose norma! time and cost are given as fo!!ows:

Murphy-pcStamp

3-5

4-5

5-6

6'76-B

7_B

lndirecl cost Rs. 9 pu day.0 Draw the netwotk and identlfy he aitical path.(ll) Whal arc lhe $qiect dwailon and associated cost ?(ii'r) Find out the total float assehted with each acttvity.Answer )..-

Er

3

6

10

50

6

4

13

10

42

0

54

67130

166

(ii)

(iiD

Critical pathA D GHJ1 *-- -2-

-- 5- -

--6-----7------8A D G H J is the critical pah having normal project duration3+9+6+4+'10=32days

Normal project cost' Direct costlndirect cost (32x9) :

Calculation of total float

Activity N(days)1-2 32-3 32-4 7

= Rs. 704

= 2b8

.992

Float (LrEr)0

1

2

Lr3

7

12

Murphy-pcStamp

't212

12

t822

3232

?-s3-5

+5$66-7

&87-8

I5

0

6

4

13

10

ooof)

12

11

t018

22

.3132

Ij:t.J". !.

0

1'

2

0

0,|

0

,4 Question 6 (Nov I DEcA network is given below:(i) Name the paths and give theh btat duration.(ii) Give th{ee diftercnt ways ot reducing rhe yoject above duralion by four days.

An swer

(i) Assuming th;t the duration of activity 3 _ 5 is 4 weeks.The various critical paths are:

1-2-5-8-9'l-34-7-8-91-3-+6-7-&9'l-35-S-9

15 weeks15 w-eeks

15 weeks

15 vueeks(ii) Note: since the duration for activity 3-5 is not specified it is open for you to assumethe duration. Depending upon the duration assume three possibilities emerge.

2.

't. lf the duration assumed is more than 4 weeks then 0rat path (13, 35, 58, g9) alone.will be critical. ln that case you can choose any ofthe u.iiulty in the critical pa*r.lf the duration assumed is exacfly 4 weeks then it will be one of the 4 critical pathsand the various possibilities are given below.

Murphy-pcStamp

lf tre duration assumed is less than 4 weeks then the solution should be based on 3 ofthe critical paths namely 12,589, 1346789 ild'134789. This has 16 combinations.

Reduce in the following ways, the project duration is. Since all the paflr are criticd,reduction is possible by combining actfuities. The activities can be independent, commonto few paths and common to dlthe paths. The vaious categories are as follotiYs:

1. Common to all the paths. 8-92. lndependent: Combination

Combination

Combination

Combination

3. Activities common to tito of the paths.CombinationCombination

Combination

Combination

1.

2.

3.

4.

1.

2.

3.

4.

'l-2,3-5,4-6 and 4-7.

2-5,&5,4-6 and 4-7.

1-2,t5,4-7, 6-7 .2-5,3-5,+7,6-7 .

1-2,1-3.

1-3,2-5.

3-4 5-8.

5-8,7-8.

1-2,3-4,3-5.

1-2,3-5,7-8.

2,5,$43-5.2-5,3-5,7-8.

4-6,+7,5-8.4-7,5.8,6-7.

4. Activities common to two of the paths and two independent activities.Combination 1.Combination ?.Combination 3.Combination 4.Combinafon 5.Combination 6,

(Any three of the above combination')r.,,/ euestion 1 fA pR / NAl toos) y,gnd.

A company had planned ils operalions as follows:

Activity1-22-4t-J3-4

t

Dutation (daYs)7

B

B

6

4q

Murphy-pcStamp

(i)@

1462-: 164_7 193-6 245-7 g6-a.77-8 I

Draw the network and find lhe attica! paths.Attter 15 days of working, the fo oWing progress ls noied:(a) Activities 1-2, 1-3 and I 4 compteted as pu original schedule.(b) Activity 2-4 is in ptogess and will be completed in 4 more days.(c) Activity 3-6 is in prcgress and wi need.lT mue days @ complete(d) The.stalt at activity 34 are specialised. They are directed to comptere 3-6

and undertake an activity 6-7. which will.(equire Trtays. This ,rurrungr^entarose due to a modilica\on in a specialisation.(e) Activity 6-B will be conpteted in 4 days instend of the orlginaily planned 7 days.(0 There is no change in the other actjvities.

update the._nerwotk diagran after 1s days or start of wotk based on the assunption givenabove. lndicate the.revised critical patis aloagwifh their dwarion.

Murphy-pcStamp

Paths1-2-5-7.-81-2- 4-1

-81-4-7-81-3-4-7-81-3-6-8

Critical path 1-2-4-7-8 =42days.Revised Duration of activities ?- 4 and3 - 6 after 15 days forupdation.Acilvity Preceding Activity Dale of completion Revised Dunion

Duration7+16+9+8=407+8+19+8=42

6alg+t=338+6+19+8=41

15 +4 = 19 drys l9-7 = 12 days15 +17 =32days 32-8=24dals

7 days

4 days

?-43-66-7(nanactivity)6-8

l-2,

1-33-6 \'

l3-6(ii)

Paths1-2-5-7 -g1-2- 4-7 -81-4-7-81-s-4-7-81-3-6-7-81-3-6-8

Duration7 + 16 + 9 + I = ilO

7+12+19+8=tl66+19+8:33

8+6+19+8=4'l8+24+1+8=4:l

8+24+4=36Critical pa0r = I - 3 - 6-7 - I = 47 days-

4o

Murphy-pcStamp

y'l Question B CNov/DEc ,ol7) 2(nl.v/ruua ,zocll) t tr:, ! ,Thelorrowing rable gives the acriviries in a conslruction.project and the rime diration oleach activity:

AcilvrtyABLDEF

heceding actjvity Nwmal Time (Day)1620I10612

AA"

B,,CD,E

AtoBzocb

0

0't6

0

4

t6

't6

24

24

16

20

24

Free

0

4

0

Required:

0 fuaw the activity netwuk of the projecl(ii) Find critica! path.(ii| Find the total float and freefloat for each activity.3Iry(D

EA-+D-+F=16+i0+,1!=36B-+E-+F=20+6*12=3g

(iD A- C- E -F = 16 +8 +6 +12= 42(iii) Total float and free float for each actMty

Activity Nomat tjne Earliest Tine linish(Days) staft

Critical patr

Latest Tine finishstarl

Floattotal

0

4

0

Murphy-pcStamp

DE

F

20

24

30

"Z Question 9What do mean by a dumny activtty? Why is it used in netwo*ing?

Dummty acbvity is a hypothetical activity which consumes no resource or time. lt isrepresented by dotted rines and is inserted in the network to crariff an activity patternunder the following situations.(D To make activities with common starting and finishing events distinguishabre.(iD To identifo and maintain the proper precedence rerationship between activities hat

are not connected by events.(iit) To bring all 'roose ends" to a singre initiar and singre terminar event.e. g.

10

6

12

16

2430

3030

42

26

30

42

4 '40000

An swer

Dummyand (3)

u/,fuesrion 10

(2) -

(3) is used to convey that can start only afrer eventsare over

numbered (2)

Working Mehodology of PERT:The rrvo*ing mehodology d pERT vutrich includes bofir cpM and pERr, consists of follorrutrg fivesteps:

't. Analyze and break down the project in terms ofspecific activities andor events.2. Determine the interdependence and sequence of specific activities and prepare a net-

wor*.

List the 5 steps involved in the methodolo

Murphy-pcStamp

3. Assign estimdes of time, cost or both to dl the activities of the network.4. ldentify 0re longest or critical pa$ through the netuork.5. Monitor, evaluate and control the progress of Bre project by reflanring, resched.rlingand reassignment of resources.s,,lQuestion 1l

A snall ptoject is composed of swen activities, whose time estimales arcActivities arc identifies by theh besinning Ai ;;;;di;;-il riii"nu^tr,r,

l#!rr!; "tor"o duralion and variance for each activity. ttvhat is the expx.ted proiectGiven: Z 0.50 0.61 1.00

P 03085 0 2514 0.1587AnswerAdivity Eslimated Dumtions :

Adivity estinded durations (days) L = -G + iriD pumt on

listed below.

(a)(b)

it:

I

1.33 2.000.0918 0.0228

Murphy-pcStamp

8t8l;T;I3

I50 0 8

2

4 zI

I 34 ly6

is 1-3$6. '6

ACdtical pattr

The otpected project duration = 8+l!+lrt= ltt 67y5EXERCISE

Question 1The ilne schedule fu difierent activiales of a Noject is given below:

I10I1016171814I

Construct the PERI network and compute.

0 Critical path and its dwation.(ii) lotal and ftee tloat fot each activity.Answer

The critical pah is given by 1 -i - 3 - 5 - 6. The path represents he minimum possibletime to complete the project.The ptoject duration = 8 + l0 + 17 + 9 = 44 days.

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l0

1-21-31-42-32-63-54-54-65"6'

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Question 2A project'has the followittg Ame schedule:

1-21-32-43-43-54-95-6

5-76-87.88-9

B-109-10

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B7

Congruct a PtRf nework and compute: : .,(,) Te and Tt for each event;(ii) Floa.t for each activity; and(t0 Critical path and its duation. ':iAnswer

Critical path is given by all those activities whicli have zero floats. Along the zero floatactMties, trere are tvrir such critical paths: .*'(D 1-*3-5-.7-8-'9---10(ii) I ..- 3 ..- 5

-r 7 -, 8 -" 10The project duration is 25 weeks.question 3Girnn the following inlomration:

41

1

I654

Aclivity: 0-1Ouatim: 2

1-2 t-3I 10

2-5 3-433

3-6 4-775

5-7 6-728 (in days)

2-4

6

(i) Draw ihe anow diagram.(ii) ldentify ait:tcal path and tlnd the totat project duration.(iil Deternine tota!, free and independent floats.AnswerThe critical path is - 0---+1-3.-,8-7Total project duration'F 27 days.

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