Critical Path Method_yatri

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CRITICAL PATH METHOD

The Critical Path Method, abbreviated CPM, or critical pathanalysis, is a mathematically based algorithmfor scheduling a set ofproject activities. It is a very important tool for effective projectmanagement.

It was developed in the 1950s in a joint venture between u!ont"orporation and #emington #and "orporation for managing plantmaintenance projects. Today, it is commonly used with all forms of

projects, including construction, software development, researchprojects, product development, engineering, and plant maintenance,among others. $ny project with interdependent activities can applythis method of scheduling.

The essential techni%ue for using "!& is to construct a model of theproject that includes the following'

1. $ list of all activities re%uired to complete the project (also)nown as *or) brea)down structure+,

.The time (duration+ that each activity will ta)e to completion, and

-.The dependenciesbetween the activities.

sing these values, "!& calculates the longest path of plannedactivities to the end of the project, and the earliest and latest thateach activity can start and finish without ma)ing the project longer.This process determines which activities are /critical/ (i.e., on thelongest path+ and which have /total float/ (i.e., can be delayed without

ma)ing the project longer+. In project management, a critical pathisthe se%uence of project networ)activities which add up to the longestoverall duration. This determines the shortest time possible tocomplete the project. $ny delay of an activity on the critical pathdirectly impacts the planned project completion date (i.e. there is nofloaton the critical path+. $ project can have several, parallel, near

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critical paths. $n additional parallel path through the networ) with thetotal durations shorter than the critical path is called a subcritical ornoncritical path.

These results allow managers to prioritie activities for the effectivemanagement of project completion, and to shorten the plannedcritical path of a project by pruning critical path activities, by /fasttracking/ (i.e., performing more activities in parallel+, and2or by/crashing the critical path/ (i.e., shortening the durations of criticalpath activities by adding resources+.

3riginally, the critical path method considered only logicaldependenciesbetween terminal elements. 4ince then, it has beenepanded to allow for the inclusion of resources related to each

activity, through processes called /activitybased resourceassignments/ and /resource leveling/. $ resourceleveled schedulemay include delays due to resource bottlenec)s (i.e., unavailability ofa resource at the re%uired time+, and may cause a previously shorterpath to become the longest or /resource critical/ path. $ relatedconcept is called the critical chain, which attempts to protect activityand project durations from unforeseen delays due to resourceconstraints.

4ince project schedules change on a regular basis, "!& allows

continuous monitoring of the schedule, allows the project manager totrac) the critical activities, and alerts the project manager to thepossibility that noncritical activities may be delayed beyond their totalfloat, thus creating a new critical path and delaying projectcompletion. In addition, the method can easily incorporate theconcepts of stochastic predictions, using the !rogram 6valuation and#eview Techni%ue(!6#T+ and event chain methodology.

"urrently, there are several software solutions available in industrythat use the "!& method of scheduling, see list of projectmanagement software. 7owever, the method was developed andused without the aid of computers.

$ schedule generated using critical path techni%ues often is notrealied precisely, as estimations are used to calculate times' if onemista)e is made, the results of the analysis may change. This could

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cause an upset in the implementation of a project if the estimates areblindly believed, and if changes are not addressed promptly.7owever, the structure of critical path analysis is such that thevariance from the original schedule caused by any change can bemeasured, and its impact either ameliorated or adjusted for. Indeed,an important element of project postmortem analysis is the $s 8uilt"ritical !ath ($8"!+, which analyes the specific causes and impactsof changes between the planned schedule and eventual schedule asactually implemented

*hat is the CPM CPMCritical Path Method (CPM! is a procedure for using networ)analysis to identify those tas)s which are on the critical path' ie whereany delay in the "ompletion of these tas)s will lengthen the project

Timescale, unless action is ta)en. :or all tas)s off the critical path, adegree of tolerance is possible (e.g. late start, late completion, 6arlystart, etc.+.;etwor) charts and "!& analysis used to be carried outby hand. 4oftware is now available which re%uires the user only toenter the tas)s, duration of each tas) and dependencies upon othertas)s< a networ) chart and "!& is then automatically created.

*hy "!&The CPM formally identifies tas)s which must be completed on timefor the whole project to be completed on time Identifies which tas)scan be delayed for a while if resource needs to be reallocated tocatch up on missed tas)s It helps you to identify the minimum lengthof time needed to complete a project The "!& determines both theearly start and the late start date for each activity in the schedule. The"ritical !ath &ethod ("!&+ is one of several related techni%ues fordoing project planning. "!& is for projects that are made up of anumber of individual /activities./ If some of the activities re%uire otheractivities to finish before they can start, then the project becomes acomple web of activities.

"!& can help you figure out'

how long your comple project will ta)e to complete which activities are /critical,/ meaning that they have to be done

on time or else the whole project will ta)e longer

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If you put in information about the cost of each activity, and howmuch it costs to speed up each activity, "!& can help you figure out'

whether you should try to speed up the project, and, if so, what is the least costly way to speed up the project.

Acti"ities

$n activity is a specific tas). It gets something done. $n activity canhave these properties'

names of any other activities that have to be completed beforethis one can start

a projected normal time duration

If you want to do a speedup cost analysis, you also have to )now

these things about each activity' a cost to complete a shorter time to complete on a crash basis the higher cost of completing it on a crash basis

"!& analysis starts after you have figured out all the individualactivities in your project.

CPM Analysis #teps! $y E%a&ple

This document describes the steps for doing "!& analysis for thiscourse. The steps will be illustrated by two eamples. I recommendthat you wor) through the eamples, so that you can follow the stepsyourself when you do the homewor).

E%a&ple ' Acti"ities! precedence! and ti&es

This first eample involves activities, their precedence (whichactivities come before other activities+, and the times the activitiesta)e. The objective is to identify the critical path and figure out how

much time the whole project will ta)e.

E%a&ple ' #tep ' List the acti"ities

"!& analysis starts when you have a table showing each activity inyour project. :or each activity, you need to )now which other

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activities must be done before it starts, and how long the activityta)es.

7ere=s the eample'

Activity Description Required Predecessor Duration

$ !roduct design (;one+ 5 months

8 &ar)et research (;one+ 1

" !roduction analysis $

!roduct model $ -

6 4ales brochure $

: "ost analysis " -

> !roduct testing ?

7 4ales training 8, 6

I !ricing 7 1

@ !roject report :, >, I 1

E%a&ple ' #tep ) Dra* the diagra&

raw by hand a networ) diagram of the project that shows whichactivities follow which other ones. This can be tric)y. The analysismethod we=ll be using re%uires an /activityonarc/ ($3$+ diagram. $n

$3$ diagram has numbered /nodes/ that represent stages of projectcompletion. Aou ma)e up the nodes= numbers as you construct thediagram. Aou connect the nodes with arrows or /arcs/ that representthe activities that are listed in the above table.

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4ome conventions about how to draw these diagrams'

$ll activities with no predecessor come off of node 1. $ll activities with no successor point to the last node, which has

to have highest node number.

In this eample, $ and 8 are the two activities that have noprecedessor. They are represented as arrows leading away fromnode 1.

@ is the one activity that has no successor, in this eample. It

therefore points to the last node, which is node B. If there were morethan one activity with successor, all of those activities= arrows point tothe highest number node.

4tudents sometimes ma)e the mista)e of creating a diagram withseveral starting or ending nodes. Don'tdo this.

The tric)iest part for me of building the above diagram was figuringwhat to do with activity 7. I had drawn an arrow for activity 8 comingoff node 1 and going to mode -. I had later drawn an arrow for activity6 coming off node and going to node C. 4ince 7 re%uires both 8and 6, I had to erase my first 6 arrow and redraw it so it pointed tothe same node - that 8 did. 7 then comes off of node - and goes tonode C.

*hen designing these diagrams, wor) in pencil.

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E%a&ple ' #tep + #et ,p the CPM spreadsheet

There are specialied commercial programs for doing "!& analysis.#ather than purchase and learn one of those, we=ll leverage thespreadsheet )nowledge we already have. *e will use one freewareprogram written for this course and made available to you through theInternet.

4tart up a new blan) spreadsheet. If you are viewing this documenton the web, minimie your browser window and then start Excel. Thatway you can switch from one to the other by pressing $ltDTab.

In a blan) spreadsheet, type the word /$ctivities/ in cell $1. In row ,type the names of the activities, or their letters. (To ma)e my

spreadsheet screen shots fit better on these pages, I set the columnwidths to ?. Aou do not have to do this.+

In row -, type /;odes/. In row ?, type in each activity=s start node where the tail of its arrow is. 8elow that, in row 5, type each activity=send node where the head of its arrow is. o this carefully. &ista)eshere mess up everything that follows.

To the right, in E and E-, type the words /4tart/ and /6nd/ to labelthose rows.

In cell $C, type /Times/. In row F, type the time each activity ta)es.Then, select the range of cells containing the node numbers

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and copy it to the clipboard.

E%a&ple ' #tep - .se Pathfind to get the paths

!athfind is a computer program that helps you find and enter into thespreadsheet all of the possible paths through your diagram along thearrows from the first node to the last. Aou could do this by hand, ofcourse. This diagram shows the four possible paths in this eample.

The four paths are $ > @, $ " : @, $ 6 7 I @, and 8 7 I @. *e=llcode them in the spreadsheet with a matri of 0=s and 1=s. #atherthan do this all by hand, we=ll get !athfind help do it.

To use !athfind, start up your Internet connection and your browser

Goading this html file into your browser starts !athfind, which is a

@ava applet that runs inside your browser. *hen !athfind is loaded'

1. "lic) in !athfind=s upper tet area.. !aste the range you just copied from your spreadsheet into that

upper tet area. ("lic) in the tet area and press "trlDH or4hiftDInsert.+

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-. "lic) on !athfind=s button. !athfind=s lower tet area will giveyou a bloc) of numbers, all highlighted so you can copy them.

?. "opy the highlighted numbers to the clipboard for pasting laterinto your spreadsheet. ("trlD" or "trlDInsert copies what ishighlighted.+

Aou can now close the !athfind web page, if you wish.

E%a&ple ' #tep / Paste the path infor&ation into yo,rspreadsheet

*hen you=re done with !athfind, go bac) to your spreadsheet. &oveyour cell selector to cell $B. Type /!aths/ in that cell. Then move thecell selector to $9, as shown here'

!aste to that cell, to see this'

The pasted cells are all 0=s and 1=s. 6ach row represents a path. The1=s indicate which activities are in that particular path. :or eample,row 9 (cells $9'@9+ has 1=s under activities $, ", :, and @. This saysthat this path includes activities $, ", :, and @. This corresponds to

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the path through the middle of the diagram that goes' 1 $ " ?: F @ B.

The diagram above shows four paths from node 1 to node B. 4ureenough, !athfind gives you four rows of 0=s and 1=s, one row for eachpath.

E%a&ple ' #tep 0 Calc,late the paths1 ti&es

&ove the cell selector to E9. !ut J4&!#3"T($9'@9,K$KF'K@KF+in that cell.Luattro !ro' M4&!#3"T($9'@9,K$KF'K@KF+.

This formula multiplies each entry in row 9 by the corresponding entry

in row F. 8ecause the entries in row 9 are all 0=s and 1=s, this has theeffect of selecting the times from row F that go with the activitiesrepresented in row F, and adding all those times.

*hen you enter the formula, the number 11 should appear in E9.That=s the time it would ta)e to complete activities $, ", :, and @. Aoucan verify that $ ta)es 5 months, " ta)es , : ta)es -, and @ ta)es 1,for a total of 11.

(If you are doing a CPM proble of your o!n" odify t#e forula so

t#at t#e ranges cover t#e coluns you actually #ave$ %#is adviceapplies to all t#e forulas !#ic# follo!$&

To fill in the other paths= times, copy cell E9, then paste it to E9'E1.The K signs in the formula see to it that each path=s 1=s are multipliedby the corresponding numbers in row F.

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E%a&ple ' #tep 2 Identify the critical path

The critical path is the path that ta)es the longest. In this eample,the critical path is the one in row 10, which ta)es 1- wee)s. Theproject will therefore ta)e 1- wee)s, if everything is done on schedulewith no delays. The time a project ta)es is e%ual to the time of itscritical path.

The 1=s in row 10 tell us that the critical path is 1 $ ? > F@ B. $s managers, we must be sure that activities $, , >, and @are done on time. If any of those activities is late, the project will belate.

3ther paths are not critical because they can waste some timewithout slowing the project. :or eample, activity ", in row 9=s path,can ta)e up to two etra wee)s and not hold up the project.

To ma)e it easier to see what activities are in each path, go to cell$1?. Type Jif($9J1,$K,//+ there.The letter $ should appear in cell $1?. Luattro !ro'Mif($9J1,$K,//+.

This Jif($9J1,$K,//+ function wor)s this way' Inside the parenthesesare three epressions separated by commas. The first epression($9J1+ is something that can be either true or false. If the epressionis true, the second epression ($K+ is shown in the cell. 3therwise,the third epression (//+ is shown in the cell.

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In $1?, the epression $9J1 is true, so the cell shows what is in $,which is the letter /$/. If $9 had not contained a 1, the $1? wouldhave shown a blan), which is what // means.

"opy $1? to the clipboard. Then, starting in $1?, select a range ofcells that goes over to column @ and down four rows. The selectedrange should be the same sie as the space that the paths= 1=s and0=s ta)e up.

!aste. Aou should get this'

;ow you can see which activities are in each path. If your results donot loo) li)e the above, ma)e sure that there is one K in your formula,and that it=s in front of the and not in front of the $.

>o to cell @1- and type /&a/. Then go to cell E1-. Type =MAX(K9:K12)to display the longest path time.

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&ove to cell E1? and type JI:(E9JEK1-,/"ritical/,//+ there.

This will put the word /"ritical/ net to a path whose time e%uals themaimum of all the path times. 3therwise, it will put in a blan), as itdoes here, because the 11 in E9 does not e%ual the 1- in E1-.

"opy E1? to the clipboard. (It will seem strange to copy what appearsto be an empty cell, but do it anyway.+ 4elect cells E1? to E1F, and

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paste.

Aou=re doneN Aou=ve found the time the project will ta)e, and youhave identified the critical path, which tells you which activities mustbe done on time to ma)e the project finish in the least time.

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