X+5.8+Project+Management

= 5.8 PROJECT MANAGEMENT = __**KEY WORDS:**__ NETWORK ANALYSIS A.K.A. CRITICAL PATH [ANALYSIS] NODE EARLIEST START TIME LATEST FINISH TIME FLOAT [FREE & TOTAL] DUMMY TASK

Key Idea :
 * It is a DECISION MAKING TOOL
 * This is a topic that is relevant only to LARGE Projects - usually connected to engineering and construction projects. The schools contractors created and followed one for the construction of the LRC!
 * For large construction projects you need to hire a team of workers ( //it is often difficult to hire quality workers and create a committed team when you hire workers by the day, saying 'come in today, don't come in tomorrow, maybe the day after'//) and you need to lease different equipment at different times. In both cases you don't want your resources lying idle : workers being paid but no work for them to do, paying for a leased machine but no work for that machine to do.
 * The CPA helps you control this, identify which parts of the project are depended on & connected to others, and which can be delayed //(and by how much)// with no knock-on effect and which ones can't. The ones that can't be delayed we call 'critical tasks'
 * Remember that just like Tree's, Fishbone etc the CPA is a //diagram// and so **needs labels & a key**!

In **May 2012, Paper 1** posed the following question for 4 marks (Begin with a definition) CPA is a Project Management tool that identifies the different tasks involved in a project and places them in sequential order. (State what it is used for) The purpose is to aid decision making and does this by identifying data such as the minimum amount of time needed to complete a project, and which tasks can be delayed with or without affecting this earliest finishing time. (Give example of its value) Moving resources such as personnel and equipment, plus determining start dates of equipment hire can be done more effectively.
 * "Describe the use and value of a Critical Path Analysis" **


 * So How To Construct It.. **


 * All CPA's are made up of (i) Nodes & (ii) Activities/Tasks.
 * ALL CPA's will have (at least one) **Start Node** - //that indicates how the Project gets started// & (only one) **Finish Node** - //indicates the Project is over//
 * Each **Node** (apart from the Final Node) will also have at least one **Task** protruding out from it.
 * The picture at the top gives a //general// idea of what a CPA ends up looking like. The Start Node is on the extreme left with the numbers 0&0, the Finish Node is on the extreme right with the numbers 22&22. All Tasks are labelled and 3 Dummy Tasks exist too (shown by the dotted line). An online research will provide a variety of versions of a CPA, all looking similar but also slightly different. Below is the method that the IB recommends.



THERE IS NO LIMIT ON THE NUMBER OF START AND END NODES THOUGH NOTE THAT IF THERE ARE MORE THAN ONE, THEN THE RULES OUTLINED ABOVE [IN THE RED BOX] DO NOT HOLD TRUE.





**EXAMPLE (EASY)** So if there is no table Step 1 will be to create the table - assuming a Table is given it will look like the one below //WARNING : If there is a magic trick to get expert on these I don't know it. Practice, Practice, Practice. Also maybe be prepared to scribble up a draft on a scrap piece of paper first, as its quite likely you'll find yourself crossing things out, and re-drawing arrows as you work out your correct Network.//
 * The information //might be// presented in a paragraph, but usually it is in Table format **
 * Activity..... || Duration (weeks) .... || Preceded by ...... ||
 * A || 3 || - ||
 * B || 4 || A ||
 * C || 6 || A ||
 * D || 4 || B ||
 * E || 2 || C&D ||

We know by the fact that __only__ Task A has no preceding Tasks that there will be only one Start Node and it will have just the one Task (TaskA) protruding from it - and that Task A lasts 3 weeks. We also know the EST & LST of TaskA will be zero
 * Step 1**: (easy)



We know that from Node 2 there must be 2 Activities, as both B&C require A to finish before they can start. mm
 * Step 2:** (gets a bit more complicated)

We know that TaskD requires TaskB to finish but is unconnected to TaskC. //A simple tip here is to - for the moment anyway - leave the Task arrow headless, as we may need to change its direction in later Steps//
 * Step 3:**



TaskE is the final Task and requires both C & D to be finished before it can start. //Don't be afraid to extend or re-direct an arrow//
 * Step 4:** (probably the trickiest step in this e.g.)

[[image:1_Node4.JPG width="425" height="228"]] error alert! Task E lasts 2 weeks not 4!
No more Tasks : 'Project is Finished'. Time for the END Node.
 * Step 5:** (easy again)

Notice that for a Project that has 19 weeks worth of work [3+4+6+4+2], a CPA shows it can in fact be finished in 13 weeks. It is a decision making tool that helps with Project efficiency after all!

We need to put the LFTs. The trick is to work backwards. Node 5 is 13 - we know that because in all End Nodes the EST & LFT are the same. So for... ..... * this makes sense because Task A cannot wait until the 5th week to finish or else Task C & B get delayed. Now delaying Task C by 2 weeks isn't going to matter - it will still finish by Week 11 which is the deadline (LFT) however delaying Task B is going delay Task D - and Task D then won't finish until Week 13, and then you've still got Task E to do -- thus pushing the Project Finish Time to Week 15 .. and this means more costs, disappointed customers etc
 * Step 6:** (final - for now)
 * Node 4 the LFT for Task D&C must be [13 - 2 = 11],
 * Node 3 the LFT for Task B must be [ 11-4 = 7]
 * Node 2 the LFT for Task A must be [ 11-6 = 5] or [7-4 = 3]. whichever is smallest * which is 3

__**PS**__ : The Key is missing the Critical Path, but we haven't covered that yet so i left it off

** Q/ So what is this idea of a 'Critical Path' ? **
It can be defined as : "all the tasks in which __any__ delay will //cause an overall delay in the Project Finish Time//"

In the example above the **Critical Path would be A, B, D, E. :** A delay to any of those Tasks will lead to an overall delay of the Project

Task C is non-critical, and as we saw you can delay it by up to 2 weeks and have no affect. A delay of 3 weeks to Task C clearly would affect the overall finish time, but that doesn't stop it being 'non-critical' because a delay can occur and no affect can take place.

Below is how the CP would be identified on the CPA. A little curious fact - remember with Decision Trees the double lines mean the options __ignored__, here it means the route that needs __attention__ i.e. the CPA

= ANOTHER EXAMPLE =

(A LITTLE BIT MORE DIFFICULT BUT STILL FAIRLY EASY)
See if you can do it. The answer is attached below. So if there is no table Step 1 will be to create the table - assuming a Table is given it will look like the one below //ATTEMPT IT BEFORE LOOKING UP THE ANSWER!!//
 * Activity..... || Duration (weeks) .... || Preceded by ...... ||
 * A || 3 || - ||
 * B || 2 || - ||
 * C || 1 || A,B ||
 * D || 3 || C ||
 * E || 4 || C ||
 * F || 4 || D ||
 * G || 2 || D ||
 * H || 6 || E ||
 * I || 2 || F ||
 * J || 4 || G,H ||
 * **TOTAL** || **31 WEEKS OF WORK** ||  ||



//Which of the following did you get right...the Project Final Finish Time? ... the Critical Path?... the LFTs?... the ESTs?// //Remember it not a case of 0% right, or 100% right - there are significant marks to be gained if there is general sense to the Network despite some errors.//

** Q/ So what are we missing to complete our knowledge? **
There are 2 aspects missing. These are the aspects that tend to confuse and turn students off the topics, but they are not as hard as they always seem to be :


 * ** FLOATS : FREE AND TOTAL **
 * ** DUMMY TASKS **

TRUE STORY : I asked an practicing licensed engineer I know about CPA's and their usefulness in the 'real world' - his reply was "They are hard to do. I have worked on Projects where a CPA exists but it seems it was just drawn up because someone though they had to - and it was full or errors, didn't make sense and was stuck up on a wall and ignored by everyone. I have also worked on projects were we don't have one at all - but i think the best projects I have worked on have a CPA that is accurate and works, and in these cases, its the best thing, a document that guides us almost every day."

The basic idea is simple. Float refers to '//spare time//' - time that can be 'wasted or lost' without affecting the Projects Final Finishing Time. Remember NOT all Tasks will have spare time. In fact a Golden Rule is 'Tasks along the Critical Path have __NO__ float'
 * FLOATS **

Distinguishing between Free Float and Total Float can be confusing although there is a clear difference in the formulae used to calculate them....
 * TOTAL FLOAT ( of the Sequence of which Task A is part) ** = LFT of Task A - Task A duration - Task A EST **
 * Defined as 'the amount of time a connected SEQUENCE OF TASKS can be delayed without affecting the WHOLE PROCESS'
 * FREE FLOAT (of Task A) ** = EST of next Task (Task B) - Task A duration - Task A EST **
 * Defined as 'the amount of time a TASK can be delayed without affecting the NEXT TASK'

There CAN BE CONFUSION here. With questions being asked like ...... Q. Is it true that all Tasks with a Sequence will have the same Total Float? Q. Do I add up all the Total Floats of each of the Activities to get the Total Float of the Sequence?

//These are irrelevant questions do NOT bother yourself with them//

I have found it is best to present your answers/figures in a table. IB MarkSchemes prefer this method therefore IB Markers prefer it too. Presume you have been given the information in the table below - and you have added the final 2 columns The CPA would be as follows.....
 * Task || Preceding Task || Duration || Total Float || Free Float ||
 * A || - || 5 ||  ||   ||
 * B || - || 6 ||  ||   ||
 * C || A,B || 3 ||  ||   ||
 * D || C || 6 ||  ||   ||
 * E || C || 10 ||  ||   ||
 * F || D || 4 ||  ||   ||
 * G || E || 1 ||  ||   ||
 * H || F,G || 3 ||  ||   ||

Error alert! Node #7? So you can work out the Free & Total Floats as.... In some cases you will find that Tasks on the Critical Path don't have a Float of '0', they are just left blank.
 * Task || Prec. Task || Duration || Total Float || Free Float ||
 * A || - || 5 || 1 || 1 ||
 * B || - || 6 || 0 || 0 ||
 * C || A,B || 3 || 0 || 0 ||
 * D || C || 6 || 7 || 0 ||
 * E || C || 10 || 0 || 0 ||
 * F || D || 4 || 7 || 7 ||
 * G || E || 1 || 0 || 0 ||
 * H || F,G || 3 || 0 || 0 ||

Now the Critical Path is B(6)+ C(3) +E(10)+G(4)+ H(3). The Tasks in red are common to both the Critical and Non-Critical Path The non-Critical Path, along which there are Floats then is A(5)+D(6)+F(1). A quick sum of uncommon Critical Tasks shows us a duration of 6+10+4 = 20 weeks A quick sum of uncommon non-Critical Tasks shows us a duration of 5+6+1 = 12 weeks A difference of 8 weeks ! - this is NOT our answer for anything but it gives us a basis for the difference between Free & Total Floats.

It shows both the Free Float and the Total Float, but for purposes of understanding I'll go on a little...
 * In fact for IB purposes you can just leave your answer like that - in Table Format!!**

Clearly it is not possible to delay all tasks by their full Total Float (//ie Task A by 1week __and__ TaskD by 7 weeks __and__ TaskF by 7 weeks//) and not delay the Final Finishing Time. This would be impossible (our '8 week' total clues us in on that). So __Project Managers__ like to know the non-Critical Tasks that can be delayed without affecting the EST of proceeding Tasks, as these are the Tasks where real flexibility is possible : in this Case Tasks A & F - as they have Free Floats!

So essentially non-Critical Tasks are divided into 2... [1] those that can be delayed without affecting the proceeding Task (//ie have a Free Float//) ** A & F ** and [2] those that that cannot (//ie their Float comes from the Sequence they are in rather than the Task itself hence no Free Float - just Total Float//) ** just D **

Try one yourself EXAMPLE __**Calculate**__ the Free Float and Total Float within Project Z in the Table below.. //ATTEMPT IT BEFORE LOOKING UP THE ANSWER!!//
 * Task || Preceded by || Duration ||
 * A || / || 2 ||
 * B || A || 3 ||
 * C || B || 4 ||
 * D || B || 10 ||
 * E || C || 2 ||
 * F || D,E || 6 ||
 * G || F || 5 ||
 * H || F || 2 ||
 * I || H || 4 ||
 * J || G,I || 6 ||


 * .. and that is it for Floats! ..**
 * ...I hope it makes a bit more sense : remember the question that causes the most confusion is below. Here is the ANSWER before you read the question ..... //"__No__ - the Total Float of the Sequence is not a relevant number. Simply show which Tasks have Total Floats and which have Free Floats, and the size of these Floats in Table Format"//**


 * "**//Q. Do I add up all the Total Floats of each of the Activities to get the Total Float of the Sequence?"//

Another idea that can confuse - which is ironic because the purpose of a Dummy Task is to help keep the CPA accurate and making sense!! Students think Dummy Tasks are complicated because they are required to make complicated CPA's work - but its the CPA that is complicated, Dummy Tasks are used to make them easier.
 * DUMMY TASKS **

A workable __definition__ of a Dummy Task is ... (i) a dotted arrow on the Network that helps connect sequential tasks,(ii) it is not a //real// task, nothing happens, no labelling such as Task description/duration, is needed or possible.

Here is an example of a Project that would require a Dummy Task I have circled Task H as this is the one that will complicate issues.

We could try draw it as below and you'd get some marks for your attempt however do you see the problem?

or you could try draw it like this, and again you would get some marks - maybe even a few more than above but again NOT FULLY ACCURATE - do you see the problem?

. Error Alert! misspelling of 'Activity' So, like i said Dummy Tasks are required to make a complicated CPA, actually work. Here how .. not a million miles different from the above actually



and thats it! Again ,, no magic wand other than the explanation above - the best way to develop expertise it to practice.

GOOD WAY TO PRACTICE - YOU NEED A PARTNER (Step 1) Draw a made-up CPA, give it a Dummy Task (Step 2) From the CPA create a Table, such as the ones we have been using, and will most likely appear in the IB exams. (Step 3) Swap your Table with that of a partner (keeping the CPA - which is the Answer - secret) (Step 4) From your Partners table draw a CPA (Step 5) Compare your CPA with their CPA

EXAMPLE Here's a Practice Question with an answer.... Try draw the CPA. And here is the answer!

FINAL POINTS (1) Do include Dummy's on your CPA - if appropriate (2) Do Remember to follow the Dummy's path when working out ESTs & LFTs

__** An alternative explanation **__:
 * Warning** : while [|this video] is very clear it is __not__ aimed at IB students, so does not use IB language. There are terms such as algorithm, precedent diagrams, + forward and backward passes which the IB do not require you to use however the explanation is clear and the ideas are the same. As a tool to aid understanding I do particularly like the first 3 or 4 minutes of this video where he creates a 'cascade chart'- (another non-IB term!)

Do you know the //__** Disadvantages & Limitations **__// of a CPA?

PRACTISE, PRACTISE, PRACTISE:




__//**SUMMARY PPT**//__ : Most of the slides we have used in class are on this powerpoint.

//(didn't upload - try again later! - called 1.CPA2.ppt)//

A short 5 Question Quiz - with answers!