PJM6000 - Project Management Practices Class Exercise Week 4 - Critical Path 1. Forward Pass 2. Backward Pass 3. LSES = ? Identify Critical Path: 4. LSES = ? Find Slack time management Figure out the early start and early finish Coming up with the float for each activity is useful, but you can actually do better! When you have a long critical path, but the other paths in your network diagram are short, then you have a lot of freedom in when you can start and finish each of the activities that are not on the critical path. You can use early start and early finish to get a handle on exactly how much freedom you have in your schedule. ion ath has a durat The critical p = 18 of 6 + 5 + 7 6 5 7 Activity B Activity A Activity C Start Finish 2 Even if Activity D starts really late, since the path it's on is so much shorter than the critical path, the project will still be on time. The other path has of 2 + 3 = 5. It's a duration shorter than the cra lot so there should be a itical path, play in those activit lot of ies. 3 Activity D Activity E Early start Is the earliest time that an activity can start. An activity near the end of the path will only start early if all of the previous activities in the path also started early. If one of the previous activities in the path slips, that will push it out. Early finish Is the earliest time that an activity can finish. It's the date that an activity will finish if all of the previous activities started early and none of them slipped. That mean and early fsinthe early start E are really ish for D and end a lot sooearly - they can and C, which ner than A, B resources for will free up their you to use. When you find the early start and early finish for each task, you know exactly how much freedom you have to move the start dates for those activities around without causing problems. you are here 4 257 starting late Figure out the latest possible start and finish It's also important to know how late any activity can run before it delays the project. That's what late start and late finish are for! They let you figure out how late you can start a certain task and how much it can slip before it delays your project. 5 6 Activity B Activity A This is the same networ diagram from the last k page . 7 Activity C Start Finish 2 This path is much shorter than the critical path, so you should be able to start Activity D very late and still complete the project on time! Activity D Late start Is the latest time that an activity can start. If an activity is on a path that's much shorter than the critical path, then it can start very late without delaying the project - but those delays will add up quickly if other activities on its path also slip! Late finish Is the latest time that an activity can finish. If an activity is on a short path and all of the other activities on that path start and finish early, then it can finish very late without causing the project to be late. 258 Chapter 6 The path Activity D is on has a much shorter duration than the critical path. So even if it has a long delay, it still won't harm the project. Figuring out the late start and late finish will help you see how much \"play\" you have in your schedule. An activity with a large late start or late finish means you have more options. time management Add early and late durations to your diagrams Early start and finish go the upper corners. Write in name of the activity abovthe and the duration and flo e it, at inside the box. You can use a method called forward pass to add the early start and finish to each path in your network diagram. Once you've done that, you can use backward pass to add the late start and finish. It makes your network diagrams look a little more complicated, but it gives you a lot of valuable information. special You can use thistwork node in your ne down diagram to write the early and late start and finish. The early start for this activity is 4. The early finish for this activity is 8. There's no way it can end before day 8. Design Invitations 8 4 Duration = 4 Float = 3 Write the late start in the low lefthand corner. As long as the erinvitation design starts by won't delay the critical patday 7, it h. 7 The late finish for the Design Invitations activity is 11, which means the latest it can finish without delaying the schedule is on day #11. If it hasn't finished by then, Kathleen should worry! 11 Take a forward pass through the network diagram. Start at the beginning of the critical path and move forward through each activity. Follow these three steps to figure out the early start and early finish! 6 Start Activity A 5 Activity B 7 Activity C Finish 1 The ES (early start) of the first activity in the path is 1. The EF (early finish) of any task is its ES plus its duration minus one. So start with Activity A. It's the first in the path, so ES = 1, and EF = 1 + 6 - 1 = 6. 2 Now move forward to the next activity in the path, which is Activity B in this diagram. To figure out ES, take the EF of the previous task and add one. So for Activity B, you can calculate ES = 6 + 1 = 7, and EF = 7 + 5 - 1 = 11. 3 Uh-oh! Activity C has two predecessors. Which one do you use to calculate EF? Since C can't start until both B and D are done, use the one with the latest EF. That means you need to figure out the EF of activity D (its ES is 1, so its EF is 1 + 2 = 3). Now you can move forward to Activity C and calculate its EF. The EF of Activity D is 2, which is smaller than B's EF of 11, so for Activity C the ES = 11 + 1 = 12, and EF = 12 + 7 - 1 = 18. B C D you are here 4 259 backward pass Take a backward pass to find late start and finish You can use a backward pass to figure out the late finish and start for each activity. Now take a backward pass through the same network diagram. The backward pass is just as easy as the forward pass. Start at the end of the path you just took a pass through and work your way backward to figure out the late start and finish. Activity B Activity A 1 7 6 Duration =5 Duration =6 Start ? 11 ? ? ? 12 3 18 Duration =7 ? Activity D 1 Activity C We've already figured out the ES and EF, so they're filled in here! ? Finish Duration =2 ? Start with the critical path. You're calculating the latest any activity can start and finish, so it makes sense that you need to start at the end of the project and work backwards - and the last activity on the critical path is always the last one in the project. Then do these three steps, working backwards to the next-longest path, then the nextlongest, etc., until you've filled in the LS and LF for all of the activities. Fill in the LF and LS for the activities on each path, but don't replace any LF or LS you've already calcualted. ? 1 Start at the end of the path, with Activity C. The LF (late finish) of the last activity is the same as the EF. Calculate its LS (late start) by subtracting its duration from the LF and adding one. LS = 18 - 7 + 1 = 12 2 Now move backwards to the previous activity in the pathin this case, Activity B. Its LF is the LS of Activity C minus one, so LF = 12 - 1 = 11. Calculate its LS in the same way as step 1: LS = 11 - 5 + 1 = 7. 3 Now do the same for Activity A. LF is the LS for Activity B minus one, so LF = 7 - 1 = 6. And LS is LF minus duration plus one, so LF = 6 - 6 + 1 = 1. 4 Now you can move onto the next-longest path, Start-D-C-Finish. If there were more paths, you'd then move on to the next-longest one, etc., filling in LF and LS for any nodes that haven't already been filled in. Activity B Activity A 1 7 6 Duration =5 Duration =6 Start 1 8 6 260 Chapter 6 12 Activity C 12 1 3 Duration =2 9 11 18 Duration =7 12 Activity D First do the forward pass for both paths. When you do that, you get a different LF for Activity B, which makes all the numbers change ! 11 They're the same if . there's only one path But with more paths, ! things get interesting 18 ate We use Activity D to calculause C bec the LF for Activity it has the lower LS. Finish time management Let's take some time out to walk through this! Calculating the ES, EF, LS, and LF may seem complicated, but it only takes a little practice to get the hang of it. Once you walk through it step by step, you'll see that it's actually pretty easy! All of this critical path stuff seems pretty serious, right? It's one of the toughest concepts on the exam. But don't sweat it, because it's actually not hard! It just takes a little practice. Once you do it yourself, you'll see that there's really nothing to worry about. There are four paths in this network diagram. Fill in each of the activity names and durations for each of the paths. 3 4 4 B C A 8 E Start 7 F 5 D End 4 6 H G __ Start __ __ __ __ __ __ __ __ __ __ __ __ __ Start __ __ Start __ __ Start __ __ __ __ __ __ Put an asterisk (*) next to the critical path. Finish Finish Finish Finish We're not done yet! There's more on the next page... you are here 4 261 critical path practice Take a forward pass through each of the four paths in the diagram and fill in the early starts and early finishes for each activity. Start with the first one. 4 Start Remember, the ea start of the firstrly activity in a path is one. 3 B A 4 C ES=__ ES=__ EF=__ EF=__ The early finish of an activity is its ES plus its duration minus one. ES=__ EF=__ The early start of an activity is the finish of the previous activity plus early one. Let's move on to the second path. 4 Start Finish 3 7 A B F Finish ES=__ ES=__ ES=__ EF=__ EF=__ EF=__ The next path isn't as straightforward as it looks. Start by filling in its values. 5 Start 6 4 D E H Finish ES=__ ES=__ ES=__ EF=__ EF=__ EF=__ Now take another look at it, and how it mixes with the last path. It includes activity H, which was also in the last path. H will have a different ES depending on 5 which path you use! So which predecessor Start D do you use - E or G? The idea here is that you use the ES=__ predecessor with the EF=__ larger EF value when you calculate the ES for activity H (because you want the latest possible start date). 262 Chapter 6 8 E ES=__ 4 EF=__ H 6 G ES=__ EF=__ Finish Wait up! These two aren't so EF=__ ? straightforward. Once you have the EF for both activities E and G, you can use the bigger one to come up with the ES for activity H. ES=__ ? time management You've calculated the ES for each activity. Use that information and take a backward pass through the paths, starting with the first two paths. First start with the critical path. Take the EF of the last activity in the critical path and use it as the LF for the last activity in every path. If you take a minute to think about it, it makes sense to do that. The point of LF is to figure out the absolute latest that the activity can end without making the project late. And as long as every non-critical-path activity ends before the last activity in the critical path, then they won't be late. We'll start by giving you the LF of critical path, Start-D-E-H-Finish, which is 17. Start by filling in the LF of the last activity in each path, which is the same as the EF of the last activity in the critical path. 4 C 4 The LF for each activity is the LS of the next one on the path minus one. 3 LF=__ A Start Move backwards through path, filling in the LS by the subtracting the duration from the LF and adding one. We've filled in the first two for you . B LS=__ Finish LF=__ LF=__ 7 LS=__ LS=__ F For activity B, you have a choice - you can calculate the LF using the LS from either activity C or F. Use the lower value, subtract one, and fill it in. Finish up by calculating the LS and LF for the last two paths! Activities B and D have two possible choices for which LS to use for the calculation. For activity B, do you use the LS of C or the LS of F? And for activity D, do you use the activity E or G? The answer is that you always use the lowest value of LS to calculate the LF. The reason is that you're trying to find the latest possible start date that won't make the project late. If you use an activity with a later LS, and the activity really is delayed by that much, then it'll cause a delay in both following activities. And that will make the one with the lower LS start too late. LF=__ LS=__ 8 E 5 Start LF=__ 4 D LS=__ H LF=__ 6 LF=__ LS=__ G Finish LS=__ Activity D is another one where you have to chose which LS to use in order to calculate the LF. You can either use the LS from activity E or activity G. Use whichever is lowest, subtract one, and fill it in. LF=__ LS=__ you are here 4 263 exercise solutions If you got a few of these wrong, don't and worry. It's easy to miss one calculation,path. that leads to a problem on the whole Activity A 1 4 Duration =4 Start 4 7 For the exam, you'll only have to do one or two of these calculations, not a whole string of them like this. You'll definitely be able to handle the exam questions now! Activity B 5 7 Duration =3 8 10 Activity C 8 11 Duration =4 14 17 Activity D Activity E Activity F 1 6 8 5 Duration =5 1 5 Now you know that activity G can start as late as day 8 of the project (assuming the units are days) - or it could finish as early as day 11.. 13 Duration =8 6 13 Activity G 6 11 Duration =6 8 13 14 Duration =7 11 17 Activity H 14 17 Duration =4 14 17 Wait a minute... I've never had to do this for my projects at work! I've got projects with dozens of activities, and this would take all day! You won't have to do this kind of thing on the job... that's what computers are for! Project management software like Microsoft Project will do these calculations for you. But you need to know how to do it yourself, because when the computer is doing critical path analysis, this is exactly how it figures it out! 264 Chapter 6 Finish time management Q: Would I really use this critical path stuff in real life, or is it just something I need to memorize for the PMP exam? A: Yes, critical path analysis really is important in real life! Sure, for a small project with a dozen or so activities, it's pretty easy to figure out which activities are critical and which can slip by a little bit. But what happens if you've got a project with dozens of team members and hundreds of activities? That's where critical path analysis can come in very handy. For a project like that, you'd probably be using project management software rather than calculating the critical path yourself, and the software will be able to highlight that path for you. Pay special attention to all of the activities that are on the critical paththose are the ones that could potentially delay the project. Q: A: What about the other numbers? How do I use float? Float is a very powerful planning tool that you can use to figure out how well your project is going, and to predict where your trouble spots might be. Any activity with a low or zero float absolutely must come in on time, while the people performing an activity with a larger float have more freedom to slip without delaying the project. So you might want to assign your \"superstar\" resources to the low-float activities, and those people who need a little more mentoring to the ones with higher float. Q: Okay, but what about late start, early finish, and those other numbers? Do those do me any good? Early and late start and finish numbers are also very useful. How many times have you been in a situation where you've been asked, \"If we absolutely had to have this in two months, can we do it?\" Or, \"How late can this project realistically be?\" Now you can use these numbers to give you real answers, with actual evidence to back them up. start. Do you need to find someone to fill in for him? If he'll be back before the late start date, then your project won't be late! But that comes at a cost - you'll have used up the extra slack in the schedule. Q: I can see how the critical path is useful on its own, but what does it have to do with the rest of time management? A: If you start putting together your schedule but the activities are in the wrong order, that's really going to cause serious problems... and sometimes doing critical path analysis is the only way you'll really figure out that you've made that particular mistake. That's why you need to pay a lot of attention to the Activity Sequencing tools and techniques. If you've come up with an inefficient or inaccurate sequence, with too many or incorrect predecessors and dependencies, then your entire critical path analysis will be useless. Here's an example. Let's say you've got an activity in the middle of your project, and one of your team members wants to plan a vacation right at the time that the activity will The critical path is the path that has the longest duration. You should be able to figure out the number of paths in a network diagram, and the duration of each path. The float for an activity is the amount that its duration can slip without causing the project to be delayed. The float for any activity on the critical path is zero. You'll need to know how to calculate the early start, late start, early finish, and late finish for an activity in a network diagram using the forward pass and backward pass. This is the core of critical path analysis. You may see a PDM (or activity-on-node) diagram with special nodes that have extra boxes in the corners for the ES, EF, LF and LS. You may see an ADM (or activity-on-arrow) diagram too, but that's much less common. Don't forget that when two paths intersect, you have to decide which ES or LF value to take for the calculation in the next node. For the forward pass, use the larger value; for the backward pass, use the smaller one. you are here 4 265 Critical Path Can a Network have more than 1 Critical Path? - Yes! 1 3 3 B 2 day 0 1 A 1 day 0 1 1 3 C 2 day 3 1 5 D 4 day 1 5 5 5 5 6 E 1 day 5 6 Critical Path Slack vs. Float - Different names for the same thing - the amount of time a task can be delayed Total Slack (Total Float) - The amount of time a task can be delayed without delaying PROJECT - Calculated from LS-ES = Slack - For this class, assume Slack means Total Slack, unless otherwise specified Free Slack (Free Float) 2 - The amount of time a task can be delayed without delaying another task Critical Path 5 9 E 4 day 1 3 B 2 day 0 1 4 A 1 day D 1 day 1 5 5 10 F 5 day 5 G 4 day 3 H 1 day 4 C 3 day 10 9 11 Critical Path 5 9 E 4 day 1 3 6 B 2 day 0 1 2 4 4 A 1 day 0 5 10 5 D 1 day 1 1 4 C 3 day 1 4 10 F 5 day 5 5 9 G 4 day 4 11 H 1 day 10 5 6 4 10 10 10 11 Critical Path 5 9 E 4 day 1 3 6 B 2 day 0 1 2 Critical Path 4 4 A 1 day 0 10 5 5 D 1 day 1 1 4 C 3 day 1 4 10 F 5 day 5 5 9 G 4 day 4 11 H 1 day 10 5 6 5 10 10 10 11 1 Day Slack 6-5=1 Critical Path 5 E 4 day 1 Day Slack 2-1=1 1 3 6 B 2 day 0 1 2 10 Critical Path 4 4 A 1 day 0 9 5 5 D 1 day 1 1 4 C 3 day 1 4 10 F 5 day 5 5 9 G 4 day 4 11 H 1 day 10 5 6 6 10 10 10 11 1 Day Slack 6-5=1