Linkage Relationships. Lagging Techniques for Scheduling a Network

Project Management Lags and Slack Analysis 59 Linkage Relationships Lagging Techniques for Scheduling a Network Why is this Topic on LAGS Important to the project manager? Finish-to-Start is NOT THE ONLY way to link tasks in a network. A task could start after another task starts A lag just represents a delay in something happening, such as waiting for an order to arrive. Time can be saved by creatively sequencing (linking) tasks. This part will explain lagging relationships and illustrate the above points of importance. Topics we will discuss Four different relationships (linkages) between two tasks. Forward / Backward passes, but including the lags. Expanded understanding of the Critical Path

Project Management Lags and Slack Analysis 60 Lagging Techniques for Scheduling a Network 1. Four Types of Task Relationships The following four types kinds of task linkages represent the various ways that two task activities can be connected or related together in a network schedule. a. Finish-to-Start (FS) very common First task must be finished before next task starts. o Example: FINISH prototype model before STARTing the prototype testing. o Example: FINISH building walls, then START painting the walls. o Example: Place order and wait one week to start receiving/storing in warehouse. This FS shows no lag, i.e., B does NOT WAIT to start after the finish of A. Task B starts IMMEDIATELY after A. Example: Pour concrete (task A), then wait 6 days before installing sub-flooring (task B). This FS shows that task B must WAIT at least 6 days after the finish of A, before Task B can start. Dur = Work Effort = days b. Start-to-Start (SS) quite common Two tasks must start at the same time or one task start later (earlier) than the other. o Example: As soon as the MIS department is ready to begin testing new software, the computer security sub-contractor must also be ready to begin at same time. Security sub-contractor must be ready to START when the software is ready. When the software is ready to START, the sub-contractor must be able to START. o Example: START installing the hardware (task A), then START installing the software (task B) six days later. Task B is WAITING for Task A to start. This SS shows that task B can only start 6 days after task A starts, i.e., the lag makes the START of task B wait. Dur = Work Effort = days On your own after class (answers after two pages) * What is the difference IF the durations WERE A=10 and B=3? This one is moderately difficult. If you successfully figure it out, then congratulations! The duration of the 2-task project would be days. The days of work effort would be days. * * Return to these notes after class and try this one (Finish to Start) Draw a task relationship diagram to represent 1 day to place an order with Amazon and then waiting 3 days to receive the order, and then 3 days to install the video device. The duration of the 2-task project is days. The days of work effort are days.

Project Management Lags and Slack Analysis 61 c. Finish-to-Finish (FF) occurs sometimes Two tasks must finish at the same time or one task finish later (earlier) than the other.. May occur when two tasks must finish simultaneously, but have different task durations. o Example: Advertising sales must FINISH when advertising page layout FINISHES. When page layout is finished and completed, advertising sales must terminate, because there would be no more opportunity or time to incorporate new sales ads. o Example: FINISH installing the software no later than two weeks after FINISHing the installation of the computer hardware. This FF shows that task B cannot finish any earlier than 9 days after the finish of task A. I.e., the finish of B must WAIT at least 9 days after the finish of Task A. d. Start-to-Finish (SF) happens, but not so common Second task must finish at the same time or one task finish later (earlier) than the other. o Example: START training the management on new Windows software, but schedule the employees to FINISH their training as soon as possible one month later. It s not important when the employees start, only that they FINISH at a particular date. They must finish one month later because we have facility rented for only one month. o Example: The scaffolding will be used from the start of the exterior set up to the finish of exterior repairs. The summer Olympics MUST have the closing ceremony (B) of the Swimming Event 14 days after the beginning of the Swimming Event (A). This SF shows that task B cannot finish any earlier than 14 days after the START of task A. I.e., the finish of B must WAIT at least 14 days after the START of Task A. *****On your own after class Return to these notes after class and try this one: This is a START-START (SS) linkage. Draw a task relationship diagram to represent starting the guest list (3 day task) two days after beginning of reserving the reception room (4 day task). Reserving is 1 st, and then starting the guest list is 2 nd. The duration of the 2-task project is days. The days of work effort are days.

Project Management Lags and Slack Analysis 62 ANSWERS These are answers to the previous two pages. Pour the Concrete Hardware then Software * What is the difference IF the durations WERE A=10 and B=3? The duration = _10 days. The work effort = _13_ days. Amazon Order and Waiting -----à -----à -----à This FS shows that task B must WAIT at least 6 days after the finish of A, before Task B can start. Dur = 15 Work Effort = 9 days. Sum of task durations Dur = 11 Work Effort = 9 days. Sum of task Duration = 7 days Work Effort = 4 days ============================================================================ This FF shows that task B cannot finish any earlier than 9 days after the finish of task A. I.e., the finish of B must WAIT at least 9 days after the finish of Task A. Duration = 13 days Work Effort = 9 days This SF shows that task B cannot finish any earlier than 14 days after the START of task A. I.e., the finish of B must WAIT at least 14 days after the START of Task A. Duration = 14, Work Effort = 9 Guest List and Reserving Reception Room The duration is 5 days. The work effort = 7 days.

Project Management Lags and Slack Analysis 63 Lag Start and Finish Time The following discussion explains how lags (delays usually) can affect the relationship of one task to another. It is important to keep track of the kind of linkage you are working with. 1. Forward Pass with Lags a. Forward pass, add lag to early times. Normally ES(F) would be 14. However, Lag forces ES to be 18 (10 + 8) A lag means delayed later into the future. Lag means CANNOT START any earlier than. But is OK to start later than. 10 14 D 4 Lag +8 (10 + 8) 18 21 F 3 2. Backward Pass with Lags b. Backward pass, subtract lag from late times. Only an FF relationship between Task D & F. Lag constrains LF(D) to be 7 time units earlier than LF(F), i.e., 23 7 = 16 10 14 D Lag + 7 (23 7) 4 16 18 21 F 20 3 23 Try this simple lagged project network to get some feeling for lags in the forward and backward passes. Answers at the end of this section 1. What is the Critical Path? 2. How do I interpret these critical paths? Brief Summary for Using Lags: Same rules as performing the FW and BW passes in a network WITHOUT lags Forward and Backward Pass with Lags a. Forward pass, add lag to early times. Use largest value with Merge. b. Backward pass, subtract lag from late times. Use smallest value for Burst.

Project Management Lags and Slack Analysis 64 Forward and Backward Pass (more detailed explanations) Forward Pass Forward Passes in network scheduling always assume: o Start as early as possible policy, BUT o Start no earlier than (date or constraint) when relationships are specified. o Also, OK to start later than the indicated relationship, just CANNOT START any earlier. When performing the forward pass (FP), cover up the bottom squares at the bottom of the task box. o FP only deals with the top squares, i.e., the ES and EF times. o Remember that the highest, latest, or largest value is used going forward. o Meeting cannot start until the last (latest) person arrives. o Notice in the example to the right that the Task F would normally have an ES = 14 Question: So how does a lag affect the forward pass? Answer: Assume we have a new linkage of SS+8 from Task D to Task F. If the lag is positive, such as SS+8, then the successor task (F) would start 8 periods later than the start of its predecessor (ES D =10) or ES(F) = no earlier than 8 periods after ES(D). o Notice in the example to the right, without the lag+8, task F would have a normal start of ES = 14 (because 14 > EF=8 from predecessor. o Notice that EF F = 21 = ES F ( 18) + task duration of 3. Question: If I have two lags, How do I determine the effect on the successor task. Answer: Assume two lags as indicated to the right. o The FS + 10 lag from D (EF=14) means that task F cannot finish any earlier than EF=24. The lag forces F to have a EF at 24 as its earliest possible finish time (EF). 10 14 D o The SS + 8 lag from D (ES=10) means that task F cannot start any earlier than 18. The lag will force F to wait and start (ES) on ES=18. o Notice that 18 + 3 = 21, which is less than the EF(F) = 24. Although it looks like we have six time periods of flexibility to start and finish task F, we really need to know the Late start and finish times before we can conclude how much slack we have in Task F. The duration = 3, so that is fixed. The slack will be six (6) time periods, because of 24 18. This means that you have 3 days of flexibility or slack inside the task. You could schedule the task to start later, but still finish at 24 OR, you could start at 18, pause a few days, but then still finish at 24. 4 EF=8 from predecessor 10 14 D 4 Lag +8 EF=8 from predecessor 10 14 D 4 Lag +8 14 17 F 3 18 21 F 3 Lag +10 (14 + 10) 18 24 F 3

Project Management Lags and Slack Analysis 65 Backward Pass Remember Backward Passes in network scheduling always assume: o Start no later than the time specified. o But it is OK to start earlier than (date or constraint) when relationships are specified. Cover up the top numbers. You only work with the lower values, i.e., LS and LF on the bottom. I drew lines through the top numbers to indicate we do NOT NEED the top numbers for Backward Pass. Question: So how does a lag affect the backward pass? Answer: Assume we have the linkage of SS+8 from D to F as shown at the right. o The LF(D) = 22 because LS(F) is 22 and no lag. o But a SS-relationship constrains D and F. o LS(D) would normally be 19 calculated as 22 3. o But, 19 is NOT the LS for D as would be expected. It is 14. The lag means that LS D started 8 periods earlier than the LS of F (22 value). 11 14 D 14 3 22 19 Lag +8 19 22 F 22 3 25 EF=8 from predecessor Note: LF=25 comes from successor task. Assume correct. So, the late start, LS D is determined from the LS F (22) less the lag of 8 resulting in LS D = 14. The only way F could have a late start (LS) = 22 would be that task D started 8 periods earlier due to the lag +8 forcing F to start late at 22. Question: If there are two lags, How do I determine the Late finish and start values for the predecessor task. Answer: Assume the lags as indicated to the right. o Assume that the LF F = 25. o The FF+10 lag requires that the LF D = 15, i.e., task D finishes 10 periods earlier than F finishes. o Now, how do we determine the LS(D)? 11 14 D 12 3 15 Lag +8 Lag +10 19 24 F 22 3 25 Note: LF=25 comes from successor task. Assume correct. o The SS+8 lag from the ES of Task D means that the LS for D must have started at 14. o I placed a 14 below Task D to represent the backward pass of 22 8. o The normal calculation for LS D would be 15 3 = 12. Going backwards, we use the earliest (smallest value) times for LS D, e.g., the 12 in this case. 15 3 = 12 is earlier (starting sooner) than the 14 from 22 8. The SS + 8 lag simply means that the late start of D could not occur any later than 14, but it could occur earlier, such as in this case at period 12. 14

Project Management Lags and Slack Analysis 66 OK, let s analyze this complex looking set of BURST relationships. o Analyze ONE TASK at a time. o FOLLOW the arrows o Verify the Forward Passes o Verify the Backward Passes Late Finish Assume the lags as indicated to the right. o Tracing back from the LS(24) of Task G, subtract 4 from 24 to get possible LF D value of 20 o Tracing back from the LF(27) of Task F, subtract 10 from 27 to get possible LF D value of 17. o So, we have late finish values of 20 and 17 for task D. o Select the least value (smallest value on backward pass), which would be 17, i.e., LF D = 17. Late Start The LS value of 14 for activity D results from being the least of the possible late start times from the following: o Activity F: 16 calculated as 24 SS lag 8 = 16 connecting to task F. o Activity D: 14 calculated as 17 duration 3 = 14 inside the activity. o Activity C: 15 calculated as 25 SS lag 10 = 15 connecting task C. The late start cannot begin any later than the earliest time (smallest number in backward pass), i.e., 14. Another way to say this is, If you are going to be late, try to still get started as EARLY as possible. Simple summary. Backward passes use the least or lowest values going backward through the network. Use the lowest value from: OR o just a simple non-lagged relationship o if it is a value calculated from subtracting a lag value

Project Management Lags and Slack Analysis 67 Quick Check on your Learning Do the following for this small project: 1. What is the project duration (assume days)? 2. How many days of work effort are people engaging in for this project? Now, assume that this project has been modified to utilize Start-to-Start (SS) relationships 1. What is the project duration (assume days)? 2. How many days of work effort are people engaging in for this project?

Project Management Lags and Slack Analysis 68 In-Class Exercise #1: Lagged Relationships. What is the Critical Path, EF, and slack analysis for this network diagram. In-Class Exercise #2 What is the Critical Path, EF, and slack analysis for this network diagram.

Project Management Lags and Slack Analysis 69 Answers 1. The critical path is A(s,f) - D(s,f) - C(f) - E(s,f). The interpretation of the D C(f) part of the critical path is the following: The finish of C is on the critical path (TS = 0), so Task C CANNOT be late or it will delay the project. If it is late by one day (12), then task E will be forced to start at 12, thus making it be late with a finish at 17, Thus making the project late. It is OK for the start of Task C to start one day later, i.e., LF(C) = 7. So it has total slack, on the start side of one day. IF it is late by more than one day, then the project will be late, because it would force the finish time to be 12, thus forcing task E to be one day later. 2. What is the interpretation of Task C: Task C has one day of slack on the start side. It would be acceptable to start one day late on day 7 instead of the early start on day 6. It would NOT be acceptable to finish late. The Task C must finish perfectly on time at day 11, otherwise the project will be later than day 16. 2. What is the slack analysis for this network diagram? FS(A) = 0 because B and D start immediately after the finish of task A. FS(B) =2 because (EF=5+4=9 which is 2 less than ES(E)=11. The lag is a hard constraint that must be obeyed and means cannot start any earlier than. Hence equivalent to an EF for task B equivalent 9. FS(C)=0 because finish wide of task C has LF-EF=0 and is on critical path. FS(D)=0 because EF(D)=8 + lag 3 means must wait until 11 for task C to finish, i.e., cannot finish any earlier than the FF and also any lags that may be in the FF relationship.

Project Management Lags and Slack Analysis 70 ANSWERS Quick Check on your Learning The network answer is not provided, because you can use the numerical answers to figure out how to do the forward and backward passes in the network. 1. What is the project duration (assume days)? 18 i. TOP path will be 3 + 4 + 7 + 4 = 18 ii. BOTTOM path will be 3 + 3 + 5 + 4 = 15 2. How many days of work effort are people engaging in for this project? 16 Work effort = sum of task durations. Each task duration is days of work. Now, assume that this project has been modified to utilize Start-to-Start (SS) relationships 1. What is the project duration (assume days)? 9 TOP path will be 1 + 3 + 4 = 8 BOTTOM path will be 2 + 3 + 4 = 9 (we must obey the lag constraints) 2. How many days of work effort are people engaging in for this project? 16 Work effort = sum of task durations. Each task duration is days of work. The Work Effort has not changed. It is still the same collection of tasks.

Project Management Lags and Slack Analysis 71 ANSWER to Exercise #1. Lag +4 Lag +4 Lag +3 Lag +3 CP = A(s,f) - D(s,f) - C(f) - E(s,f) - G(f) EF for the project = 19. Slack Analysis. Task A: FS and TS are zero (on critical path with slack = zero for start/finish. Task B: FS = 2 and TS = 2 because next neighbor is critical task. o Why FS=2? Because must wait 4 periods minimum between EF(B) and ES(E), makes it be same AS IF B had EF=9. Hence 11-9 = 2. Task C: FS = 0, and TS = 0 (cannot be late or critical task E will be late. Task D: FS = 0 because both burst paths immediately affect next neighbors. Task E: FS = 0 because lag requires a mandatory waiting for 4 time periods=19. Task F: FS = 0. Task G: FS and TS = zero as it is the last task in the network.

Project Management Lags and Slack Analysis 72 Exercise #2. Slack Analysis. Task A: FS and TS are zero (on critical path with slack = zero for start/finish. Task B: FS and TS are zero (on critical path with slack = zero for start/finish. Although B-D looks like it has 20-15=5 slack, it is the mandatory lag at work here. Task B is a burst activity, hence least Free Slack option. Task C: FS and TS are zero (on critical path with slack = zero for start/finish. ES+lag20=EF(25--finish no earlier than at 25). Task C has NO CONNECTION with START of Task D. Task D: FS = 0 because all three burst paths immediately affect next neighbors (D S - E S /D F - E F /D F - H S ), i.e. the lags leave no flexibility, all the lags are mandatory minimum waiting times. Task E: FS = 0 because the lag =0, hence EF for F would be 50. Task F: FS = 0, because of finish side being critical with slack = zero. Task G: FS and TS are zero (on critical path with slack = zero for start/finish. The lag=10 is part of the path and mandatory delay time that results in G F +10=50. Task H: FS and TS = zero as it is the last task in the network. ========================= Answers to Your Turn ================== Your Turn #1: Draw a task relationship diagram to represent 1 day to place an order with Amazon and then waiting 3 days to receive the order, and then 3 days to install the video device. The duration of the 2-task project is 7 days. The days of work effort are 4 days. Your Turn #2: Draw a task relationship diagram to represent starting the guest list (B=3 days) two days after beginning of reserving the reception room (A=4 days). The duration of the 2-task project is 5 days. The days of work effort are 7 days. Note that we can have Work Effort > Project Duration because the tasks OVERLAP. Lags, Task Duration, Work Effort, and Project Duration

Project Management Lags and Slack Analysis 73 The following terms will be used in analyzing and explaining a network schedule. Each term has a different and distinct meaning for a project manager. Lag Task Duration Work Effort Project Duration Linkage between two tasks. Lags affect the start or finish dates of tasks. They can also affect the duration of a project. However, they DO NOT affect the work effort. This is the amount of work effort associated with a task. It will be measured in days or weeks. In the WBS, task duration (work package, activity) is calculated from estimated hours or labor required to complete a task (work package) objective. This is the time that will be spent on a task, such as hours, days, or weeks. It is what people do, such as make telephone calls, dig a hole in the ground, film a take for a TV commercial, or design some plans for an item to be manufactured. Work effort is associated with verbs, i.e., doing something. This is the amount of time (days or weeks, etc.) required to complete a collection of scheduled tasks (project network schedule, usually shown as a Gantt chart). Lags can affect a project s duration, such as shortening the project with SS lags, or making the project longer with FS or FF lags that stretch the project out into the future (see Nightingale and Zuma for such lags). A project s duration is not directly related to its work effort. Due to lags, the project duration could be longer than the work effort time, or it could be shorter. Assume the following durations are in days: 0 A 4 B 3 What is the lag time? What is the work effort? What is the project duration? Project EF = 0 A 3 FS lag + 8 B 2 What is the lag time? What is the work effort? What is the project duration? Project EF = 0 A 4 FF Lag + 4 B 5 What is the lag time? What is the work effort? What is the project duration? Project EF = 0 A 8 SS Lag + 10 B 3 What is the lag time? What is the work effort? What is the project duration? Project EF = Here is a tricky one. 0 A 8 SS Lag + 3 B 3 What is the lag time? What is the work effort? What is the project duration? Project EF =

Project Management Lags and Slack Analysis 74 ANSWERS What is the lag time? 0 0 A 4 B 3 What is the work effort? 7 da What is the project duration? 7 Project EF = 7 0 A 3 FS lag + 8 B 2 What is the lag time? 8 What is the work effort? 5 What is the project duration? 13 Task A(3) + 8 + Task B(2) = 13 Project EF = 13 0 A 4 FF Lag + 4 What is the lag time? 4 What is the work effort? 9 B 5 What is the project duration? 8_(4+ lag 4) EF (project) =8. End of B = end of the lag of 4. 0 A 8 SS Lag + 10 B 3 What is the lag time? 10 What is the work effort? 11 What is the project duration? 13 Lag + 10 and Task B (3) = 13 NOTICE, Task A = 8. The lag (10) makes Task B start +2 after EF(A). Task A finishes at 8, but the SS lag (10) forces Task B to start 2 periods after Task A finishes. Here is a tricky one. 0 A 8 SS Lag + 3 In this last example, the Task A starts at zero. Task B starts at 3 (because of the lag+3). But Task A is 8 periods, so, although Task A finishes at 8, Task B will finish at 6 (lag 3 + 3 duration). So, the entire project of tasks A and B finishes inside of when Task A finishes, i.e., EF=8. Task A for 8 time periods B 3 Task B is 3 What is the lag time? 3 What is the work effort? 11 What is the project duration? 8 EF is NOT Lag + 3 and Task B (3) = 6 Task A is longer duration than the Lag+Dur(B) EF=8, NOT 6.

Project Management Lags and Slack Analysis 75 Analysis of Slack: Free Slack and Total Slack Slack Free Slack: o Amount of time my task can be late before I make my next neighbor start late. Total Slack o Amount of time my task can be late before I make the project late. Understanding Slack allows you to know o How much you can be late (we all want life to cut us some slack ) o How much flexibility or extra time can (or do) I have? Why is it Important to Understand Slack? Free Slack 1. You are a task leader. a. Things happen. b. You want to know how much you can be late. c. You are concerned about making your next neighbor late (free slack). d. How much can I be late before I make my next neighbor (successor) late? Total Slack 2. You are a project manager. a. You have several task leaders reporting to you. b. They want to know if they can be late. c. You are concerned about making the project late (total slack) d. How much can they be late before it makes the project late?

Project Management Lags and Slack Analysis 76 Analysis of Slack: Free Slack and Total Slack This discussion will focus on the following two topics, all related to slack in a project network schedule. Free slack Total slack We will investigate Total Slack and how it is the sum of the free slack along a path. The discussion will progress in two stages, in which we progressively enlarge the project network to include additional tasks. As we include additional tasks, we will see: how the total slack changes for different tasks (that are off the critical path), and how changes in total slack are due to changes in free slack for specific tasks (off the critical path) 1. Free slack for a task. The amount of flexible time a task can be late or early without affecting its successor task (next neighbor) A task can only have one free slack value. o When the task is a non-burst task activity, then the free slack is simply along that single path to the successor task, i.e., ES(successor) EF(predecessor). o When the task is a burst task, then each path bursting out of the task can have a calculated slack value with the successor. However, the only free slack value for a burst activity would be the smallest value, or the value for which the total slack of the network would be most sensitive (part of point #2 below). 2. Total slack for a task. The amount that a task can be early or late without affecting the finish time of the project. Total slack means the TOTAL FREE SLACK. It is the sum of the free slacks along a path. This will be explained more down below. Total slack calculation: Difference between early and late times for a task, i.e., LS ES or LF EF. o o o When the project EF = project LF, then the total slack will = 0 for all tasks along the critical path. When the project EF > project LF, i.e., TS < 0 for the terminal task, then the total slack along the critical path will be negative, because all CP tasks will have the CP EF > CP LF. This means that either the project should start earlier or somebody (politician or marketing person) should not promise the project so early. When the project EF < project LF, i.e., TS > 0 for the terminal task, then the total slack along the critical path will be positive, because all CP tasks will have the EF (CP) < LF (CP). This means that the project has begun earlier than is necessary with respect to a desired finish date, i.e., the latest time to finish (LF) is later (greater than) the earliest time to finish (EF). Or it means that you can wait to start the project (by as much as the positive total slack). BUT, WHY is the Total Slack a certain value for a task? There are TWO ANSWERS. CALCULATION ANSWER: (Late Early) Total slack is calculated as Late Early times for a task EXPLANATION ANSWER: (sum of the free slacks). Total slack is the sum of the free slack along a particular path. But Notice!! o Total slack for a non-burst task = sum of the current task free slack and including all the succeeding task free slacks along a path up to a CP task. o Total slack for a burst task = least sum of the free slack values along the burst paths, beginning with the current task activity and including all the succeeding tasks along the least path up to a CP task. Test Awareness Note: You will be asked to explain some total slack problems. Be alert to whether the question is asking for an explanation or a calculation of the total slack. Do NOT use the Calculation of Late Early as an EXPLANATION of what Total Slack is all about.

Project Management Lags and Slack Analysis 77 Analysis of Total Slack Using Free Slack Values along Sub-Path Refer to the diagrams and graphics below and the next pages for the slack analysis discussion. Analysis of network ABCDEF: TS(D) = 4. o L E = 16-12 or 13-9 = 4. Not an explanation, just the TASK FORMULA calculation. o FS on path from task D to CP task F = 4, hence TS = 4. Why? Because D is a single task sub-path leading up to a critical task (CP is A-C-F). TS(B) = 2. o Burst Activity ES(D) EF(B) = 0 and ES(E) EF(B) = 0. FS=0 for both burst paths out of Task B. But ALSO Path BDF has TS = 4 = (FS of D=4) + (FS of B=0). Path BEF has TS = 2 = (FS of E=2) + (FS of B=0). FS (E) = 2 (16-14), hence Path BEF has least cumulative FS value and it determines the TS for task B. MS Project result for the project displayed above. **Total slack is the LEAST sum of the sub-path free slacks bursting from a task.

Project Management Lags and Slack Analysis 78 Let s expand the project to include the tasks A L. Notice that additional tasks are added to the sub-path. Notice that the tasks are merge tasks (multiple arrows coming into the tasks). Notice that with the additional merge tasks, the total slack value increases. The TS increases because of the additional FS values along the sub-paths. MS Project results for the project displayed (A-L) Total slack is the LEAST sum of the sub-path free slacks BURSTING from a task.

Project Management Lags and Slack Analysis 79 Free Slack and Total Slack EXERCISE: (on your own) Complete the following diagram with forward and backward passes, and Calculate the Total Slack and Free Slack Values. Legend ES ID EF SL LS DUR LF Use the Free Slack along the sub-path for each task to explain why each total slack calculates the way it does. Task Explanation A TS = 0 because on CP. FS = 0 because on CP. B H E TS = because on sub-path B-F-H-J with respective free slacks of,, TS = because on H-J path and FS(H) =. TS = because on E-H-J path and FS( ) = and FS(H) =. F TS = _0_ because on F-H path and FS( ) = 0. C TS = because on CFHJ path and FS( )=, FS(F) = 0, and F( )=.

Project Management Lags and Slack Analysis 80 ANSWERS Legend ES ID EF Analysis of Task B Slack: A task can only have ONE free slack value Task B is a BURST with two successor paths (B-E and B-F) Which path represents the free slack? o Least slack value (ZERO in this case) o The path value that will get me in trouble the earliest. o Task E will immediately be unhappy if Task B is late SL LS DUR LF Use the Free Slack along the sub-path for each task to explain why each total slack calculates the way it does. Task Explanation A TS = _4_ because on CP. FS = 0 because on CP. B TS = _4_ on sub-path B-F-H-J with respective free slacks of 1, 0, and 3 Note on Total Slack: TS for a BURST Task is the PATH with the sum of the free slacks with the LEAST SUM, which is FOUR. B-E-J = 10 = 0 + 10 B-E-H-J = 8 = 0 + 5 + 3 B-F-H- = 4 = 1 + 0 + 3 This is path with the LEAST SUM H TS = _3_ because on H-J path and FS(H) = 3. E TS = _8_ because on E-H-J path and FS(E) = 5 and FS(H) = 3. F TS = _0_ because on F-H path and FS(F) = 0. C TS = _6_ because on CFHJ path and FS(C)=3, FS(F) = 0, and FS(H)=3.

Project Management Lags and Slack Analysis 81 Independent Class Exercise Your Turn. I have completed the Forward Pass. You complete the backward pass. Determine the Total Slack Determine the Critical Path. Complete ALL the Free Slack Values indicated.

Project Management Lags and Slack Analysis 82 Questions: 1. Which are the critical (and only) Free Slack values for the non-critical path tasks? a. b. c. 2. Why is the TS for Task D2 = 15? This is a rather straightforward question. 3. Why is the TS for Task B = 2, when the FS = 0? This is only a moderately difficult question. 4. Why is the FS=2 between C and E when the TS for Task C is only = 1. This is a higher difficulty question to see at what depth you understand free slack and total slack.

Project Management Lags and Slack Analysis 83 1. The circled FS values are incorrect. Answers FS=2 (C-E). Must be least Free Slack value (C-F) =1 because of 9 8 for the burst activity. FS=3 (F-H). Must be FS(F-I) = Zero because on Critical Path. FS=2 (G-I). Must be least Free Slack value (G-J) = Zero because of 11 11. 2. Why is the TS for Task D2 = 15? This is a rather straight forward question. Simple calculation answer is Late Early = 25 10 = 15. But the explanation is that it is on a path of two free slacks, D2-J (=1) and J-L (=14), hence TS = least sum of FS along the path = 1 + 14 = 15 3. Why is the TS for Task B = 2, when the FS = 0? This is only a moderately difficult question. You cannot answer this with saying that Late Early = 2 because the answer does not address the FS=0 part of the question. Best Answer: TS = 2 because = the least sum of the sub-path free slacks (FS B =0 + FS E =0 + FS H =2 + FS K =0) 4. Why is the FS=2 between C and E when the TS for Task C is only = 1. This is a difficult question to see at what depth you understand free slack and total slack. This is a WRONG understanding to say that Task C has a FS = 2 between C and E. A Task only has ONE free slack value, AND it is the LEAST value bursting out. It is the value that will get you in trouble first with making a successor LATE. Task C does not have a FS value between C-E because of the rule stating Free slack is the least sum of the sub-path free slacks. The TS=1 because of the FS value of +1 between C-F which is the least sum for the sub-paths bursting from task C.

Project Management Lags and Slack Analysis 84 Your turn: Refer to the Diagram above: What are the free slacks for the following tasks? Can you explain WHY? F H K Total Slack for Task F = What are the free slacks for the following tasks? Can you explain WHY? M J L Total Slack for Task J = Explain why the total slack for Task C = 1.

Project Management Lags and Slack Analysis 85 This is a more difficult kind of question to get you thinking about free slack and total slack. Assume that the predecessor for Task H is changed from task C to task A. 1. Explain the changes in free slack and total slack for task D. 2. Explain the changes in free slack and total slack for task C. a. Free slack. (FS = 4) b. Total Slack. (TS = 4) 3. When would task H begin? 4. When would task J begin? 5. What would be the free and total slack for Task H?

Project Management Lags and Slack Analysis 86 1. When does task D start? 2. When does Task H finish? 3. What is the Late Finish (LF) for Task H?

Project Management Lags and Slack Analysis 87 Answer to Slack Exercise What are the free slacks for the following tasks? Can you explain WHY? F 0 ES(H) EF(F) = 12-12 H 1 ES(K) EF(H) = 16-15 K 2 ES(N) EF(K) = 21-19 Total Slack for Task F = 3 Explanation is that the total slack for F is the sum of the free slacks along the sub-path F H K - N What are the free slacks for the following tasks? Can you explain WHY? M 2 ES(N) EF(M) = 21-19 J 0 ES(M) EF(J) = 15-15 L 0 ES(N) EF(L) = 21-21 Total Slack for Task J = 1 Why? Because the sub-path with the least sum is J L N. Explain why the total slack for Task C = 1. Because the least sum sub-path is C D E J L - N = 0 + 0 + 0 + 1 + 0

Project Management Lags and Slack Analysis 88 ANSWER: This is a more difficult kind of question to get you thinking about free slack and total slack. Assume that the predecessor for Task H is changed from task C to task A. 1. Explain the changes in free slack and total slack for task D. Nothing will change for task D. It is not in any sub-path for task H. 2. Explain the changes in free slack and total slack for task C. a. Free slack. (FS = 4) There would no longer be any connection between C and H, limiting the FS = 0. So, the free slack of task C would change to 4 days (end of C, Monday 5 pm to start of Task f, Monday 8 a.m. The free slack days would be Tues, Wed, Thurs, and Fri. b. Total Slack. (TS = 4) Total slack would be the sum of the free slacks along the sub-path to a critical task, i.e., C-F. The free slack is 4 days (see 2.a above) so the total slack would be 4 days, also. 3. When would task H begin? Immediately after the finish of Task A, i.e., Monday, 8 a.m. on August.11, 2006. 4. When would task J begin? At the end of Task H. Duration of task H is 6 days, so end of task H would be Monday, 5 pm, August 18. Beginning of Task J would be Tuesday, 8 a.m., August 19, 2006. Working Back from Task I. Task I starts, 8 a.m., Tues, 9/9. Task H will be pulled back 11 days earlier, so Task J would start 11 days earlier. Task J would begin Tuesday 8 a.m., Aug 19 and finish 3 days later, Thursday 5 p.m., August 21. 5. What would be the new free slack and total slack for Task H? FS(H) would still be ZERO, because J follows immediately after Task H. New FS(J) would be old FS=1 plus the additional extra 11 days = 12 days. TS H = FS H (0) + FS J (12)= 12 days

Project Management Lags and Slack Analysis 89 ANSWERS 1. When does task D start? Monday 8 a.m., August 25. Task D starts when its predecessor, Task B, finishes on Friday 5 p.m., August 22. Alternative Analysis: Task D is a predecessor of Task F. Task F starts on 8 a.m. Monday, September 1. Task D has 3 days duration and 2 days free slack with Task F. Hence must start 5 days earlier, i.e., one week earlier, 8 a.m. Monday, August 25. 2. When does Task H finish? Work backwards from Task I. 1 day free slack (J) occupies Monday, September 8, because (I) starts on Tuesday. 3 day duration of task J occupies Wed, Thurs, Fri (Sept 3, 4, 5) Hence, Task H finishes on 5 pm on Tuesday, September 2 3. What is the Late Finish (LF) for Task H? You already know the early finish (EF) for H. The Late Finish would be EF + TS, i.e., just add the total slack to the early finish. Alternatively, H-J can only move over one day. Hence late finish is only one day later.