\r\nActivity<\/strong><\/td>\r\nDuration (week)<\/strong><\/td>\r\nPredecessors<\/strong><\/td>\r\n<\/tr>\r\n\r\n| A<\/td>\r\n | 1<\/td>\r\n | -<\/td>\r\n<\/tr>\r\n | \r\n| B<\/td>\r\n | 2<\/td>\r\n | -<\/td>\r\n<\/tr>\r\n | \r\n| C<\/td>\r\n | 2<\/td>\r\n | A<\/td>\r\n<\/tr>\r\n | \r\n| D<\/td>\r\n | 4<\/td>\r\n | A<\/td>\r\n<\/tr>\r\n | \r\n| E<\/td>\r\n | 1<\/td>\r\n | B<\/td>\r\n<\/tr>\r\n | \r\n| F<\/td>\r\n | 2<\/td>\r\n | C, D<\/td>\r\n<\/tr>\r\n | \r\n| G<\/td>\r\n | 3<\/td>\r\n | E<\/td>\r\n<\/tr>\r\n | \r\n| H<\/td>\r\n | 1<\/td>\r\n | G<\/td>\r\n<\/tr>\r\n | \r\n| I<\/td>\r\n | 4<\/td>\r\n | G<\/td>\r\n<\/tr>\r\n | \r\n| J<\/td>\r\n | 1<\/td>\r\n | F<\/td>\r\n<\/tr>\r\n | \r\n| K<\/td>\r\n | 3<\/td>\r\n | J, H<\/td>\r\n<\/tr>\r\n | \r\n| L<\/td>\r\n | 4<\/td>\r\n | I<\/td>\r\n<\/tr>\r\n | \r\n| M<\/td>\r\n | 1<\/td>\r\n | K, L<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n \r\n\r\nWe are using rectangular nodes for each activity with labels on them. Different software programs can be utilized to create these nodes. In this exercise, we are using Microsoft Visio. When we click \u201cNew\u201d and search \u201cPERT Chart\u201d on Visio, we can select \u201cPERT Chart\u201d to open a new sheet. PERT stands for \u201cProgram Evaluation Review Technique\u201d. It was developed by Booz-Allen and Hamilton as part of the United States Navy's Polaris missile submarine program. PERT is a method for analyzing the tasks involved in completing a project, especially the time needed to complete each task, the dependencies among tasks, and the minimum time needed to complete the total project. Another method, CPM, the critical path method was developed in a joint venture by DuPont Corporation and Remington Rand Corporation for managing plant maintenance projects. The critical path determines the float, or schedule flexibility, for each activity by calculating the earliest start date, earliest finish date, latest\u00a0start date, and latest finish date for each activity. This will be discussed in detail in the following sections (7.4.3 and 7.4.4). Rather than dealing with both methods separately, project managers use these methods together as they have been treated as a single method over time.\r\n\r\nOn Microsoft Visio, from PERT Chart Shapes, we drag PERT 1 shape (node) to the blank page. Activities are named as tasks here as is the case with Microsoft Project. We can choose the black color to fill and make the text white color for a good contrast. We can copy this shape, and paste it as needed. In our exercise, we have 13 nodes in total.\r\n\r\n[caption id=\"attachment_621\" align=\"aligncenter\" width=\"380\"]![\"An](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.8.jpg\") Figure 7.8: Activity Node with Labels[\/caption]\r\n\r\nAn activity node includes the labels as seen in Figure 7.8.\r\n\r\n \t- Early Start (ES): The earliest time we can start an activity.<\/li>\r\n \t
- Duration: How long it takes to finish all the tasks in an activity. It can be hours, days, weeks, or months.<\/li>\r\n \t
- Early Finish (EF): The earliest time we can finish an activity.<\/li>\r\n \t
- Late Start (LS): The latest time we can start an activity. Some activities may have some flexibilities (slacks or floats) that allow us to have some delay to start without affecting the overall project duration and other activities.<\/li>\r\n \t
- Late Finish (LF): The latest time we can finish an activity. Based on the slacks (floats), we can finish an activity later than its scheduled completion time.<\/li>\r\n \t
- Slack (Float): It is the difference between LS and ES, or between LF and EF. Both subtractions generate the same result.<\/li>\r\n<\/ul>\r\nIn order to connect nodes, we can drag a line connector to the Visio page and connect two activities (Figure 7.9).\r\n\r\nFigure 7.9. Connecting a Predecessor to its Successor (FS dependency)\r\n\r\n[caption id=\"attachment_622\" align=\"aligncenter\" width=\"738\"]
![\"Connecting](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.9.jpg\") Figure 7.9. Connecting a Predecessor to its Successor (FS dependency)<\/strong>[\/caption]\r\n\r\nWe should place each activity node on the diagram by adhering to their precedence relationships with other activities (Table 7.4). After we connect all the nodes, we can type the duration for each activity as can be seen in Figure 7.10. All other parts in the nodes are zero for now. Besides, as all the dependencies are finish-to-start, the arrows (connectors) start from the right side of a predecessor activity and finish on the left side of a successor activity. For instance, when we finish Activity A, we can start both Activity C and Activity D. When we finish both, we can start Activity F.\r\n\r\n[caption id=\"attachment_623\" align=\"aligncenter\" width=\"936\"]![\"Activity](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.10.jpg\") Figure 7.10: Activity Network Diagram with Durations<\/strong>[\/caption]\r\n7.4.3\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Forward Pass:<\/strong><\/h2>\r\nNow, we can start with a forward pass to determine the early start and early finish dates, and on the last activity, the overall time to finish the whole project. It is an additive move through the network from start to finish.\r\n\r\n \t- For two starting activities (A and B), ES is marked zero, which means that it is the very first day of the project (Figure 7.11).<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_624\" align=\"aligncenter\" width=\"142\"]
![\"Computing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.11.jpg\") Figure 7.11: ES and EF times<\/strong>[\/caption]\r\n\r\n \t- We add ES to the duration for each activity to find EF. For A, EF is (0+1) = 1 week, and for B, it is (0+2) = 2 weeks. It means that we can finish A at the end of the first week, and finish B at the end of the second week (Figure 7.11).<\/li>\r\n \t
- Then, we carry the EF time to the nodes immediately succeeding the recently completed nodes (predecessors). C and D inherit 1 (EF) from A, and it becomes ES for both successor activities. For E, we pass 2 (EF for B) to E as the ES time. Then, we add new ES times to the duration of activities to find the EF for new successors (Figure 7.12).<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_625\" align=\"aligncenter\" width=\"379\"]
![\"Computing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.12.jpg\") Figure 7.12: Passing predecessor ES times to successors as EF times<\/strong>[\/caption]\r\n\r\n \t- At a merge point, as is the case when C and D merge at F, we pass the highest EF time of predecessors (C and D) to the successor activity (F) (Figure 7.13). EF time of D becomes ES time for F.<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_626\" align=\"aligncenter\" width=\"514\"]
![\"Passing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.13.jpg\") Figure 7.13: Passing predecessor ES times at merge points<\/strong>[\/caption]\r\n\r\n \t- When the forward pass is done, we can generate all ES and EF times for all the activities. The EF of the last activity (M) gives us the overall duration of the project which is 15 weeks (Figure 7.14).<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_627\" align=\"aligncenter\" width=\"936\"]
![\"Completing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.14.jpg\") Figure 7.14: Completion of the forward pass <\/strong>[\/caption]\r\n7.4.4\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/strong>Backward Pass<\/strong><\/h2>\r\nBefore starting the backward pass process, we should explain the critical path which is the path through the network that results in the latest completion date of the project. If any activity on the critical path is delayed, the completion of the project will be delayed by an equal amount. It is the path with the greatest total duration. Therefore, we can add the amount of time estimated for the duration of each activity to the previous activity to determine which path through the network has the longest total duration. As we will explain below, slack will be zero for all the activities on the critical path.\r\n\r\nAfter we complete the forward pass process for all the activities, we can start backward pass by moving from the last activity to the starting activities. It is a subtractive move through the network from finish to the start. In our exercise, the last activity is M with a one-week duration, an ES of 14 weeks, and an EF of 15 weeks which also indicates the overall duration of the project.\r\n\r\n \t- Late Finish (LF) for the last activity M is passed from EF (15 weeks). Then, we subtract LF from the activity duration to find the Late Start (LS). It is (15-1) = 14 weeks (Figure 7.15).<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_628\" align=\"aligncenter\" width=\"203\"]
![\"Starting](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.15.jpg\") Figure 7.15: Starting backward pass at the last activity<\/strong>[\/caption]\r\n\r\n \t- Now, it is possible to compute slacks for each activity. It is the difference between LS and ES, or between LF and EF. Both calculations will generate the same result. For Activity M, it is (14-14) or (15-15), which is zero. Therefore, there are no slacks for this activity. We don\u2019t have any flexibility for this activity. We cannot have any delays to start the activity or to finish it. The activities where slack is zero are critical.<\/li>\r\n \t
- Then, we carry back the LS time to the nodes immediately preceding the successor node. K and L inherit 14 (LS) from M, and it becomes LF for both predecessor activities. Then, we subtract LF times from the duration of activities to find the LS for these predecessors (Figure 7.16). The slack for L is (10-10) or (14-14), which is zero. Therefore, L is also a critical activity. The slack for K is (11-8) or (14-11), which is 3. It means that we can wait for an additional three weeks to start K because we need to wait until week 14.<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_629\" align=\"aligncenter\" width=\"335\"]
![\"Passing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.16.jpg\") Figure 7.16: Passing LS times to successors as LF times<\/strong>[\/caption]\r\n\r\nFigure 7.16: Passing LS times to successors as LF times\r\n\r\n \t- At a burst point, as is the case when G is followed by two successors, H and I, we pass the lowest LS time of successors (H and I) to the predecessor activity G as its LF time. Therefore, 6 becomes the LF for Activity G (Figure 7.17).<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_630\" align=\"aligncenter\" width=\"341\"]
![\"Passing](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.17.jpg\") Figure 7.17: Passing successor LS times at burst points as LF times<\/strong>[\/caption]\r\n\r\n \t- When the backward pass is done for all the activities, we can generate all LS and LF times as well as slack times for all of them (Figure 7.18). Thus, we can determine the critical path where the total slack is zero.<\/li>\r\n<\/ol>\r\n[caption id=\"attachment_631\" align=\"aligncenter\" width=\"624\"]
![\"Completion](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.18.jpg\") Figure 7.18: Completion of the backward pass<\/strong>[\/caption]\r\n\r\nThe critical path of this project is B \u2013 E \u2013 G \u2013 I \u2013 L \u2013 M. It is also the longest path. We need to start and finish all these six activities on their scheduled time not to cause any delay in the overall project. Non-critical paths are:\r\n\r\n \t- A \u2013 C \u2013 F \u2013 J \u2013 K \u2013 M: 1+2+2+1+3+1=10 weeks<\/li>\r\n \t
- A \u2013 D \u2013 F \u2013 J \u2013 K \u2013 M: 1+4+2+1+3+1=12 weeks<\/li>\r\n \t
- B \u2013 E \u2013 G \u2013 H \u2013 K \u2013 M: 2+1+3+1+3+1=11 weeks<\/li>\r\n<\/ol>\r\nWe should always keep in mind that the WBS is not a schedule, but it is the basis for it. The network diagram is a schedule but is used primarily to identify key scheduling information that ultimately goes into user-friendly schedule formats, such as milestone and Gantt charts. The network diagram provides important information to the project team. It provides information about how the tasks are related, where the risk points are in the schedule, how long it will take as currently planned to finish the project, and when each task needs to begin and end.\r\n\r\nSchedules must be communicated to project stakeholders. Generally speaking, stakeholders want to know when the work will be completed. Once the completion date is determined, it is important to confirm whether this date can meet the expectations of the stakeholders, in particular the project sponsor, and internal or external clients. Once timeline commitments have been made, stakeholders must be kept up to date on any delays that will cause deviation from the agreed-upon schedule.","rendered":"
After we define the activities and estimate their duration, we are ready to create an activity network diagram which is a graphical representation of the logical relationship (i.e., dependencies) among the project activities | | | |
![\"Figure](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.1.jpg\")
Figure 7.1: Activity Networks (either on Arc or Node)<\/strong>[\/caption]\r\n![\"Finish-to-Start](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/02\/Figure-7.2.jpg\")
Figure 7.2: Finish-to-Start<\/strong>[\/caption]\r\n\r\nExamples:\r\n![\"Finish-to-Start](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.3.jpg\")
Figure 7.3: Finish-to-Start with a Lag<\/strong>[\/caption]\r\n\r\nLead<\/strong>\r\n\r\nA lead is the opposite of a lag. A lead is the amount of time a successor activity can be advanced with respect to a predecessor activity[footnote]Project Management Institute. (2017). A guide to the Project Management Body of Knowledge (PMBOK guide) (6th ed.). Project Management Institute.[\/footnote]. In Figure 7.4, Activity B (successor) can start three days before Activity A (predecessor) finishes. For example, in the project, we should elicit the requirements of stakeholders first. Then, we can start designing the product based on the requirements. If we have ten stakeholder groups, and five of them are key stakeholders, we can start the design before we finish all the elicitation.\r\n\r\n[caption id=\"attachment_617\" align=\"aligncenter\" width=\"382\"]![\"Finish-to-Start](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.4.jpg\")
Figure 7.4: Finish-to-Start with a Lead<\/strong>[\/caption]\r\n\r\nFinish-to-Finish (FF) Relationship<\/strong>\r\n\r\nIn this relationship, we cannot finish a successor activity (Activity B) if we don\u2019t finish a predecessor activity (Activity A). Therefore, Activity A must be finished to ensure that we can finish Activity B as well (Figure 7.5). These tasks can be carried out in parallel. It is common to have a lag between the predecessor and successor.\r\n\r\n[caption id=\"attachment_618\" align=\"aligncenter\" width=\"499\"]![\"The](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.5.jpg\")
Figure 7.5: Finish-to-Finish<\/strong>[\/caption]\r\n\r\nExamples:\r\n![\"The](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.6.jpg\")
Figure 7.6: Start-to-Start<\/strong>[\/caption]\r\n\r\nExamples:\r\n![\"A](\"https:\/\/pressbooks.ulib.csuohio.edu\/project-management-navigating-the-complexity\/wp-content\/uploads\/sites\/121\/2022\/03\/Figure-7.7.jpg\")
Figure 7.7: Start-to-Finish<\/strong>[\/caption]\r\n