The Critical Path Method (CPM) is a project planning management method based on mathematical calculations. It is a type of network diagram planning method and is a positive network diagram. The critical path method decomposes the project into multiple independent activities and determines the duration of each activity, and then connects the activities with logical relationships (end-start, end-end, start-start and start-end) to calculate the duration of the project. Construction period, time characteristics of each activity (earliest and latest time, time difference), etc. After loading resources on the activities of the critical path method, the resource requirements and allocation of the project can also be analyzed. The critical path method is the most important analytical tool in modern project management.
The critical path refers to the logical path with the longest delay from input to output in the design. Optimizing the critical path is an effective method to increase the speed of design work. During the optimization design process, the critical path method can be used repeatedly until it is impossible to reduce the critical path delay.
Table of contents
3. Calculation of critical path parameters
3.2 Example questions to deepen and consolidate 1
3.3 Example questions to deepen and consolidate 2
1. List all paths
figure 1
As shown in Figure 1 above, we mark the duration of each activity on the activity, add all the activity durations on each path together, and get the total duration of the four paths respectively, as shown in Figure 2 below:
figure 2
2. Obtain the critical path
image 3
As shown in Figure 3, the total duration of the second path A-B-E-F is 11 days, which is the longest among the paths. This path is the critical path of the project. This path determines the total duration of the project.
The critical path can not only help us judge which path determines the total construction period, but also learn to calculate the critical path parameters and obtain a lot of valuable information.
3. Calculation of critical path parameters
Figure 4
As shown in Figure 4, in the single-code grid diagram, each activity uses a table to represent its parameters:
- Earliest Start Time (ES): If the activity has a predecessor activity, it needs to wait for the predecessor activity to complete before it can start. ES is the earliest possible time for the activity, which depends on the end time of the previous activity.
- Activity duration (DU): Activity duration is the duration required to complete an activity estimated using methods such as analogy tips, expert judgment, and three-point estimation methods.
- Earliest Finish Time (EF): We add the earliest start time (ES) to the activity duration (DU) to get the earliest end time of the activity ( EF = ES + DU).
- Latest Finish Time (LF): If the activity has successor activities and is subject to the total duration, sufficient time must be left for the subsequent activities, then the activity must be completed at a certain point in time , this time point is the latest time it must end.
- Latest Start Time (LS): We subtract the activity duration (DU) from the latest time that must end (LF) to get the latest time that the activity must start< /span>. (LS = LF - DU)
- Total Float (TF): The total float time is the difference between LF and EF, or the difference between LS and ES (TF = LF - EF, TF = LS - ES), the two differences are equal. The total float reflects the total time that the activity can be postponed without affecting the total duration.
3.1 Parameter calculation
Figure 5
As shown in Figure 5 above, we have decomposed the office decoration project into seven activities from A to Q, estimated the duration of each activity, and also understood the prelude activities of each activity.
calculate:
- Step 1: Draw a single-code network diagram based on the dependencies of the preceding activities, as shown in Figure 6 below:
Figure 6
- Step 2: As shown in Figure 6 above, fill in the earliest time that the activity can start. We use the scale value on the timeline to represent it, as shown in Figure 7 below:
Figure 7
Because activity A is the first activity, the start time is the origin 0 on the timeline; activity A lasts for 2 days, so the earliest end time can be the timeline scale 2 (0 + 2).
The predecessor activity of the second activity B is A. Activity A ends at the time of timeline scale 2, so activity B can only start at the earliest time of time axis scale 2. By analogy, from left to right, the earliest start time (ES), activity duration (DU), and earliest end time (EF) of all activities are calculated.
Figure 8
- Step 3: As shown in Figure 8 above, starting from the last activity G, calculate from right to left the latest required end time (LF), the latest required start time (LS) and the total floating time (TF) of the activity. G is the last activity. If the total duration is 10 days, then the latest end time (LF) of activity G is the time axis scale 10. Then subtract the activity duration of 2 days to get the late start time (LS), which is Timeline scale 8.
Because the latest end time LF and the earliest end time EF of activity G are both time axis scale 10, the total floating time TF = LF - EF = 10 - 10 = 0 .
The latest end time (LF) of the predecessor activity E of activity G is determined by the latest start time (LS) of activity G, so the latest end time (LF) of activity E is the timeline scale 8 , get the latest start time of activity E LS = LF - DU = 8 - 1 = 7. By analogy, the latest finish time (LF), latest start time (LS) and total float time (TF) of each activity are calculated from right to left.
- Step 4: Find all activities with a total float time (TF) of 0 and mark them with a red pen. This colored path is the critical path of the project; the white path is the non-critical path.
Drawn as shown in Figure 8, you can see that the total excitement time of activities on the critical path is 0, while the activities on the non-critical path have total float time.
3.2 Example questions to deepen and consolidate 1
What are the characteristics of activities on the critical path?
- A. Activities with float = 0
- B. Activities with float time <= 0
- C. Activities with float time > 0
- D. All of the above are possible
Figure 9
Analysis:A, is the total float time of activities on the critical path necessarily 0? As shown in Figure 8 above, the earliest start time of the activity is determined by the preceding work, and the latest end time is determined by the succeeding work. When we arrange the plan, in order to meet the 5-day construction period required by the previous work C, the earliest time that F can start is the timeline scale 5, plus F requires a 3-day construction period, so the earliest end time (EF) of F is time The axis scale is 8; and we need to leave enough 3 days for the subsequent work G of F, and the total construction period cannot be delayed. The latest start time (LF) of Gr is the time axis scale 7, so the latest end time of F is 7. In this case, the total float of F is -1 (7 - 8 = -1).
The total float time is -1: the total duration of the entire path is 10 days, C takes 5 days, G takes 7 days, then only 2 days are left, and F also takes 3 days, so the less one day is the total float Time -1.
When preparing a project schedule, if the total construction period is fixed, then you will encounter a situation where the total floating time is less than 0, that is, there is not enough time. At this time, the technology of compressing the construction period can be used to solve the problem, such as working overtime and adding people or setting advance amounts for subsequent activities so that subsequent activities can start in advance, with the purpose of completing these activities within a limited time.
Analysis:B, that’s not right either. For example, if the total construction period has a time reserve, the activities on the critical path will have floating time. Then all three items ABC are possible, and the correct answer is D. Then the path with the least total float time should be described as the critical path.
3.3 Example 3.3
The following statement about the "key path" is correct?
- A. The critical path determines the total duration of the project
- B. The critical path takes the longest time
- C. Minimize float time on the critical path
- D. There can only be one critical path for a project
- E. Activities on the critical path have high technical content
- F. Delays in activities may lead to changes in the critical path
- G. The duration of activities on the critical path cannot be compressed
A, correct. The characteristic of the critical path is that the total duration of activities is the longest, and the longest path determines the total duration of the project.
B, correct. The reason is the same as above.
C, correct. 3.2 Conclusion.
D. Error. A project may have more than one critical path. If the total float of multiple paths is 0, then these paths are all critical paths.
E, Error. Activities on the critical path only have no float time or minimal float time, and have nothing to do with technical content. Even if it is a very simple activity that anyone can do, as long as there is no room for it in time, it is on the critical path.
F, correct. If activities on the non-critical path are delayed and the delay time exceeds the total floating time, then this path will delay the total project duration, and this path will become the critical path. As the total construction period becomes longer, the original critical path has floating time and becomes a non-critical path. So, in this case, the critical path of the project has changed.
G, error. The activities on the critical path just don't have time leeway, it doesn't mean they can't be compressed. Generally, when customers or sponsors ask us to compress the project schedule, they want us to compress activities on the critical path.