A method for identifying related activities and recalculating TF based on CPM

Abstract

The invention discloses a method for identifying and recalculating associated activities based on CPM, comprising the following steps: establishing a double-code network diagram of a project; calculating the total floating time of each activity in the project network table and generating a total floating time calculation table; establishing an associated activity identification operation table, listing the TF, PLP and related paths of each activity, finding a non-critical activity A and its associated activities from the associated activity identification operation table, and recording the associated activities in the associated activity set of activity A; establishing a total floating timetable with associated activity annotations, and explicitly indicating all activities in the associated activity set of the non-critical activity in the TF information column of the non-critical activity; when a non-critical activity is delayed, performing TF recalculation on the non-critical activity and the associated activities according to the total floating timetable with associated activity annotations, so as to update the total floating timetable with associated activity annotations.

Description

Technical Field

[0001] The present invention relates to the field of project management, and in particular to a CPM-based associated activity identification and TF recalculation method. Background Art

[0002] Schedule planning is an important task in project management. If there is no plan, the project will be in chaos due to many accidental events. In essence, one of the main purposes of schedule planning is to plan and control the project so that resources are balanced. There are many scheduling analysis methods, such as the critical path method (CPM), the program evaluation and review technique (PERT), etc. CPM assumes that the activity time is certain, while PERT regards the time to complete the activity as a random variable, which is characterized by optimism, pessimism and the most likely estimate of its duration. Since mainstream scheduling software such as Microsoft Project and Omni Plan are designed based on CPM, CPM is still the main method for scheduling analysis. CPM is usually used to provide an overall view of the project, activity duration, sequence and activity criticality. The model contains the priority relationship of activities and defines the path with the longest duration among all possible paths in the project as the critical path. The main output information of the critical path method is the activity time range, key activities and the floating time of activities.

[0003] The successful implementation of CPM requires that each activity has a clearly determined duration. However, in actual situations, this requirement is often difficult to meet because many activities are performed for the first time. Therefore, there is always uncertainty in the duration of activities in network planning. This has led to the development of fuzzy CPM. For example: Changming Hu et al. (2018) proposed an improved fuzzy critical path method, which uses an integrated vector similarity algorithm to solve the fuzzy duration sorting problem, while the improved fuzzy subtraction standard algorithm avoids the negative and infeasible solutions generated in the fuzzy subtraction operation. Liu Dajiang et al. (2021) proposed a new fuzzy node labeling method. This method quickly gives an effective solution to the critical path and total duration of the project from a dynamic perspective, and fully considers the fact that the critical path may change in a fuzzy environment. This method incorporates fuzzy concepts into dynamic thinking, which improves the objectivity and "accuracy" of the analysis.

[0004] These documents provide a wealth of examples for the application of the CPM, but there are few documents that address the dynamic nature of project management and improve the CPM itself. The current forward method + reverse method can only calculate the total float time of a certain activity, but cannot determine whether the total float time of the current activity is shared with other activities. Therefore, when an activity is delayed, planners cannot immediately know which activities will also be affected by the float time. Summary of the invention

[0005] In view of the above-mentioned defects of the prior art, the purpose of the present invention is to provide a CPM-based associated activity identification and TF recalculation method, which can facilitate project managers to recalculate and make decisions when the execution time of certain activities is delayed.

[0006] To achieve the above object, the present invention provides a method for identifying associated activities based on CPM, comprising the following steps:

[0007] Step S1: Establish a project double-code network diagram;

[0008] Step S2: Calculate the total float time TF of each activity according to the project double-code network diagram, and generate a total float time calculation table; each activity in the project contains information: activity sequence number, ES, EF, LS, LF and TF; among which ES represents the earliest start time, EF represents the earliest finish time, LS represents the latest start time, LF represents the latest finish time, and TF represents the total float time;

[0009] Step S3: Establish an associated activity identification operation table, wherein the associated activity identification operation table lists the TF, PLP and related paths of each activity; find the PLP of the activity through the path and path length value of each activity, the PLP of activity B refers to the longest path length value passing through activity B, recorded as PLP(B); TF(A) and TF(B) represent the total floating time of activity A and activity B respectively; from the associated activity identification operation table, determine whether activity A is a non-critical activity according to TF(A) not being zero; find the associated activities of non-critical activity A, and record the activity sequence number of the associated activity in the associated activity set of activity A;

[0010] Step S4: Establish a total float schedule with associated activities marked, the total float schedule with associated activities marked explicitly indicates the values ​​of ES, EF, LS, LF and TF of each activity, and explicitly indicates all activities in its associated activity set in the TF information column of the non-critical activity.

[0011] Furthermore, in step S3, the method of finding the associated activity B of the non-critical activity A includes the following steps:

[0012] Step 301: When both activity A and activity B are non-critical activities, go to step 302, otherwise go to step 308;

[0013] Step 302: Check whether activity A and activity B are connected, if so, go to step 303, if not, go to step 308;

[0014] Step 303: Check whether PLP(B) has passed through activity A. If it has passed through activity A, go to step 304; otherwise, go to step 305;

[0015] Step 304: Record activity B as a fully associated activity of activity A, and end;

[0016] Step 305: Calculate the critical value affecting the float time of activity B, that is, PLP(B)-PLP(A,B), recorded as m0, and go to step 306;

[0017] Step 306: When TF(A)>m 0 , go to step 307, otherwise go to step 308;

[0018] Step 307: Record activity B as a conditionally associated activity of activity A, with a critical value of m 0 , transfer ends;

[0019] Step 308: Determine that activity B is not an associated activity of activity A, and then end.

[0020] Furthermore, in step S4, the TF information column of the non-critical activity is explicitly indicated by marking the TF of the activity in the total float schedule in a superscript manner.

[0021] Furthermore, in step S4, all activities in the associated activity set are explicitly indicated in the TF information column of the non-critical activity, specifically: the activity sequence number of all associated activities and the activity sequence number and critical value m of the conditionally associated activities are marked in the TF information column. 0 .

[0022] Furthermore, in the step S3, the TF, PLP and all paths Pi of the entire project are listed, with TF and PLP occupying one column each and each path occupying one column. Then, the activities are listed in order of the activities on each path to form an associated activity identification operation table. The corresponding cell is filled with the cumulative time spent on completing the corresponding activity on the path, that is, the path length value of the activity on the path; the maximum value is selected from the path length value of the activity and filled into the corresponding cell of the PLP of the activity.

[0023] Furthermore, in the step S3, the associated activities of the non-critical activity A are found, and the activity sequence numbers of the associated activities are recorded in the associated activity set of activity A. Let S be the associated activity set of A, find the column with numbers of activity A from left to right in the associated activity identification operation table, and then find the non-critical activities with numbers in the same column. If the number is unique or the largest in the same row, the activity corresponding to the number is the full associated activity of activity A; if it is not the maximum value, find the column where the maximum value is located, and the grid corresponding to activity A in the column where the maximum value is located has a number, then activity A and activity B are also full associated activities; if the corresponding grid does not have a number, but TF(A)>m 0 , then the activity is A with m 0 A is a conditional associated activity with a critical value, otherwise it is not an associated activity of A; each time an associated activity is found, it is recorded in the S set, and no judgment will be made when a non-critical activity that is already in the S set is encountered later.

[0024] The present invention also proposes a TF recalculation method based on CPM, which adopts the CPM-based associated activity identification method described in any of the above schemes to obtain a total floating schedule with associated activity annotations. When a non-critical activity is delayed, its associated activity set is obtained according to the total floating schedule with associated activity annotations, and TF and critical values ​​of conditionally associated activities are recalculated for the non-critical activity and all activities in its associated activity set to update the total floating schedule with associated activity annotations, including the following steps:

[0025] Step S5: When a non-critical activity is delayed, its associated activity set is obtained according to the total floating schedule with associated activity annotations, and TF recalculation is performed on the non-critical activity and all activities in its associated activity set to update the total floating schedule with associated activity annotations, specifically including:

[0026] Select the non-critical activity A that is delayed, and enter the delay time of non-critical activity A, recorded as m;

[0027] Define PLP'(B), PLP'(A,B), TF'(A), and TF'(B) as the values ​​of the relevant indicators after the extension of activity A;

[0028] When m≤TF(A):

[0029] If activity B is a fully associated activity of activity A, then

[0030]

[0031] If activity B is a conditionally associated activity of activity A, and m≤m0, then TF'(B)=TF(B);

[0032] If activity B is a conditionally associated activity of activity A, and m>m0, then

[0033]

[0034] When m>TF(A) or TF'(B)=0, the critical path changes, and the TF of each project activity is recalculated using the forward and reverse methods;

[0035] Step S6: recalculating the critical value of conditionally associated activities according to the total floating schedule with associated activities marked, specifically including:

[0036] Select the non-critical activity A that is delayed, enter the delay time of non-critical activity A, denoted as m, and activity B is its conditionally associated activity;

[0037] Definition m 0 'It is the new critical value after the extension of activity A;

[0038] When m<m 0 When, m 0 '=m 0 -m;

[0039] When m≥m 0 , activity B becomes a fully associated activity of activity A, and the original critical value is deleted.

[0040] Furthermore, in step S5, the method for updating the total float schedule with associated activities marked is: after the identification is completed, the TF value of the non-critical activity A of the new total float schedule is marked with the value of TF'(B) to indicate the update of related data.

[0041] Furthermore, in step S6, the method for updating the total floating schedule with associated activity annotations is: after the identification is completed, use m 0 The critical values ​​of the conditionally associated activities of non-critical activity A in the new total float schedule are marked with the value of ' to indicate the update of related data.

[0042] The present invention - the method and application of CPM-based related activity identification and TF recalculation, proposes the concept of related activities, and designs a judgment and solution method for finding related activities whose floating time will change accordingly when the current activity is delayed, and marks the results on the floating schedule to provide intuitive reflection. When the completion time of a certain activity in the project changes, the floating schedule marked with related activities can recalculate a new floating schedule more quickly, and the impact on the overall progress of the project can be judged more quickly. The calculation is simple, which is convenient for on-site project managers to recalculate and make decisions. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1It is a schematic diagram of the network diagram of single-code and double-code projects;

[0044] Figure 2 It is an example of a seven-grid network diagram;

[0045] Figure 3 It is the initial project network diagram of a project;

[0046] Figure 4 yes Figure 3 Project network diagram after project adjustment;

[0047] Figure 5 It is a flowchart for identifying project-related activities and calculating float time changes;

[0048] Figure 6 It is a dual-code network diagram for another project. DETAILED DESCRIPTION

[0049] To further illustrate the various embodiments, the present invention provides drawings. These drawings are part of the disclosure of the present invention, which are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, a person of ordinary skill in the art should be able to understand other possible implementations and advantages of the present invention. The components in the figures are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0050] The present invention will now be further described with reference to the accompanying drawings and specific implementation methods.

[0051] The present invention proposes a method for identifying associated activities and recalculating TF based on CPM, proposes the concept of associated activities, and designs a judgment and solution method for finding associated activities whose floating time will change accordingly when the current activity is delayed, and marks the result on the floating schedule to provide intuitive reflection. When the completion time of a certain activity in the project changes, the floating schedule marked with associated activities can be used to recalculate a new floating schedule more quickly, and the impact on the overall progress of the project can be judged more quickly. The calculation is simple, which is convenient for on-site project managers to recalculate and make decisions.

[0052] First, briefly explain the terms involved in the embodiment.

[0053] 1. Project Network Planning. Project network diagrams are divided into single-code network diagrams and double-code network diagrams. In single-code network diagrams, nodes represent project activities, and arrows only represent the order of activities. In double-code network diagrams, the nodes at both ends of the arrows represent the start and end of activities, and the arrows represent activities. Figure 1 In this embodiment, a double-code network diagram is used.

[0054] 2. Seven-grid project network diagram - an improved network diagram that includes 7 types of information about activities, such as Figure 2 As shown. The activity nodes in the seven-grid diagram include: activity identifier, ES, EF, LS, LS, LF, DU, where ES represents the earliest start time, EF represents the earliest finish time, LS represents the latest start time, LF represents the latest finish time, DU represents the activity duration, and TF represents the total float time. However, the seven-grid diagram still cannot determine the total float time correlation of each activity.

[0055] 3. Critical path - Among all the paths from the starting node to the end node in the network diagram, the path with the longest duration is called the critical path. According to whether the activities are on the critical path, they can be divided into activities on the critical path, i.e., critical activities, and activities not on the critical path, i.e., non-critical activities. According to whether the activities are connected, they can be divided into two activities that are interconnected and two activities that are not interconnected.

[0056] 4. Total float time - refers to the time that activities on the path can be postponed without delaying the project completion date. The total float time is obtained by subtracting the earliest start time from the latest start time of the activity, and is expressed by the formula TF = LS-ES. It is for the entire path. The total float time of all activities on the critical path is equal to zero, and the total float time of non-critical path activities is the time difference between the critical path and the non-critical path. In the same path, the total float time of each activity is the same, and the total float time is shared.

[0057] 5. Free float time - refers to the time that an activity can be postponed without affecting the earliest start date of all subsequent activities. The formula is: FF = the minimum ES of the subsequent activity - the EF of the current activity. When the network path converges, some of the predecessor activities of the convergent activity may have free time difference.

[0058] 6. Sharedness of total float time - For two non-critical activities A and B, when A is postponed, the total float time of B will become smaller. The total float time of A and B is said to be shared.

[0059] 7. Associated activities - The delay of non-critical activity A will affect the float time of another non-critical activity B. Activity B is called an associated activity of activity A.

[0060] 8. Fully dependent activities – For two non-critical activities A and B, when activity A is delayed, the total float time of activity B is reduced by the same amount of time. B is called a fully dependent activity of A.

[0061] 9. Conditionally associated activities - For two non-critical activities A and B, when the delay of activity A is less than or equal to the value m0, the total float time of activity B remains unchanged. Only when the delay is greater than a certain value, the total float time of activity B will decrease. The two are called conditionally associated activities.

[0062] Example 1

[0063] The initial project network diagram of a project is as follows Figure 3 As shown in Figure 1, the critical path is ACH. If activity B is postponed for 1 day, the adjusted network diagram is Figure 4 The time unit is day.

[0064] It can be seen that activity B is delayed by 1 day within its total float time, and the total project duration does not change. Not only does its own total float time decrease by 1 day, but the total float time of activities D, E, and F is also reduced by 1 day. From the definition of fully-associated activities, it can be seen that activity B and D, E, and F are all fully-associated activities.

[0065] If activity D is delayed by 1 day, the total float time of activity F remains unchanged; when activity D is delayed by 3 days, the total float time of activity F decreases by 1 day. From the definition of conditionally associated activities, it can be seen that activities D and F are conditionally associated activities. Because activity E, which is parallel to D, is 2 days longer than D, D has 2 days of free float time. The duration change of D within 2 days of free float time will not affect other activities.

[0066] From the above two examples, it can be seen that the total float time of an activity is shared with other activities in the path where the activity is located.

[0067] However, the relationship between activities cannot be explicitly shown through a network diagram.

[0068] Assume that activity B is an associated activity of activity A. When activity A is delayed by m days, the following impact will occur on activity B:

[0069] 1. Calculate the critical value of the total float time that affects activity B, denoted as m0, where m0 = PLB(B)-PLB(A,B); when m0 is equal to zero, it means that activity B is a fully dependent activity of activity A; when m0 is greater than zero, it means that activity B is a conditionally dependent activity of activity A;

[0070] 2. When activity B is a fully associated activity of activity A, then

[0071]

[0072] 3. When activity B is a conditionally associated activity of activity A and m≤m0, then TF'(B)=TF(B);

[0073] When activity B is a conditionally associated activity of activity A, and m>m0, then

[0074]

[0075] 4. When TF'(B) = 0, the critical path changes, and the TF of each project activity is recalculated using the forward and reverse methods.

[0076] In order to identify the correlation between any two activities (activity A and activity B) in the project network and calculate the impact of the previous activity A on the subsequent activity B, that is, to perform TF recalculation, the following process is given, as follows: Figure 5 shown.

[0077] First, identify related activities, including:

[0078] Step 1: Start by inputting the delay m of activity A and evaluating the impact of delay m on another activity B in the project network table;

[0079] Step 2: When both activity A and activity B are non-critical activities, go to step 3, otherwise go to step 16;

[0080] Step 3: Check whether activity A and activity B are connected. If so, go to step 4. If not, go to step 16.

[0081] Step 4: Check whether PLP(B) passes through activity A. If it does, go to step 5, otherwise go to step 6;

[0082] Step 5: Record activity B as the fully associated activity of activity A, end the associated activity identification, and go to step 7;

[0083] Step 6: Calculate the critical value that affects the float time of activity B, that is, PLP(B)-PLP(A,B), denoted as m 0 , go to step 8;

[0084] Step 8: When TF(A)>m 0 , go to step 9; otherwise go to step 16;

[0085] Step 9: Activity B is recorded as a conditionally associated activity of activity A, and the critical value is m 0 , end the associated activity identification and go to step 11;

[0086] Step 16: Determine that activity B is not an associated activity of activity A, go to step 18, and end.

[0087] The above steps complete the identification of the associated activities of activity A. The identified associated activity B can be recorded in the associated activity set of activity A, and the information of the associated activity set can be marked in the row of activity A in the total float schedule.

[0088] Then the TF recalculation process is performed to recalculate the TF of activity B in the associated activity set:

[0089] Step 7 (continued from step 5, activity B is the fully associated activity of activity A): when TF(A)≥m, go to step 10, otherwise go to step 15;

[0090] Step 10: TF'(B) = TF(B) - m, go to step 18;

[0091] Step 11 (continued from step 9, activity B is a conditionally associated activity of activity A): compare TF(A) and m. When TF(A)>m, go to step 12, otherwise go to step 15;

[0092] Step 12: Compare m and m 0 , when m>m 0 When , go to step 14, otherwise go to step 13;

[0093] Step 13: TF'(B) = TF(B), go to step 18;

[0094] Step 14: Compare TF(B) and mm 0 When TF(B)≥mm 0 When , go to step 17, otherwise go to step 15;

[0095] Step 15: The critical path changes. Recalculate the TF of each activity using the forward and backward methods, and go to step 18;

[0096] Step 17: TF'(B) = TF(B) - (mm 0 ), go to step 18;

[0097] Step 18: End.

[0098] After the associated activity identification and TF recalculation process is completed, the recalculated TF'(B) is updated to the total float schedule. The updated information can be highlighted in bold, underline, italics, different colors, etc. when the chart is displayed for easy identification.

[0099] Example 2

[0100] In order to explicitly represent the associated activities in the project network diagram, this embodiment provides a CPM-based association identification and TF recalculation method, including the following steps:

[0101] Step 1: Create a dual-code network diagram for the project. Figure 6It is a double-code network diagram of a certain project. Taking this network diagram as an example, the forward and reverse methods, as well as the related activity identification and TF recalculation methods are used. According to the complete process in the algorithm design, a certain activity in the project is postponed, and the impact on the total float time of other activities is analyzed.

[0102] Step 2: Calculate the total float time TF of each activity. First, use the forward and backward methods to calculate that the key activities of the project are B, F, I, K, N, and O, and the critical path length is 28. The total float time of each activity in the project is calculated as shown in Table 1.

[0103] Table 1 Traditional total float time calculation table

[0104]

[0105]

[0106] Step 3: Create a table for identifying related activities. Figure 6 , list all the paths Pi of the entire project, with each path occupying one column, and then list the activities in the order of each path activity to form an associated activity identification operation table, and fill in the corresponding cell with the cumulative time spent on completing the corresponding activity on the path, as shown in Table 2. In the table, PLP(X) refers to the longest path length value (Previous Longest Path, PLP) passing through activity X, that is, the largest number in the row (excluding TF value).

[0107] Table 2 Related activity recognition operation table

[0108]

[0109]

[0110] Step 4: Determine whether it is a non-critical activity. Start from the first row in the order of Table 2. If TF is 0, it is a critical activity, and the associated activity of this activity does not exist. Go to the next row to continue the determination; if TF is not 0, it is a non-critical activity, and go to step 5.

[0111] Step 5: Find the associated activities of non-critical activities. Taking activity A as an example, the specific search ideas are as follows: Let S be the set of associated activities of activity A. In the calculation table, find the column with numbers in activity A from left to right, and then find the non-critical activities with numbers in the same column. If the number is unique or the largest in the same row, the activity corresponding to the number is the fully associated activity of activity A. If it is not the maximum value, find the column with the maximum value. If the grid corresponding to activity A in the column with the maximum value has a number, then activity A and activity B are also fully associated activities. If there is no number in the corresponding grid, but TF(A)>m 0, then the activity is activity A with m 0 A is a conditional associated activity with a critical value, otherwise it is not an associated activity of A; each time an associated activity is found, it is recorded in the S set, and no judgment will be made when a non-critical activity that is already in the S set is encountered later.

[0112] According to the above ideas, the cells with numbers for activity A in Table 2 correspond to paths P1-P4. Then, starting from path p1, the cells with numbers on path p1 and whose TFs are not equal to 0 correspond to activities C, G, and L. Therefore, they are all non-critical activities connected to activity A. Then, check horizontally to see if the number is the only or largest number in the row. The number in the row where activity C is located is unique, which means that activity C has a unique path and has no other immediate predecessor activities. Therefore, it is affected by the delay of activity A and is a fully associated activity of activity A. Then, activity C is marked as a superscript on the shared float time of activity A in Table 3. The same is true for activity G and activity C. Activity L is a non-critical activity and is connected to activity A, but the largest number in the row is 22, and the difference with 18 is greater than the TF of activity A, which means that activity L has other immediate predecessor activities that will be completed later. Therefore, the delay of activity A in the float time will not affect activity L, so activity L is not an associated activity of activity A. Activity D in path p2 is a non-critical activity connected to activity A, and 4 is the maximum value in this row, so it is a fully associated activity of activity A. D is marked after activity C in Table 3 as the floating time superscript of activity A; activity H is a non-critical activity and connected to activity A. The maximum number in this row is 15, and the difference with 12 is not greater than the TF of activity A, so it is not affected by activity A; the same is true for activity L. Activity D in path p3 is already an associated activity of activity A and does not need to be considered. Activity I is a critical activity and does not need to be considered. Activity M is the same as activity H and is not affected by activity A. Activity D in path P4 is already an associated activity of activity A, and the others are all critical activities. In summary, the delay of activity A will affect activities C, D, and G.

[0113] Taking activity G as an example, only the row corresponding to G on the P1 path has a number. The only non-critical activity with a number after activity G on the P1 path is activity L.

[0114] PLP(G,L)+TF(G)=18+10=28>PLP(L)=22, so L is a conditionally associated activity of G,

[0115] m 0 =PLP(L)-PLP(G,L)=22-18=4. In Table 3, the total floating time of activity G is marked in superscript form as L(4).

[0116] Next, let's look at activity H. The columns corresponding to the cells with numbers in the row where activity H is located are P2 and P5. Let's look at P2 first. The only non-critical activity with numbers after activity H on the P2 path is activity L. PLP(H,L)+TF(H)=19+6=25>PLP(L)=22, but the path corresponding to PLP(L) is P5, and activity H also has numbers in this column, which means that PLP(L) comes from activity H. Therefore, activity L is a fully associated activity of activity H, not a conditionally associated activity.

[0117] Step 6: Determine whether there are any rows in Table 2 that have not been considered. If so, go to the next row and go to step 3; if not, end.

[0118] It should be noted that in the judgment process, we only need to consider which subsequent activities will be affected after the activity is postponed, that is, the activities below the activity in Table 2. Each fully associated activity is marked as a superscript of the corresponding activity TF, and the critical value is marked in brackets after the associated activity for conditional association. Finally, the total floating schedule with associated activities is obtained. The calculation results of this case are shown in Table 3. This table can explicitly indicate the association of activities, which is convenient for on-site project managers to recalculate and make decisions.

[0119] Table 3 Total float schedule with associated activities marked

[0120]

[0121]

[0122] From the TF column in the total float schedule with associated activities marked, we can see that: Activity A has associated activities C, D, and G, with a total float time of 3 days; Activity C has fully associated activity G and conditionally associated activity L, with a total float time of 10 days and a free float time of 4 days; Activity E has associated activity J, with a total float time of 10 days; Activity G has a conditionally associated activity L, with a critical value of 4 days.

[0123] It can be seen that the total float schedule with associated activity annotations can explicitly indicate the relevance of activities, making it easier for on-site project managers to recalculate and make decisions.

[0124] Example 3

[0125] In order to explicitly represent the impact of the association between activities in the project network diagram on the total construction period, this embodiment delays the TF of activity A, recalculates the TF of the associated activity identification method, and analyzes and explores the impact of its fully associated activities and conditionally associated activities on the total construction period.

[0126] Assume that in the above project (such as Figure 6(As shown in the figure, Activity A is delayed by 2 days, and Activity D is also delayed by 2 days. According to the traditional CPM method, both are within the total float time, and it is generally believed that there will be no impact on the total duration. However, in fact, the correlation between the activities has an impact on the total duration.

[0127] Step 1: Assuming that activity A in the project is delayed, recalculate the total float time of each activity according to the associated activities method designed in this manual.

[0128] From Table 3 in Example 2, we know that A has three fully associated activities C, D, and G. If A is postponed for 2 days, according to the definition of fully associated activities, the total floating time of all its associated activities must be reduced by 2 days, and the TFs of activities C, D, and G become 8, 1, and 8 respectively. At the same time, the critical value of the conditionally associated activity L of activities C and G is also reduced by 2 days, as shown below:

[0129] Take activities A, C, and L as an example: if activity A is postponed for m days, then the length of all paths passing through activity A will increase by m; and activity C is a fully associated activity of activity A, so there is a path from activity A to activity C, and activity L is a conditionally associated activity of activity C, so there is a path from activity C to activity L, and there is a path between activities A, C, and L. Therefore, if activity A is postponed for m days, PLP(C, L) will also increase by m days, that is, PLP'(C, L) = PLP(C, L) + m. On the other hand, activity L is a conditionally associated activity of activity C, so PLP(L) does not pass through activity C, and activity L is not an associated activity of activity A, so PLP(L) does not pass through activity A, so the postponement of activity A will not cause a change in PLP(L), that is, PLP'(L) = PLP(L). Therefore, the new critical value m 0 '=PLP'(L)-PLP'(C,L)=PLP(L)-[PLP(C,L)+m]=m 0 -m, that is, if activity A is postponed for m days, the critical value of the conditionally associated activity of all its associated activities will also be reduced by m accordingly. Substituting the relevant values, the critical value of the conditionally associated activity L of activities C and G changes from 4 to 2.

[0130] Step 2: Use the total float time calculation results of related activities after A is postponed to establish a new total float schedule, as shown in Table 4.

[0131] Table 4 Calculation of total float schedule based on associated activity annotations

[0132] Activity ES EF LS LF TF A 0 5 1 6 <![CDATA[1 CDG ]]> B 0 4 0 4 0 C 5 7 13 15 <![CDATA[8 GL(2) ]]> D 5 6 6 7 1 E 4 9 14 19 <![CDATA[10 J ]]> F 4 7 4 7 0 G 7 13 15 21 <![CDATA[8 L(2) ]]> H 7 15 13 21 <![CDATA[6 L ]]> I 7 11 7 11 0 J 9 11 19 21 10 K 11 21 11 21 0 L 15 22 21 28 6 M 11 15 18 22 7 N 21 22 21 22 0 O 22 28 22 28 0

[0133] Step 3: Assume that another activity D in the project is delayed and determine the changes in the project's critical path.

[0134] If activity D is delayed for another 2 days, the new float time of activity D will exceed 1 day, which will affect the completion time of the entire project. After recalculation, the critical path becomes ADIKNO.

[0135] Step 4: Assuming that a non-critical activity in the project is delayed, discuss the critical value change of the total float time of its conditionally associated activity Y.

[0136] If a non-critical activity X is delayed by m days, the change in the total float time of its conditionally associated activity Y needs to be discussed in terms of the change in the critical value, which is calculated as follows:

[0137] When m≤m 0 TF'(Y) = TF(Y);

[0138] When m>m 0 hour,

[0139] The specific discussion can be divided into the following two situations:

[0140] When m≤m 0 When TF'(Y) = TF(Y), the total float time of activity Y remains unchanged, and PLP(Y) remains unchanged, that is, PLP'(Y) = PLP(Y), but PLP'(X,Y) = PLP(X,Y) + m, then the new critical value m 0 '=PLP'(Y)-PLP'(X,Y)=PLP(Y)-PLP(X,Y)-m=m 0 -m, that is, the critical value of the associated activity Y is reduced by m days.

[0141] When m>m 0 When TF'(Y)=TF(Y)-(mm 0 ), indicating that the change in activity X has caused PLP(Y) to increase by mm 0 units, the free float time of X has been consumed. If activity X is postponed for another m 1 days, the total float time of activity Y will be reduced by m 1 day, so at this time, activity Y is a fully associated activity of activity X.

[0142] Based on the above derivation, we now assume that activity C in Table 4 is delayed by 1 day, then the total float time of activity C is marked as 7 GL(1) , causing the total floating time stamp of all associated activities G to change to 7 GL(1) , because the extension time is less than the critical value of the conditionally associated activity L, the total float time of activity L remains unchanged. If activity C in Table 4 is extended by 3 days, the activities that cause the total float time mark to change are C, G, and L, which become 5 GL , 5 L、5.

[0143] It can be seen that the TF recalculation method designed based on the associated activity identification method in this specification is convenient for project managers to identify the impact of a certain activity on the total construction period and other activities in the project, and can reasonably allocate resources and shorten the total construction period of the project.

[0144] Although the present invention has been specifically shown and described in conjunction with the preferred embodiments, it should be understood by those skilled in the art that various changes may be made to the present invention in form and details without departing from the spirit and scope of the present invention as defined by the appended claims, all of which are within the scope of protection of the present invention.

Claims

1. A method for identifying associated activities based on CPM, characterized in that: The following steps are involved: Step S1: Establish a double-code network diagram for the project; when establishing the network diagram, mark each activity as the activity serial number in the order of occurrence, so as to ensure that in the same path, the serial number corresponding to the activity that occurs first is in the first order; Step S2: Calculate the total float time TF of each activity in the project network diagram and generate a total float time calculation table; each activity in the project contains information: activity sequence number, ES, EF, LS, LF and TF; where ES represents the earliest start time, EF represents the earliest finish time, LS represents the latest start time, LF represents the latest finish time, and TF represents the total float time; Step S3: Establish an associated activity identification operation table, wherein the associated activity identification operation table lists the TF, PLP and related paths of each activity; find the PLP of the activity through the paths and path length values ​​of each activity, and the PLP of activity B refers to the longest path length value passing through activity B, which is recorded as PLP(B); TF(A) and TF(B) represent the total floating time of activity A and activity B respectively; from the associated activity identification operation table, determine whether activity A is a non-critical activity according to TF(A) not being zero; find the associated activity B of non-critical activity A, and record the activity sequence number of the associated activity in the associated activity set of activity A; Step S4: establishing a total float schedule with associated activity annotations, wherein the total float schedule with associated activity annotations explicitly indicates the values ​​of ES, EF, LS, LF and TF of each activity, and explicitly indicates all activities in its associated activity set in the TF information column of the non-critical activity; In step S3, the method for finding the associated activity B of the non-critical activity A includes the following steps: Step 301: When both activity A and activity B are non-critical activities, go to step 302, otherwise go to step 308; Step 302: Check whether activity A and activity B are connected, if so, go to step 303, if not, go to step 308; Step 303: Check whether PLP(B) has passed through activity A. If it has passed through activity A, go to step 304; otherwise, go to step 305; Step 304: Record activity B as a fully associated activity of activity A, and end; Step 305: Calculate the critical value affecting the float time of activity B, that is, PLP(B)-PLP(A,B), recorded as m0, and go to step 306; Step 306: When TF(A)>m0, go to step 307, otherwise go to step 308; Step 307: record activity B as a conditionally associated activity of activity A, with a critical value of m0, and then end; Step 308: Determine that activity B is not an associated activity of activity A, and then end; In step S3, the TF, PLP and all paths Pi of the entire project are listed, with TF and PLP occupying one column each and each path occupying one column. Then, the activities are listed in order of the activities on each path to form an associated activity identification operation table. The corresponding cell is filled with the accumulated time spent on completing the corresponding activity on the path, that is, the path length value of the activity on the path; the maximum value is selected from the path length values ​​of the activity and filled into the corresponding cell of the PLP of the activity; In the step S3, the method of finding the associated activities of the non-critical activity A and recording the activity serial number of the associated activity in the associated activity set of activity A is as follows: let S be the associated activity set of A, find the column with numbers of activity A from left to right in the associated activity identification operation table, and then find the non-critical activity with numbers in the same column. If the number is unique or the largest in the same row, the activity corresponding to the number is the full associated activity of activity A; if it is not the maximum value, find the column where the maximum value is located, and the grid corresponding to activity A in the column where the maximum value is located has a number, then activity A and activity B are also full associated activities; if the corresponding grid has no number, but TF(A)>m0, then the activity is a conditionally associated activity of A with m0 as the critical value, otherwise it is not an associated activity of activity A; each time an associated activity is found, it is recorded in the S set, and no judgment is made when the non-critical activities that are already in the S set are encountered later.

2. The method for identifying associated activities based on CPM as claimed in claim 1, characterized in that: In step S4, the TF information column of the non-critical activity is explicitly indicated in the total float schedule in the form of a superscript of the activity TF.

3. The method for identifying associated activities based on CPM as claimed in claim 1, characterized in that: In step S4, all activities in the associated activity set are explicitly indicated in the TF information column of the non-critical activity, specifically: the activity sequence numbers of all associated activities and the activity sequence numbers of conditionally associated activities and the critical value m0 are marked in the TF information column.

4. A TF recalculation method based on CPM, characterized by: The method for identifying associated activities based on CPM according to any one of claims 1 to 3 is adopted to obtain a total floating schedule with associated activity annotations. When a non-critical activity is delayed, its associated activity set is obtained according to the total floating schedule with associated activity annotations, and TF and critical values ​​of conditionally associated activities are recalculated for the non-critical activity and all activities in its associated activity set to update the total floating schedule with associated activity annotations, including the following steps: Step S5: When a non-critical activity is delayed, its associated activity set is obtained according to the total floating schedule with associated activity annotations, and TF recalculation is performed on the non-critical activity and all activities in its associated activity set to update the total floating schedule with associated activity annotations, specifically including: Select the non-critical activity A that is delayed, and enter the delay time of non-critical activity A, recorded as m; Define PLP'(B), PLP'(A,B), TF'(A), and TF'(B) as the values ​​of the relevant indicators after the extension of activity A; When m≤TF(A): If activity B is a fully associated activity of activity A, then If activity B is a conditionally associated activity of activity A, and m≤m0, then TF'(B)=TF(B); If activity B is a conditional associated activity of activity A and m > m0, then When m > TF(A) or TF'(B) = 0, the critical path changes, and the TF of each activity in the project is recalculated using the forward and backward pass methods; Step S6: When a non-critical activity is delayed, obtain its associated activity set according to the total float time table marked with associated activities, and recalculate the conditional associated activity threshold of the non-critical activity to update the total float time table marked with associated activities, specifically including: Select the non-critical activity A that has been delayed, input the delay time of the non-critical activity A, denoted as m, and activity B is its conditional associated activity; Define m0' as the new threshold after activity A is postponed; When m < m0, m0' = m0 - m; When m ≥ m0, activity B becomes a fully associated activity of activity A, and the original threshold is deleted.

5. The TF recalculation method based on CPM as claimed in claim 4, characterized in that: In step S5, the method for updating the total float time table marked with associated activities is: after the identification is completed, use the value of TF'(B) to mark the TF value of the non-critical activity A in the new total float time table to identify the update of relevant data.

6. The TF recalculation method based on CPM as claimed in claim 4, characterized in that: In step S6, the method for updating the total float time table marked with associated activities is: after the identification is completed, use the value of m0' to mark the conditional associated activity threshold of the non-critical activity A in the new total float time table to identify the update of relevant data.

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