Network model. Methodology for drawing up network diagrams

Example 1. The project includes the following works, presented in the table. Build a network schedule for the implementation of a set of works.

Solution. Works a 1 and a 2 is not preceded by any work, therefore, on the graph they are depicted by arcs emerging from the initial event (1), which means the moment the project starts. Work a 3 preceded by work a 1, so on the graph the arc a 3 immediately follows the arc a 1 . Event (2) means the moment of the end of work a 1 and the beginning of the work that it precedes. Work a 4 precede works a 1 and a 2. This dependence is reflected in the graph by introducing fictitious work (2, 3). The moment of the event (3) will be the moment at which the work will be performed a 1 and a 2 and work can begin a 4 . Similarly, taking into account the relationships, all other works are depicted on the graph. The final event (6) means the moment of completion of the entire project.

The rules used when building a network diagram.

1) there should be no dead ends in network diagrams; events from which no work exits (except for the ending event);

2) there should be no events in the network schedules (except for outgoing events) that are not preceded by at least one job;

3) when building network diagrams it should not be allowed that two adjacent events are connected by two or a large number the number of works, which is most often the case when depicting parallel work. This error leads to confusion due to the fact that two various works will have the same designation. To avoid this, it is advised to introduce additional events and link it to a subsequent dependency or dummy work;

4) there should be no closed loops in the network, i.e. chains connecting some events with themselves;

5) in addition, if any complex work can be started before the complete completion of the immediately preceding work, the latter is depicted as a series of sequentially performed work, each of which ends with a certain event.

6) if for the performance of one of the works it is necessary to obtain the results of all the works included in the event preceding it, and for another work it is enough to obtain the result of only one or several of these works, then a new event must be additionally introduced, as well as a fictitious work connecting new event from the previous one.

A timeline drawn in compliance with these rules is a network model of project execution. At the same time, private network diagrams are usually drawn up first, covering work on individual, having independent meaning parts of the general complex of works, and then by "stitching" a complex (summary) schedule is obtained, covering the entire set of works to be performed.

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Network diagrams must be built in compliance with the following basic rules:

1. The direction of the arrows during construction is taken from left to right, the shape of the graph should be simple, without unnecessary intersections. It is not allowed to repeat the event numbers.

2. When performing parallel jobs, if one event serves as the initial or final event of two or more jobs, additional arcs are introduced that do not correspond to any jobs of the complex. Additional arcs are depicted by dashed lines (Fig. 28). Work, waiting, and dependency must have their own cipher in the form of their start and end event numbers.

Rice. 28. Networking parallel jobs:

a - incorrect; b - correct

3. If the work is divided into a number of sections (seizures), then it can be represented as the sum of sequentially performed works (Fig. 29).

Rice. 29. The image on the network diagram of works, divided into sections (captures)

4. If any two jobs C and D directly depend on the cumulative result of the other two jobs A and B, then this dependence is depicted as follows (Fig. 30).

Rice. 30. The image on the network schedule of works that depend on the cumulative result of the previous

5. If, to start work C, it is necessary to finish work A and B, and work D can begin immediately after work B is finished, then an additional event and connection are introduced into the network schedule (Fig. 31a).

Rice. 31. The image on the network schedule of works that depend on the previous and the cumulative result of previous works

6. If to start work B and C it is enough to finish work A, work D can be started after the end of work B, and work D - after the cumulative result of work B and C, then the following rule for constructing work is adopted (Fig.Z 16).

7. If work D can start after the end of work A and B and to start work C it is enough to finish work A, and to start work D - finish work B, then on network model this is depicted using two dependencies, i.e. the following construction rule applies (Figure 31 c).

8. The network should not be closed loops, that is, paths emerging from some event and converging to it (Fig. 32)

Rice. 32. Incorrect construction of the network diagram - there is a closed loop

The path, which is a set of works D, D, C, leaves event 2 and enters the same event.

The presence of a closed loop (cycle) in the network indicates an error in the accepted technological sequence of works or an incorrect image of their relationship.

9. There should be no "dead ends" in the network, that is, events from which none of the work leaves, unless this event is final, and "tails", that is, events into which no work enters, if these events are not initial for this network model (Fig. 33).

10. When developing network diagrams for large objects or complexes, for clarity and better control, the work of individual performers or technological complexes, parts of the building should be grouped, while the following rules must be observed:

a) you cannot enter additional events that are not in the detailed graphs;

b) boundary events in detailed and enlarged graphs must necessarily have the same definitions and the same number;

c) only works belonging to one performer should be enlarged;

d) the duration of the enlarged work should be equal to the length of the maximum path of the enlarged group of detailed work.

Rice. 33. Incorrect construction of the network diagram - there is a "dead end" and "tail"

Rice. 34. Examples of consolidation of the network schedule:

a - before consolidation; b - after enlargement

11. When depicting works on the network model that are not directly part of the construction process, but affect its implementation in a timely manner ( external works to which deliveries belong building materials, details, structures, technological equipment, technical documentation), introduce additional events and dashed arrows. Such works are graphically highlighted with a thickened arrow with a double circle.

Fig. 35. Network diagram of external deliveries:

a - wrong; b - correct

12. Events are numbered so that each subsequent one has a higher number than the previous one. The events are numbered (encoded) after the final construction of the network model, starting from the initial one, which is assigned the first number. Event numbers are assigned in ascending order using the "job strikeout method". After assigning the first number to the initial event, cross out all the activities that emerge from it. The next number receives an event, which does not include any work after deletion. If there are several such events, then the numbers are assigned in the order of the events from top to bottom. Outgoing works are crossed out in ascending order of event numbers.

Rice. 36. Encoding events using the "strikeout method"

13. When organizing the flow of work with a breakdown of their common front into separate sections (capture), the network topology is built in accordance with a continuous path, taking measures to eliminate logical contradictions between works by introducing zero links between works of the same name or processes performed on adjacent areas ( fig. 37)

Rice. 37. Building a network diagram topology in the stream organization of work:

a - matrix algorithm with continuous path detection; b - network diagram topology based on continuous path

When building network diagrams, you must adhere to the following rules.

1. The number of each subsequent event must be greater than the number of any previous event. The implementation of this rule allows you to ensure compliance with a logical sequence of work.
2. There should be no events from which not a single job comes out (the exception is the last event), if this rule is not met, then the network schedule is built incorrectly or unnecessary work is planned (see Fig. 10.7).

Rice. 10.7. An example of incorrect construction of a network diagram with unnecessary workV

3. There should be no events that do not include any work (the exception is the initial event). If this rule is not met, then this means that an error was made in drawing up the network schedule or work is not planned, the result of which (for example, event 5 in Fig.10.8) is necessary to start work E.

Rice. 10.8.

A. There should be no closed loops in the network graph, as this leads to a situation where the result of the sequence of works (B-C-D-E) is event 2, from which this sequence began (Figure 10.9).

Rice. 10.9.

5. Any two events must be connected by no more than one job. Such errors occur most often when depicting parallel work (Fig. 10.10, a). For the correct image of these works, it is necessary to introduce additional fictitious events 2 "and 2" and fictitious works 2 "-2 and 2" -2 (Fig. 10.10, b).

Rice. 10.10.

6. If any intermediate work of the network schedule can be started before the complete completion of the previous work, then the latter should be divided into several work performed sequentially, each of which is sufficient to start any of the above. An example of incorrect and correct construction of such a network diagram is shown in Fig. 10.11.

Rice. 10.11.

If, in order to continue work at some stages, it is necessary to obtain the results of other work, then the specified work should be divided into parts using intermediate events (in this example- event 4 in fig. 10.12).

Rice. 10.12.

If before the complete completion of the work it is necessary to see the intermediate result required before the start next job, you should also divide the work into parts by introducing intermediate events (Fig. 10.13, b), work 2-4).

Figure 10.13.

In conclusion, we note that the effective application of the technique network planning and management on this basis of the project may be sufficient challenging task... In general, it is necessary to observe following principles:

provide an image of each individual task, with the exception of tasks without a specified deadline;
Avoid details that are more appropriate in scheduling (plans for key events) or sequence lists;
use the network plan to validate, justify, and determine how to fix deviations from the schedule;
if necessary, use computer programs, given that not every software suitable for solving different tasks planning;
conduct appropriate training of project staff in network planning methods;
present the results of network planning to the top management of the organization in which the project is being carried out.

conclusions

Successful implementation of the project is possible only on the basis of the project plan, which performs a number of functions: gives a general, holistic picture of the project and the sequence of work; allows you to determine for each moment in time to what extent the project is progressing towards completion and what obstacles exist or may arise along the way; presents the general economic model of the project, it indicates the main activities and schedules of work.

Drawing up a plan or planning performs the following functions: determines the duration, structure of the project work, the amount of resources required and the order of their use, the sequence of work and their financing.

Depending on the principles underlying the basis, four types of plans are distinguished: object-oriented, function-oriented, phase-oriented and mixed-oriented.

The set of works that ensure the implementation of an integral part of the plan is called a work package. The work package contains information about the expected results of the work, specific tasks, the timing of their execution and those responsible, information on the resource costs for the work of the package.

Planning is carried out using certain methods called planning tools. They allow you to plan uniformly, ensure the coordination of the execution of work and project tasks, and improve the efficiency of control and implementation of project operations.

The following planning methods are distinguished:

1) drawing up a plan of key events and a phased plan (action plan);
2) planning with bar charts;
3) network planning.

Each of these methods has its own advantages and is used to solve certain problems. So, in particular, the compilation of lists of actions is used to small projects where you can easily coordinate execution individual works, which, as a rule, follow one after another.

Bar charts provide a visual representation of the progress of a number of concurrent project activities.

Network diagrams allow you to manage a number of interrelated project activities and calculate the critical path.

BUILDING A NETWORK GRAPHICS

A network graph or arrow chart is a directed graph with no outlines. A graph is called directed because the arrows show the directions of its edges (arcs). The absence of contours creates conditions under which, moving in the direction of the arrows, each edge can be passed only once. The network diagram allows you to visually show the sequence and relationship of work included in the program or any action plan. Works on such a diagram are depicted by arcs. Thus, each arc of the network diagram, in the form of an arrow, denotes the beginning and the end of the work, which is an event. These events will be represented by circles. The circle at the beginning of the arrow will be the starting event for the operation indicated by that arrow. The circle at the end of the arrow is the final event of this work and the starting one for the subsequent work.

The graph used to build a network graph has another property - it has no dangling vertices. In this case, all events on the chart, except for the initial and final program or action plan, have both preceding and subsequent works. Arrows in the event circle will indicate previous work. Arrows emerging from the circle characterizing the event will indicate subsequent works. The initial event is represented by a circle, from which the arrows only emerge. The final event is characterized by the fact that it has only incoming arrows (prior works).

Building a network schedule requires adherence to a number of rules.

Rule 1... The sequence of successive works is depicted in the form of a chain of arrows connected to each other by circles. For example: work b must follow work a (a ® b ), Work v should be executed after completion of work b (b ® v ) and finally work v G (v ® G ). Such a sequence of works on the network diagram will be as follows (Fig. 3.3.2):

Rule 2... Several works, simultaneously immediately preceding any one subsequent work, are called converging. For example: work G immediately preceded by work a , b and v (a , b, c ® G ). This situation on the network diagram should be depicted as shown in Fig. 3.3.3.

Rule 4... The network diagram should not show non-existing links between subsequent and immediately preceding activities. For example: work a , b , v precede work G (a B C ® G ), at the same time, work a immediately precedes work d (a ® d ). On the network graph, this situation should be displayed in the manner shown in Fig. 3.3.5 ( a) and cannot be depicted in the manner shown in Fig. 3.3.5 ( b), since in the latter case there will be nonexistent connections between the works b , v and d .

In fig. 3.3.5 ( a) the dashed arrow represents a fictitious job (4-5), indicating that the job G cannot start until completion a ... Such work does not require time or any other resources to complete it. It only serves to reflect existing link between works a and G .

Rule 5... Any two adjacent events on a network graph can be connected by a single arrow. This means that with parallel execution of works to display the indicated situation, it becomes necessary to introduce an additional event and fictitious work. For example: work a , b exiting the event 6 , are immediately preceding to work v (a, b ® v ). This situation should be depicted in the manner shown in fig. 3.3.6 ( a) and cannot be depicted in the manner shown in Fig. 3.3.6 ( b).

When building a network diagram, it is convenient to use the technology shown in Fig. 3.3.7. In this case, the construction of a network schedule for the implementation of a project is considered, which includes 11 works, indicated by letters. The works of the project have the following technological links:

® a, d, f, f

a ® b, c

v ® G

f ® s

f, h ® k, l

d, d, k, ® n

w, l ® O

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Networking is not enough to monitor and control the progress of a project. It is necessary to calculate a number of network parameters and determine the critical path. Any sequence of works on a network schedule that begins in the original event and ends in the final event is called full way... The complete path that requires the most time is called critical way... Any other sequence of work is simply way.

To control and manage the progress of work according to the network schedule, the following parameters must be calculated:

1. The time required to complete each individual work. It is called the expected time (). Since the actual time required may depend on many factors, it is defined as a probabilistic value based on expert assessments of the prospective performers. Determination of the expected time to complete the work can be carried out either by two or by three expert estimates. Based on the two estimates, the calculation is carried out according to the following formula:

where https://pandia.ru/text/78/182/images/image013_71.gif "width =" 39 height = 21 "height =" 21 "> is the expert's optimistic assessment, suggesting that there are no unexpected delays.

According to three expert estimates, the calculation is carried out according to the following formula:

where, in addition to the estimates discussed above, the estimate of the most probable time is used https://pandia.ru/text/78/182/images/image017_53.gif "width =" 24 "height =" 25 ">). It is the minimum period, necessary for the performance of all work preceding this event, and equal to the maximum length of the path from the initial event to the considered one.It can be calculated according to the following formula:

where i- the number of the initial event for this job;

j- number of the end event.

For example:

The calculation of the late time for the occurrence of events begins with the final one, which has.

4. Reserve time of events, that is, the time by which the occurrence of the corresponding event can be delayed. It is equal to the difference between the late and early dates of the event.

5. Full reserve of working time shows the time by which the working time can be increased without changing the duration of the critical path. If, when performing any work, all its full reserve of time will be consumed, then all other works of the given path following it will not have reserves of time..gif "width =" 147 "height =" 25 ">.

6. Free reserve time shows the time by which the duration of work can be increased without changing the reserves of time for subsequent works lying on the given path. Free work time calculation (https://pandia.ru/text/78/182/images/image029_32.gif "width =" 147 "height =" 25 ">.

The free slack, as well as the full slack, allows managers to make adjustments to the controlled process based on monitoring data. The difference lies in the fact that the free reserve of time can be allowed to be disposed of by the executors, since this will not affect other work of the program, and the use of the full reserve requires taking into account the capabilities of the executors of subsequent work.

7. The coefficient of work intensity () characterizes the degree of freedom in the timing of the beginning and end of work that does not lie on the critical path. Works on the critical path have no time reserves, and their stress coefficient is 1. For jobs that are not on the critical path, this coefficient is> 1. This indicator is calculated only for jobs that are not on the critical path using the following formula:

where is the duration of the maximum path passing through this work;

–Duration of the segments of the critical path lying on the considered path;

- the duration of the critical path.

Provided that the resources used in the labor process are interchangeable, their redistribution should be carried out taking into account the value of the indicator. Development of decisions "href =" / text / category / virabotka_reshenij / "rel =" bookmark " Fig. 3.3.8. For example, milling machine 3 is loaded only on September 24 and September 25. Therefore, the first three days of the week it can be loaded with unscheduled work or carry out its preventive maintenance, as provided for according to the schedule for drilling machine 1 on 09/21/22. Gantt can be used as an exercise plan technological process production of products. In fig. 3.3.8 you can see an example of a fragment of such a plan. Batch of parts A on 09.21 and a quarter of a working day on 09.22 should be processed at lathe 1. Then three quarters of the working time on 22.09, full time on 23.09 and a quarter on 24.09, these parts must be processed on milling machine 1. After performing the above operations, the batch of parts A 24.09 is transferred to drilling machine 1.

The Gantt chart shows the time required to complete the work and the sequence. The graph does not show the relationship of the work performed, and therefore it is difficult to make decisions about changing their sequence.

The strip chart does not show the relationship of jobs, but it is more visual when used to control the start and end times of individual jobs. This feature makes it preferable to use a network and Gantt strip chart together.

Suppose you want to prepare production and make a device. This must be done as soon as possible, which must be agreed with the customer. The manager intends to control and manage this project using the network and Gantt schedule.

First, a list is developed necessary work and their relationship. Then a network diagram is built (Fig. 3.3.9) and, using the expert assessments of the prospective performers, are calculated for each work (Table 3.3.3).

Table 3.3.3

	Name of works	Duration works in days
	Development of working drawings of parts (CD)
	Development of technological processes for the manufacture of parts (TD)
	Development of drawings of assembly units (ES)
	Design and ordering of tooling for the production of parts (ZOD)
	Rationing of operations of the technological process for the manufacture of parts (NTD)
	Development of assembly technological processes (TS)
	Manufacturing of tooling for performing operations of technological processes for the production of parts (IOD)
	Designing and ordering equipment for assembling a product (AIA)
	Rationing of operations of the technological process for the assembly of a product (NTS)
	Manufacturing of product parts (ID)
	Manufacturing of tooling for assembly work (IOS)
	Product assembly and testing (IC)

Based on the information received, the network schedule parameters are calculated. The calculation will be performed directly on the chart. To do this, we introduce the following form of data notation:

Rebuilding the network diagram in Fig. 3.3.9, taking into account the reflection of the above information on it, we will carry out the calculation of the parameters according to the rules formulated above. As a result, we get an image of this network graph in the form shown in Fig. 3.3.10.

For a visual analysis of the complex of works and the intensity of their timely execution, we will "tie" the network schedule to the time scale (Fig. 3.3.11).

As you can see from the diagram (Fig. 3.3.11), the network graph works formed four complete paths. The first way: BH - TD - NTD - ID - IS, on which the NTD has a full reserve of time - 20 days. The second way: BH - TD - ZOD - IOD - ID - IS, where no work has a reserve of time, and therefore it is called the critical path. The third way: BH - ChS - TS - NTS - IS, on which the work of the NTS has a full reserve of time equal to 32 days. The fourth way: BH - ES - PM - AIA - IOS - IS, where the work of ES, PM, AIA and IOS have a full reserve of time equal to 27 days. This reserve of time can be used when performing one of the named jobs or divided between the listed jobs.

Table 3.3.4

Summary table of network parameters

Initial event	End event

For convenience practical work for the control and maneuvering of resources, the calculated parameters will be summarized in table 3.3.4, and the sequence of work will be depicted in the form of a Gantt strip chart (Fig. 3.3.12). The table shows that work 3-7 (NTD) has a free time reserve equal to 20 days, work 6-9 (NTS) - 32 days, and work 8-9 (ITS) - 27 days. This shows the possibility of providing freedom in planning the start of this work, but postponing these works can only be within the free time reserve.

The Gantt strip chart shows the calendar numbers for the start and end of each job. The critical path is shown at the top of the graph. For the work of this path, the manager must constantly monitor and take managerial actions to prevent violation of the deadlines for the performance of these works.

In the system of network planning and management of construction production, the following concepts and terminology are adopted.

The concept of a project summarizes the range of organizational and technical tasks that are solved to achieve the final results. construction production... These include: the development of a feasibility study for the planned construction, selection of a construction site, engineering and geological surveys, registration of the territory for development, development and approval of technical documentation necessary for construction, including schedules and schemes for the production of construction and installation works before the delivery of the objects in operation.

The set of works performed to achieve a specific goal that determines a specific part of the project is called a project function. For example, work related to the preparation of construction production (development of working drawings of buildings and structures, a project for the production of work; placing orders for the manufacture of equipment, structures and their delivery to construction site etc.) or with the production of construction and installation works, with the erection of foundations, (installation of castoff, breakdown of axes, digging of foundation pits, preparation and installation of formwork and reinforcement, preparation concrete mix, transporting and laying it in the formwork, stripping and grabbing the sinuses of concreted foundations with soil) are functions in the construction project.

The most important indicators of project efficiency are the cost and duration of construction, which are directly dependent on similar indicators of individual project functions. If a list of all project functions has been established and the sequence of execution and time costs are determined for each of them, then by depicting these functions in the form of a graphical network, you can see which of them determine the timing of the remaining functions and the entire project as a whole.

It follows from this that the network diagram reflects the logical relationship and interdependence of all organizational, technical and production operations for the implementation of the project, as well as a certain sequence of their implementation.

The main parameters of the network schedule are work and event, and the derivatives are the network, critical path and time reserves.

Work means any time-consuming process. In network diagrams, this term determines not only certain production processes that require the expenditure of material resources, but also the expected processes associated with the observance of technological breaks, for example, for the hardening of laid concrete.

An event is an intermediate or final result of one or several jobs that is required to start other jobs. The event occurs after the completion of all the work included in it. Moreover, the moment of the event's completion is the moment of the end of the last (included in it. that has no subsequent work is called final.

The work on the network diagram is depicted by a single solid arrow. The duration of the work in units of time (days, weeks) is put under the arrow, and the name of the work is on the arrow. Each event is shown with a circle and numbered (Fig. 115).

Rice. 115. Designation of events and work m - n.

Rice. 116. Designation of the dependence of technological events.

Rice. 117. Designation of dependence of events of an organizational nature.

The duration of a particular work, established depending on the accepted method of its implementation according to the UNIR or labor cost estimates, is called a time estimate. The dependence between individual events, which does not require the investment of time and resources, is called fictitious work and is represented by a dashed arrow on the network graph.

These dependencies or fictitious work can be divided into three groups: technological, organizational, conditional.

Dependency of a technological nature means that the performance of one work depends on the completion of another, for example, the walls of the next floor cannot be laid before the floor slabs of the lower floor are installed (Fig. 116).

Dependence of an organizational nature shows the transitions of teams of workers, the transfer of mechanisms from one area to another, etc. They arise mainly when work is performed by flow methods (Fig. 117).

If there are several end events (for example, the commissioning of several objects included in the start-up complex of the enterprise), they should be linked by conditional dependencies or fictitious work together - putting the enterprise into operation (Fig. 118, b).

The starting event must be one. In cases where there are several initial events (for example, independently of each other, work begins on a fragment of the foundation pits of several objects), they should be conditionally connected by the designation of fictitious works with a single initial event (Fig. 118, a).

If the timing of the actual initial events of individual objects of the complex is different, the concept of dependencies with the cost of real time, converging in one initial node, should be introduced.

The duration, set taking into account one-shift, and for leading machines of two-shift operation and the optimal saturation of the work front, is called the normal duration of work. If the duration of work is due to the maximum load of the work front during two, three-shift work, then it is considered to be minimal.

Rice. 118. Designation of conditional dependencies.

The term of work differs in terms:

the earliest start date of work is the first day when work can begin;

earliest completion date of work - the day of completion of work, if it started at the earliest start date;

the latest date of commencement of work is the last day of commencement of work without delay in the total construction period;

the latest completion date for the work is the day when the work should be completed without delaying construction, i.e. without disrupting the overall construction period.

The difference between the latest and the earliest start date of work determines the private reserve time, that is, the time by which work can be postponed without increasing the duration of construction. The time by which work can be postponed without delaying the execution of any subsequent work determines the total (total) time reserve, which is the difference between the total time reserves of the considered and subsequent work. In the case of several subsequent jobs, the job is selected that has the smallest total reserve of time.

The continuous sequence of works and events from the initial to the final, which requires the longest time to complete it, determines the critical path, which determines the total duration of construction, since the critical works lying on it have no time reserves.

In network diagrams, the direction of the arrows representing the work can be chosen arbitrarily. Typically, these graphs are plotted from left to right. However, the arrows for certain jobs can go up, down, or from right to left.

When drawing up a network schedule, each job should be considered in terms of its relationship with other jobs and the following questions should be answered:

what work should be completed before starting this work;

what other work can be completed simultaneously with the execution of this work;

what work cannot be started before the completion of this work. Let's look at some examples graphic image connections and work sequences in network diagrams.

Rice. 119. Schemes of communication between works (a, b, c, d, e, f, g - cases 1,2,3,4,5,6,7).

Case 1 (Fig. 119, a). The relationship between works A (1-2) and B (2-3). Job B cannot start before job A.

Case 2 (Fig. 119.6). Dependence of two jobs on one. Work D (7-8) and E (7-9) cannot be started until work D (6-7) is completed.

Case 3 (Fig. 119, c). Dependence of one job on the completion of two jobs. Work E (10-11) cannot begin until work G (8-10) and D (9-10) are finished.

Case 4 (Fig. 119, d). The beginning of two jobs depends on the completion of two jobs as well. Works E (15-16) and D (15-17) can begin only after completion of works B (13-15) and C (14-15).

Case 5 (Fig. 119, 6). Dependence of two groups of works. Work B (15-16) depends only on the end of work A (14-15), and work D (21-22) depends on the end of work A (14-45) and C (19-21). Linking the network is carried out by including fictitious work D (15-21).

Case 6 (Fig. 119, f). Work Г (47-48) cannot be started before the end of work C (46-47). In turn, work B (50-51) cannot be started until the end of work C (46-47) and A (49-50). Work E (47-50) is fictitious, defining the logical linkage of the network by restraining the start of work B (50-51) until work C (46-47) is completed.

Case 7 (Fig. 119, g). Work D (8-14) cannot be started before the end of work A (2-8) and B (4-6); work Ж (12-16) cannot be started before completion Fig. 120. Scheme of the network schedule, works D (10-12), B (4-6); the relationship between these works is indicated by the fictitious work E (6-12). Since work G (12-16) does not depend on the end of work A (2-8), it is separated from the last fictitious work B (6-8).

Rice. 120. Scheme of the network schedule.

In order to understand the methodology for constructing network diagrams, consider the case when the following conditions arose during the construction of an object:

at the beginning of construction, work A and B must be performed in parallel;

work C, D and E can be started before the end of work A;

work B must be completed before the start of work E and G;

in this case, work E also depends on the end of work A;

work 3 cannot be started before the end of works D and E;

work I depends on the completion of work D and 3;

work K follows the end of work W;

work L follows work K and depends on the completion of work G and 3;

the final work of M depends on the end of work B, I and L.

In fig. 120 shows one of several possible solutions tasks determined by the given construction conditions. All decisions should be based on the same logical concept, regardless of the type of mesh. The grid must be considered from the point of view of the logical sequence of work. For this purpose, its review should begin with the last event at the facility and go back from event to event, checking the following points: whether each work, starting at an event, depends on all works leading to the event; whether all the activities on which the work in question should depend are included in the event. If both questions can be answered positively, then the network schedule satisfies the requirements of the projected construction technology of the facility.

When building a network diagram, the concept of "work", depending on the degree of desired accuracy, can mean certain types works or complexes of production processes performed at this facility by one of the organizations involved in the construction. For example, the chief engineer of a trust needs to know fewer details than the contractor. Therefore, to provide construction management at the trust level, the network schedule can be drawn up on the basis of more aggregated indicators.