Methodology for compiling network graphs. Building a network diagram: an example

The following concepts and terminology are adopted in the network planning and construction management system.

Under the concept of a project, a range of organizational and technical tasks is generalized to be solved to achieve the final results of construction production. These include: the development of a feasibility study for the planned construction, the selection of a construction site, engineering and geological surveys, the design of a territory for development, the development and approval of the technical documentation necessary for construction, including schedules and schemes for the production of construction and installation works before the delivery of those under construction objects in operation.

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

The most important performance indicators of the project 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 is 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 schedule reflects the logical interconnection 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 diagram are the work and the event, and the derivatives are the network, the critical path and the time reserves.

Work refers to any process that takes time. 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 observing technological breaks, for example, for hardening laid concrete.

An event is an intermediate or final result of one or more activities, necessary for the start of other activities. An event is fired after all the jobs included in it have been completed. Moreover, the moment of the completion of the event is the moment of the end of the last (included in it work. Thus, the event is the final results of certain works and at the same time - the starting positions for the beginning of subsequent ones. An event that does not have previous works is called initial; an event that having no subsequent works is called finite.

Work on the network diagram is depicted with one solid arrow. The duration of work in units of time (days, weeks) is put down under the arrow, and the name of the work is above the arrow. Each event is depicted by 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 the 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 costing, is called a time estimate. The dependence between individual events, which does not require the expenditure of time and resources, is called fictitious work and is depicted on the network diagram by a dotted arrow.

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

Dependence of a technological nature means that the execution of one work depends on the completion of another, for example, the walls of the next floor cannot be laid before the floor panels 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 site to another, etc. They arise mainly when work is performed by in-line methods (Fig. 117).

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

The start event must be one. In cases where there are several initial events (for example, work on excavating the excavations of several objects independently of each other begins), 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 real-time dependencies converging at one initial node should be introduced.

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

Rice. 118. Notation of conditional dependencies.

The term of work differs in terms:

the earliest start date for work is the first day on which work can begin;

the earliest end date of the work - the day the work ends, if it is started at the earliest start date;

the latest start of work - the last day of the start of work without delaying the total construction period;

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

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

The continuous sequence of works and events from initial to final, requiring the greatest time for its implementation, determines the critical path, which determines the total duration of construction, since the critical works lying on it do not have time reserves.

In network diagrams, the direction of the arrows depicting jobs can be chosen arbitrarily. Typically, such graphs are built from left to right. However, the arrows for individual jobs can go up, down, or right to left.

When drawing up a network diagram, each activity should be considered from the point of view of its relationship with other activities 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;

which work cannot be started before the completion of this work. Let's consider some examples of graphic representation of connections and work sequences in network diagrams.

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

Case 1 (Fig. 119, a). Relationship between works A (1-2) and B (2-3). Job B cannot start until Job A has finished.

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

Case 3 (Fig. 119, c). The dependence of one job on the completion of two jobs. Job E (10-11) cannot start until jobs D (8-10) and E (9-10) are finished.

Case 4 (Fig. 119, d). The start of the two jobs depends on the completion of the two jobs as well. Works F (15-16) and D (15-17) can only start after the 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 completion of work A (14-15), and work D (21-22) depends on the completion of works A (14-45) and C (19-21). Network linking is carried out by including fictitious work D (15-21).

Case 6 (Fig. 119, e). Work D (47-48) cannot be started until 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). Job E (47-50) is fictitious, which determines the logical linking of the network by holding back the start of job B (50-51) until job C (46-47) is completed.

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

Rice. 120. Diagram of a network diagram.

In order to clarify the methodology for constructing network graphs, 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 carried out in parallel;

activities C, D and E can be started before the completion of activity A;

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

at the same time, work E also depends on the completion of work A;

activity 3 cannot be started before the completion of activities D and F;

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

work K follows the end of work G;

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

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

On fig. 120 shows one of several possible solutions to the problem defined by the given construction conditions. All decisions should be based on the same logical concept, regardless of the grid type. 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 on the object and go back from event to event, checking such provisions: whether each work starting on the event depends on all the activities leading to the event; whether all activities on which the activity in question should depend are included in the event. If both questions can be answered in the affirmative, then the network schedule satisfies the requirements of the projected construction technology of the facility.

When constructing a network diagram, the concept of “work”, depending on the degree of desired accuracy, can mean certain types of work or complexes of production processes performed at a given facility by one of the organizations participating in the construction. For example, the chief engineer of a trust needs to know fewer details than a foreman. Therefore, to provide construction guidance at the trust level, the network schedule can be compiled on the basis of more aggregated indicators.

Network graphs and rules for their construction

A network diagram is a graphical representation of the processes that must be completed to achieve a set goal.

Methods of network planning and management (SPU) are based on graph theory. A graph is a collection of two finite sets: a set of points, which are called vertices, and a set of pairs of vertices, which are called edges. Two types of graphs are commonly used in economics: tree and network. A tree is a connected graph without cycles, having an initial vertex (root) and extreme vertices. A network is a directed finite connected graph that has a start vertex (source) and an end vertex (sink). Thus, each network graph is a network consisting of nodes (vertices) and oriented arcs (edges) connecting them. Graph nodes are called events, and the oriented arcs connecting them are called jobs. On the network diagram, events are depicted by circles or other geometric figures, and the works connecting them are dimensionless arrows (they are called dimensionless because the length of the arrow does not depend on the amount of work that it reflects).

Each network event is assigned a specific number ( i), and the work connecting the events is denoted by the index ( ij). Each work is characterized by its duration (duration) t(ij). Meaning t(ij) in hours or days put down as a number above the corresponding arrow of the network diagram.

In the practice of network planning, several types of work are used:

1) real work, a production process that requires labor, time, materials;

2) passive work (waiting), a natural process that does not require labor and material resources, but the implementation of which can only occur within a certain period of time;

3) fictitious work (dependence), which does not require any costs, but shows that some event cannot happen before another. When constructing a graph, such activities are usually indicated by a dotted line.

Each work, alone or in combination with other works, ends with events that express the results of the work performed. In network diagrams, the following events are distinguished: 1) initial, 2) intermediate, 3) final (final). If the event has an intermediate character, then it is a prerequisite for the start of the work following it. It is believed that the event has no duration and is carried out instantly after the completion of the work preceding it. The initiating event is not preceded by any work. It expresses the moment of the onset of conditions for the start of the implementation of the entire complex of works. The final event does not have any subsequent work and expresses the moment of completion of the entire complex of work and achievement of the intended goal.

Interconnected activities and network events form paths that connect the initial and final events, they are called complete. The full path on the network diagram is a sequence of work in the direction of the arrows from the initial to the final event. The full path of maximum duration is called the critical path. The duration of the critical path determines the deadline for completing the entire complex of works and achieving the intended goal.

Activities located on the critical path are called critical or stressful activities. All other works are considered non-critical (non-stressful) and have time reserves that allow you to move the deadlines for their implementation and the timing of events without affecting the overall duration of the entire complex of works.

Rules for constructing a network diagram.

1. The network is drawn from left to right, and each event with a higher sequence number is displayed to the right of the previous one. The general direction of the arrows depicting jobs should also generally be from left to right, with each job exiting a lower-numbered event and entering a higher-numbered event.

False Correct

3. There should be no “dead ends” in the network, that is, all events, except for the final one, must have subsequent work (dead ends are called intermediate events from which no work exits). This situation may occur when the given work is not needed or some work is omitted.

4. There should be no events in the network, except for the initial one, which are not preceded by at least one job. Such events are called "tail events". This may be the case if previous work is missed.

For the correct numbering of events in the network diagram, use the following scheme of actions. The numbering starts from the initial event, which is assigned the number 0 or 1. From the initial event (1), all outgoing jobs (directed arcs) are deleted, and on the remaining network, an event is again found that does not include any job. This event is assigned a number (2). The specified sequence of actions is repeated until all events of the network diagram are numbered. If during the next deletion, two events simultaneously occur that do not have incoming jobs, then numbers are assigned to them arbitrarily. The number of the final event must be equal to the number of events in the network.

Example.

In the process of building a network diagram, it is important to determine the duration of each work, that is, it is necessary to give it a time estimate. The duration of the work is set either in accordance with applicable standards, or on the basis of expert assessments. In the first case, duration estimates are called deterministic, in the second - stochastic.

There are various options for calculating stochastic time estimates. Let's consider some of them. In the first case, three types of duration of a particular job are set:

1) the maximum period, which is based on the most unfavorable conditions for the performance of work ( tmax);

2) the minimum period, which is based on the most favorable conditions for the performance of work ( tmin);

3) the most probable period, based on the actual provision of work with resources and the presence of normal conditions for its implementation ( t in).

Based on these estimates, the expected time to complete the work (its time estimate) is calculated using the formula

. (5.1)

In the second case, two estimates are given - the minimum ( tmin) and maximum ( tmax). The duration of work in this case is considered as a random variable, which, as a result of implementation, can take any value in a given interval. The expected value of these estimates ( t cool) (with beta probability density distribution) is estimated by the formula

. (5.2)

To characterize the degree of spread of possible values ​​around the expected level, the dispersion index is used ( S2)

. (5.3)

The construction of any network diagram begins with the compilation of a complete list of works. Then the sequence of works is established, and for each specific work, immediately preceding and subsequent works are determined. To establish the boundaries of each type of work, questions are used: 1) what should precede this work and 2) what should follow this work. After compiling a complete list of works, establishing their order and time estimates, they proceed directly to the development and compilation of a network schedule.

Example.

Consider, as an example, a program to build a warehouse building. The list of operations, their sequence and time duration will be drawn up in a table.

Table 5.1

Network Schedule Work List

Built on the basis of the data in Table. 5.1 the preliminary network work schedule is as follows (Fig. 5.1).

Rice. 5.1. Preliminary network schedule

Below is the same timetable for the construction of a warehouse building, numbered and with time estimates for the work (Figure 5.2).

Rice. 5.2. Final Network Diagram

To build a network schedule, it is necessary to identify the sequence and interconnection of work: what work needs to be done and what conditions to ensure that this work can be started, what work can and should be performed in parallel with this work, what work can be started after the completion of this work. These questions make it possible to identify the technological relationship between individual works, provide a logical construction of the network diagram and its compliance with the simulated set of works.

The level of detail of the network diagram depends on the complexity of the object under construction, the amount of resources used, the amount of work and the duration of construction.

There are two types of network diagrams:

peaks - works

peaks - events

Network graphs of the "vertex - work" type.

The elements of such a schedule are activities and dependencies. Work is a specific production process that requires time and resources to complete it, and is depicted by a rectangle. Dependence (fictitious work) shows the organizational and technological connection between the works, which does not require time and resources, is depicted by an arrow. If there is an organizational or technological break between jobs, then the duration of this break is indicated on the dependency.

If the work of the "vertex - work" network diagram has no previous work, then it is the original work of this graph. If the job has no subsequent jobs, then it is the final job of the network. There should be no closed contours (cycles) in the "nodes - work" network diagram, i.e. dependencies should not go back into the work they came from.

Network graphs of the "nodes - events" type.

The elements of this type of graphs are activities, dependencies and events. The work is represented by a solid arrow, the dependence is dotted. An event is the result of one or more activities, necessary and sufficient for the start of one or more subsequent activities, and is represented by a circle.

In this type of network diagram, each job is between two events: an initial one, from which it exits, and an end event, into which it enters. Network events are numbered, so each job has a code consisting of its start and end event numbers.

For example, in fig. 6.2 works are coded as (1,2); (2.3); (2.4); (4.5)

If the event of the network graph "vertices - events" has no previous activities, then it is the initial event of this network. The works immediately following it are called the original ones. If an event has no follow-ups, then it is the final event. The works included in it are called final.

To correctly display the relationships between jobs, you must follow the following basic rules for constructing a network diagram "Vertices - Events":

1. When displaying simultaneously or in parallel works (for example, works "B" and "C" in Fig. 6.2), dependence (3.4) and an additional event (3) are introduced.

2. If to start work "D" it is necessary to perform work "A" and "B", and to start work<В» - только работу «А», то вводится зависимость и дополнительное событие (рис.6.З.).

H. There should be no closed loops (cycles) in the network diagram, i.e. a chain of jobs that goes back to the event they came from

4. In the network diagram, with the flow organization of construction, additional events and dependencies are introduced (Fig. 6.5.).

To determine the duration of the critical path and the timing of each activity, the following are determined: time parameters :

Early start -

Early end of work - ;

Late start - ;

Late completion of work

Full slack - R;

Free time reserve

Early start- Earliest start date. The early start of the original network activities is zero. The earliest start of any activity is equal to the maximum early finish of previous activities:

Early end of work- the earliest time the work was completed. It is equal to the sum of the early start and the duration of the work.

Late end of work- the latest end point at which the duration of the critical path does not change. The late completion of finishing activities is equal to the duration of the critical path. The late finish of any job is equal to the minimum late start of subsequent jobs.

Late start- the latest start time at which the duration of the critical path will not change. It is equal to the difference between the late completion of this work and its duration.

Activities on the critical path have equal early and late start and finish dates, so they have no slack. Activities not on the critical path have time reserves .

Full slack- the maximum time by which the duration of the activity can be increased or its start can be postponed without increasing the duration of the critical path. It is equal to the difference between the late and early start or finish dates.

Free time reserve- the time by which you can increase the duration of the work or postpone its start, while not changing the early start of subsequent work. It is equal to the difference between the early start of the next activity and the early end of this activity.

Calculation of the network diagram "tops - work"

To calculate the "tops - work" network graph, the rectangle depicting the work is divided into 7 parts (Fig. 6.6).

The upper three parts of the rectangle record the early start, duration, and early finish of the work; the lower three parts show the late start, time reserves, and late finish. The central part contains the code (number) and the name of the work.

The calculation of the network schedule begins with the definition of early dates. Early starts and finishes are computed sequentially from the original job to the end job. The early start of the original job is 0, the early finish is the sum of the early start and the duration of the job:

The early start of the subsequent activity is equal to the early end of the previous activity. If a given activity is immediately preceded by several activities, then its earliest start will be equal to the maximum of the earliest finishes of the preceding activities:

Thus, the early dates of all network activities are determined and entered in the upper right and left parts.

The early completion of the completion activity determines the length of the critical path.

Late deadlines are calculated in reverse order from final to original work. The late completion of the final work is equal to its early completion, i.e. duration of the critical path.

Late start is defined as the difference between late finish and duration:

The late start of subsequent activities becomes the late finish of previous activities. If a given activity is immediately followed by several activities, then its late completion will be equal to the minimum of the late starts for the following activities:

In a similar way, the late dates of all network activities are determined and recorded in the lower left and right parts.

The full reserve of time, equal to the difference between the late and early dates, is entered in the numerator of the middle of the lower part:

The free slack, equal to the difference between the minimum early start of subsequent activities and the early completion of this activity, is recorded in the denominator of the middle of the lower part:

The free reserve is always less than or equal to the full reserve of work.

Network graphs 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 event numbers.

2. When performing parallel jobs, if one event serves as the start or end 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, wait and dependency must have their own cipher in the form of the number of their start and end events.

Rice. 28. Image on the network diagram of parallel work:

a - incorrect; b - correct

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

Rice. 29. Image on the network diagram of works divided into sections (captures)

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

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

5. If the start of work C requires the completion of work A and B, and work D can begin immediately after the end of work B, then an additional event and a connection are introduced into the network schedule (Fig. 31a).

Rice. 31. Depiction on the network diagram of works depending on the previous and cumulative result of previous works

6. If the completion of work A is enough to start work B and C, 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. 3 16).

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

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

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

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

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

9. There should be no "dead ends" in the network, that is, events from which not a single work leaves, unless this event is the final one, and "tails", that is, events that do not include any work, 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 a building should be grouped, while the following rules must be observed:

a) you can not enter additional events that are not in the detailed schedules;

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

c) only work belonging to one artist 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 works.

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

Rice. 34. Examples of network enlargement:

a - before enlargement; b - after enlargement

11. When depicting on the network model works that are not directly included in the technological process of construction, but affecting its implementation on time (external works, which include the supply of building materials, parts, structures, process equipment, technical documentation), additional events are introduced and dotted arrows. Such works are graphically distinguished by a thickened arrow with a double circle.

Fig.35. Image on the network diagram of external supplies:

a - incorrect; b - correct

12. Numbers are assigned to events so that each subsequent one has a higher number than the previous one. 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 "cross-out work method". After assigning the first number to the initial event, all outgoing works are crossed out. The next number receives an event that does not include any work after the strikeout. 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. Coding events using the "deletion of works" method

13. When organizing the in-line execution of work with a breakdown of their common front into separate sections (captures), the network topology is built in accordance with an unbreakable path, taking measures to eliminate logical contradictions between jobs by introducing zero links between jobs of the same name or processes performed on adjacent captures ( Fig. 37)

Rice. 37. Construction of the topology of the network diagram with the flow organization of work:

a - matrix algorithm with selection of a non-breaking path; b - network diagram topology based on a non-breaking path

Work planning always begins with determining the number of tasks, the persons responsible for their execution and the time required for complete completion. With such schemes are simply necessary. Firstly, in order to understand how much total time will be spent, and secondly, to know how to plan resources. This is what project managers do, they primarily carry out the construction of a network diagram. An example of a possible situation will be considered below.

Initial data

The management of the advertising agency has decided to launch a new advertising product for its clients. The following tasks were set for the employees of the company: to consider the ideas of advertising brochures, to give arguments in favor of one or another option, to create a layout, to prepare a draft contract for clients and send all the information to the management for consideration. To inform clients, it is necessary to carry out a mailing list, put up posters and call all the companies in the database.

In addition, the chief manager made a detailed plan of all necessary actions, appointed responsible employees and set the time.

Let's start building a network graph. The example has the data shown in the following figure:

Matrix construction

Before forming it is necessary to create a matrix. Graphing starts from this stage. Imagine a coordinate system where the vertical values ​​correspond to i (the start event) and the horizontal rows to j (the end event).

We begin to fill in the matrix, focusing on the data in Figure 1. The first work has no time, so it can be neglected. Let's consider the second one in more detail.

The initial event starts at number 1 and ends at the second event. The duration of action is 30 days. This number is entered in a cell at the intersection of 1 row and 2 columns. In a similar way, we display all the data, which is shown in the figure below.

Basic elements used for a network diagram

The construction of graphs begins with the designation of theoretical foundations. Consider the main elements required to compile the model:

1. Any event is indicated by a circle, in the middle of which there is a number corresponding to the order of actions.
2. The work itself is an arrow leading from one event to another. Above the arrow write the time required to complete it, and under the arrow indicate the responsible person.

A job can run in three states:

- Current is an ordinary action that requires time and resources to complete.

- Expectation- a process during which nothing happens, but it takes time to move from one event to another.

- Dummy job is a logical connection between events. It does not require any time or resources, but in order not to interrupt the network schedule, it is designated. For example, the preparation of grain and the preparation of bags for it are two separate processes, they are not connected in series, but their connection is needed for the next event - packaging. Therefore, another circle is selected, which is connected by a dotted line.

Basic principles of construction

The rules for constructing network graphs are as follows:

Building a network graph. Example

Let's return to the original example and try to draw a network graph using all the data indicated earlier.

Let's start with the first event. Two come out of it - the second and the third, which unite in the fourth. Then everything goes sequentially until the seventh event. Three works come out of it: the eighth, ninth and tenth. Let's try to display everything:

Critical values

It's not all about building a network diagram. The example continues. Next, you need to calculate the critical moments.

The critical path is the longest time taken to complete a task. In order to calculate it, you need to add up all the largest values ​​​​of successive actions. In our case, these are works 1-2, 2-4, 4-5, 5-6, 6-7, 7-8, 8-11. We summarize:

30+2+2+5+7+20+1 = 67 days

So the critical path is 67 days.

If such time for the project does not suit the management, it must be optimized according to the requirements.

Process Automation

Today, few project managers manually build network diagrams - this is an easy and convenient way to quickly calculate the cost of time, determine the order of work and assign performers.

Let's take a quick look at the most common programs:

1. Microsoft Project 2002- an office product in which it is very convenient to draw diagrams. But doing the calculations is a little inconvenient. In order to perform even the simplest action, you need a considerable amount of knowledge. When downloading the program, take care of purchasing the user manual for it.
2. SPU v2.2. Very common free software. Or rather, not even a program, but a file in an archive that does not require installation to use. It was originally designed for a student's graduation work, but it turned out to be so useful that the author posted it online.
3. netgraf- another development of a domestic specialist from Krasnodar. It is very easy, easy to use, does not require installation and a huge amount of knowledge on how to manage it. The advantage is that it supports importing information from other text editors.
4. Often you can find such an example - Borghiz. Little is known about the developer, how and how to use the program. But by the primitive method of "poke" it can be mastered. The main thing is that it works.