Network model. Network planning and management

They can be built not only in the form of formulas (analytical representation of the model), but also in the form numerical examples(numerical representation), in the form of tables (matrix) and in the form of graphs (network representation).

Accordingly, according to this principle, models are distinguished:

Analytical
Matrix
Network

The method of network planning is used. It is based on the application network diagrams... The latter are expressed in the form of a certain chain of works and events related to the technological sequence. Work here is understood as a process that precedes the occurrence of a certain event. The work includes both technological processes and the waiting time associated with interruptions in these processes. An event is understood as the result of work, without which other work cannot be started. In network diagrams, events are indicated by circles with a number inside. The arrows between the circles represent the intended sequence of work. The numbers indicated near the arrows characterize the planned duration of the work. With the help of network diagrams, either the optimization of the execution time or the optimization of the value of the cost of the work performed is achieved.

Network model(production management and planning model) - a plan for performing a certain set of interrelated operations (works) given in a specific form of the network. An example of this model is network schedule.

Network schedule

The circles indicate the numbers of events, connecting lines (arrows) work, and the numbers above them indicate the approximate cost, duration or labor intensity of the work. In accordance with the elements of the graphs (arcs and vertices), numerical estimates are put (parameters of the operation: duration, cost, or labor intensity). This allows deep analysis and, in some cases, optimization.

The network model determines, with any required degree of detail, the composition of the complex's work and the order of their execution in time.

A distinctive feature network model in comparison with other forms of presentation of plans is a clear definition of all temporal relationships of operations.

Network models are used not only as a means of solving various planning and forecasting problems. Network models are also used to build a special class of system. organizational management, called systems of network planning and management.

Among different method network planning and management systems are the most common: the critical path method - analysis of the state of the process at each given moment in time and determination of the sequence of work in order to avoid delays in the execution of the plan to the target date and the method of evaluating the revision of programs.

Lecture 11

NETWORK PLANNING AND MANAGEMENT MODELS

Purpose and scope of network planning and management

Searches for more effective ways planning complex processes led to the creation of fundamentally new methods of network planning and management (STM).

System of methods of SPU - a system of planning and management methods for the development of large national economic complexes, scientific research, design and technological preparation of production, new types of products, construction and reconstruction, overhaul fixed assets by applying network diagrams.

The first systems using network graphics were used in the United States in the late 50s and were named CPM(English abbreviation meaning critical path method) and PERT(method of evaluating and reviewing the program). System CPM was first used in management construction works, system PERT - when developing Polaris systems.

In Russia, work on network planning began in the 60s. Then the SPU methods found application in construction and scientific research. Subsequently, network methods began to be widely used in other areas. National economy.

SPU is based on modeling a process using a network diagram and is a set of calculation methods, organizational and control measures for planning and managing a complex of works.

Network planning and management models

The SPU system allows:

Formulate a schedule for the implementation of a certain set of works;

Reveal and mobilize reserves of time, labor, material and financial resources;

To manage the complex of works on the principle of "leading link" with forecasting and prevention of possible disruptions in the course of work;

To improve the efficiency of management as a whole with a clear distribution of responsibilities between managers different levels and performers of work.

The range of application of the STS is very wide: from tasks concerning the activities of individuals, to projects in which hundreds of organizations and tens of thousands of people participate (for example, the development and creation of a large territorial-industrial complex).

Under complex of works (complex of operations, or project) we will understand any task for which it is necessary to carry out a sufficiently large number of different works. This can be the construction of a building, ship, aircraft or any other complex object, and the development of a project for this structure, and even the process of drawing up plans for the implementation of the project.

In order to draw up a work plan for the implementation of large and complex projects, consisting of thousands of separate studies and operations, it is necessary to describe it using some kind of mathematical model. Such a means of describing projects (complexes) is network model.

The network model and its main elements

Network model is a plan for the implementation of a certain complex of interrelated works (operations), given in a specific form of the network, graphic image which is called network schedule. Distinctive feature the network model is a clear definition of all the temporal relationships of the upcoming work.

The main elements of the network model are developments and work.

Term Work used in the STC in a broad sense. First, it is real work - a time-consuming process that requires resources (for example, assembling a product, testing an instrument, etc.). Each valid work must be specific, clearly described and have a responsible executor.

Secondly, it is expectation - a time-consuming process that does not require labor input (for example, the drying process after painting, aging of metal, hardening of concrete, etc.).

Third, it is addiction, or fictitious work - a logical connection between two or more works (events) that do not require labor, material resources or time. She points out that the possibility of one job is directly dependent on the results of another. Naturally, the duration of the fictitious work is taken equal to zero.

Event - this is the moment of completion of a process, reflecting a separate stage of the project. An event can be a particular result of a single work or the summarized result of several activities. The event can happen only when all the work that preceded it is finished. Subsequent work can begin only when the event occurs. From here dual the nature of the event: for all immediately preceding works, it is final, and for all immediately following it - initial. Wherein it is assumed that the event has no duration and occurs as if instantly. Therefore, each event included in the network model must be fully, accurately and comprehensively defined, its formulation must include the result of all immediately preceding work.

Among the events of the network model, there are initial and the final developments. The initiating event has no previous activities and events related to the set of activities presented in the model. The ending event has no follow-up activities or events.

Events on the network graph (or, as they say, on the graph) are depicted by circles (the vertices of the graph), and the works - by arrows (oriented arcs), showing the connection between the works. An example of a fragment of a network diagram is shown in Fig. 1.

In fig. 2. a the network diagram of the problem of modeling and constructing the optimal plan of some economic object is presented. To solve this problem, it is necessary to carry out the following work: L - formulate a research problem; B - build a mathematical model of the object under study; V - collect information; G - choose a method for solving the problem; D - build and debug a computer program; E - calculate the optimal plan; F - transfer the calculation results to the customer. The numbers on the graph indicate the numbers of events to which the execution of the corresponding work leads.

From the graph, for example, it follows that the works V and G you can start executing independently of one another only after the event has occurred 3, those. when the work was done A and B; work D - after the event 4, when the work was done A, B and G, and work E can only be performed after the occurrence of the event 5, that is, when performing all the work preceding it A B C D E.

In the network model shown in Fig. 2 a no numerical ratings. Such a network is called structural. However, in practice, networks are most often used in which estimates of the duration of work are given (indicated in hours, weeks, decades, months, etc. above the corresponding arrows), as well as estimates of other parameters, for example, labor intensity, cost, etc. It is these networks that we will consider in the future.

First, let's make the following remark.... In the examples reviewed, the network schedules consisted of activities and events. However, there may be another principle of building networks - without events. In such a network, the vertices of the graph (for example, represented by rectangles) mean certain jobs, and the arrows - the dependencies between these jobs, which determine the order of their execution. As an example, the network diagram of the "event - work" task of modeling and constructing an optimal plan for some economic object, shown in Fig. 2 a, is represented as a work-communication network in fig. 2 b. And the network schedule "events - jobs" of the same task, but with an unsuccessfully drawn up list of jobs, is shown in Fig. 2 v.

It should be noted that the "work - communication" network schedule, in contrast to the "event - work" schedule, has certain advantages: it does not contain fictitious works, has a simpler construction and restructuring technique, includes only the concept of work, which is well known to performers, without the less familiar concept of an event. At the same time, networks without events turn out to be much more cumbersome, since there are usually much fewer events than jobs. (an indicator of the complexity of the network, equal to the ratio of the number of jobs to the number of events, as a rule, significantly more than one). Therefore, these networks are less efficient from the point of view of complex management. This explains the fact that (in the absence of, in general, fundamental differences between the two forms of presentation of the network) at the present time the most widespread network diagrams "events - works".

The order and rules for building network diagrams

Network schedules are drawn up at the initial planning stage. First, the planned process is broken down into individual works, a list of works and events is drawn up, their logical connections and sequence of execution are thought out, the work is assigned to the responsible executors. With their help, the duration of each job is estimated. Then compiled (stitched) network schedule. After ordering the network schedule, the parameters of events and works are calculated, time reserves are determined and critical path. Finally, the analysis and optimization of the network schedule is carried out, which, if necessary, is drawn anew with recalculation of the parameters of events and works.

When building a network diagram, you must follow a number of rules.

1. There should be no "dead-end" events in the network model; events from which no work exits, except for the end event(Fig. 3 a). Here is either work (2, 3) is not needed and it must be canceled, or the need for certain work following the event has not been noticed 3 to accomplish any subsequent event. In such cases, it is necessary to carefully study the relationship of events and works to correct the misunderstanding that has arisen.

2. The network schedule should not contain "Tail" events (except for the original one), which are not preceded by at least one work(event 3 - in fig. 3 b). Here are the works preceding the event 3, not provided. Therefore the event 3 cannot be done, and therefore the work following it cannot be done (3, 5). Having found such events in the network, it is necessary to determine the performers of the previous works and include these works in the network.

3. The network should not be closed loops and loops, i.e. paths connecting some events with themselves(fig. 3 c, d).

Imagine that in the network diagram shown in Fig. 2 a, work B and E, when formulating the initial list of works, we would combine into one work B 1. Then we would get the network diagram shown in Fig. 2c. The event means that to work B ", which cannot be performed until the choice of the calculation method (work G), and the choice of the calculation method cannot begin until the end of the model building (event 3"). In other words, the simplest contour has formed in the network: 2"->3"->2".

When a contour appears (and in complex networks, that is, in networks with a high index of complexity, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the initial data and, by revising the scope of work, achieve its elimination. So, in our example, a division of work would be required B " on B and D.

4. Any two events must be directly linked by no more than one arrow work.

Violation of this condition occurs when depicting parallel work (Fig. 3 e). If these works are left this way, confusion will occur due to the fact that two various jobs will have the same notation (7, 2); usually taken under (i, y) understand the work that connects<-е событие с j-th event. However, the content of these works, the composition of the contractors involved and the amount of resources spent on the work may differ significantly.

In this case, it is recommended to enter dummy event(event 2" in fig. 3 e) and fictitious work(Work 2", 2), in this case, one of the parallel works (7, 2) closes in on this fictitious event. Fictitious works are shown on the chart with dashed lines.

5. It is recommended to have one originating and one ending event on the network. If this is not the case in a compiled network (cm rice. 3 g), then you can achieve what you want by introducing fictitious events and activities, as shown in Fig. 3 h.

Fictitious works and events must be introduced in a number of * other cases. One of them is the reflection of the dependence of events not related to real work. For example, works A and 1 (fig. 3 and) can be performed independently of each other, but n< условиям производства работа B cannot start before the end of the work A. This circumstance requires the introduction of a fictitious work by S.

Another case is incomplete work dependency. For example, job C requires the completion of jobs to start A and B, but work D connected only with work B, but from work A does not depend. Then the introduction of a fictitious work Ф and a fictitious event is required 3", as shown in fig. 3 To.

In addition, fictitious jobs may be introduced to reflect real delays and expectations. In contrast to the previous cases, here the fictitious work is characterized by a length of time.

Network diagram (network, network graph, PERT diagram) - a graphical display of the project's work and the dependencies between them. In project planning and management, the term "network" refers to a full range of works and project milestones with dependencies established between them.

Network diagrams graphically display the network model as a set of nodes corresponding to activities, connected by lines representing relationships between activities. This graph, called a top-work network or precedence-succession diagram, is the most common representation of a network (Figure 3).

Rice. 3. Fragment of the "top-work" network

There is another type of network diagram, the node-event network, which is less commonly used in practice. With this approach, the work is represented as a line between two events (nodes of the graph), which, in turn, reflect the beginning and end of this work. PERT charts are examples of this type of chart (Figure 4).

Rice. 4. Fragment of the "vertex-event" network

A network diagram is not a flowchart in the sense that it is used to model business processes. The fundamental difference from the block diagram is that the network diagram displays only logical dependencies between activities, and not inputs, processes and outputs, and also does not allow repetitive cycles or so-called loops (in graph terminology, an edge of a graph outgoing from a vertex and returning to the same vertex, Fig. 5).

Fig. 5. An example of a loop in a network model

Network planning techniques - methods, the main purpose of which is to reduce the duration of the project to a minimum. They are based on the Critical Path Method (CPM) and the PERT (Program Evaluation and Review Technique) method developed almost simultaneously and independently.

Critical path - the longest full path in the network is called critical; works lying on this path are also called critical. It is the duration of the critical path that determines the smallest total duration of work on the project as a whole.

Duration of the entire project in general, can be reduced by reducing the duration of work on the critical path. Accordingly, any delay in the execution of work on the critical path will lead to an increase in the duration of the project.

Critical path method allows you to calculate possible schedules for the implementation of a complex of works based on the described logical structure of the network and estimates of the duration of each work, to determine the critical path for the project as a whole.

Full reserve of time, or reserve of time , is the difference between the dates of the late and early end (start) of the work. The managerial sense of the slack is that if it is necessary to settle the technological, resource or financial constraints of the project, it allows the project manager to delay work for this period without affecting the completion date of the project as a whole. The jobs on the critical path have a time reserve of zero.

Gantt chart- a horizontal line chart, in which the tasks of the project are represented by lengthy intervals in time, characterized by start and end dates, delays and, possibly, other time parameters. An example of displaying a Gantt chart using modern computer tools is shown in Fig. 6.

The network planning process assumes that all activities will be described as a set of activities or activities with certain relationships between them. A set of network procedures known as critical path method procedures is used to calculate and analyze network traffic.

The network model development process includes:

defining a list of project activities;

assessment of work parameters;

determination of dependencies between works.

The definition of a set of works is carried out to describe the project activities as a whole, taking into account all possible works. Work is the main element of the network model. Work is understood as an activity that must be performed to obtain specific results.

Work packages define the activities that need to be carried out to achieve project deliverables that can be distinguished by milestones.

Before starting the development of the network model, you need to make sure that at the lower level of the CPP, all the work is defined that ensures the achievement of all the private goals of the project. The network model is formed by defining the dependencies between these activities and adding linking activities and events. In general terms, this approach is based on the assumption that each work is aimed at achieving a particular result. The linking work, perhaps, does not require any tangible end result, for example, the work "organization of execution".

Evaluation of work parameters is a key task of the project manager, who engages team members responsible for the implementation of individual parts of the project to solve this problem.

The value of time schedules, cost and resource plans obtained as a result of the analysis of the network model depends entirely on the accuracy of estimates of the duration of work, as well as estimates of the needs of work in resources and financial resources.

Estimates should be made for each detailed work, and then can be aggregated and summarized for each of the CPP levels in the project plan.

Figure 6 Ganges diagram

7.1 NETWORK PLANNING

Network planning is one of the forms of graphical reflection of the scope of work and the duration of plans. As a rule, network planning is used in drawing up strategic plans and long-term complexes of various types of enterprise activities (project, planned,

organizational, etc.).

Along with line graphs and tabular calculations, network planning methods are widely used in the development of long-term plans and models of complex production systems and other objects of long-term use.

The network work plans of the enterprise for the creation of new competitive products contain not only the total duration of the entire complex of design and production and financial and economic activities, but also the duration and sequence of individual processes or stages, as well as the need for the necessary economic resources.

For the first time, schedules for the execution of production processes were applied at American firms by G. Gant. On linear (strip) charts along the horizontal axis in the selected scale, the duration of work is postponed for all "stages, stages of production. The content of work cycles (with the necessary degree of their dismemberment into separate parts or elements) is depicted along the vertical axis. Line charts are usually used in domestic enterprises. in the process of short-term or operational planning of production activities.The main disadvantage of such schedules is the impossibility of close interconnection of individual works into a single production system or a general process of achieving the planned ultimate goals of the enterprise.

Unlike line charts, network planning serves as the basis for economic and mathematical calculations, graphical and analytical calculations, organizational and management decisions, operational and strategic plans. Network planning provides not only an image, but also modeling, analysis and optimization of projects for the implementation of complex technical tasks, design developments, etc.

It is customary to understand network planning as a graphical representation of a certain set of work performed, which not only reflects their logical sequence, the existing relationship and the planned duration, but also ensures the subsequent optimization of the developed schedule in order to use it for the current management of work progress.

Network planning is based on graph theory. Under count means a set of points (nodes) connected by lines. The direction of the lines is shown by arrows. The segments connecting the vertices are called the edges (arcs) of the graphs. An oriented graph is a graph on which arrows indicate the directions of all its edges, or arcs. Graphs are named after maps, mazes, networks, and diagrams.

Graph theory operates with such concepts as paths, contours, etc. Way is a series connection of arcs, i.e. the end of each previous segment coincides with the beginning of the next one. Contour - it is a path whose starting vertex is the same as the ending one. In other words, a network graph is a directed graph without contours, the arcs (edges) of which have one or more numerical characteristics. On the chart, edges are considered jobs, and vertices are events.

Work any production process or other action that leads to the achievement of certain results is called. Possible waiting for the start of subsequent processes associated with interruptions or additional costs of time is also considered work. Waiting work usually requires expenditure of working time without using resources, for example, cooling of heated workpieces, hardening of concrete, etc. In addition to actual jobs and pending jobs, there are fictitious jobs, or dependencies. A fictitious work is a logical connection or dependence between some final processes or events that does not require time. On the graph, fictitious work is depicted by a dashed line.

Events the final results of previous work are considered. The event fixes the fact of the work being done, concretizes the planning process, excludes the possibility of different interpretations of various processes and works. Unlike work, which, as a rule, has its own duration in time,

The event represents only the moment when the planned action is completed, for example: the goal is selected, the plan is drawn up, the product is produced, the product is paid for, the money is received, etc. Events can be initial (initial) or final (final), simple or complex, as well as intermediate, preceding or subsequent, etc.

There are three main ways of displaying events and activities on network diagrams: work-tops, event-tops, and blended networks.

In networks of the "top-work" type, all processes or actions are represented as successive rectangles connected by logical dependencies.

As can be seen from the network diagram (Fig. 1), it depicts a simple model, or a network consisting of five interrelated jobs: A, B, C, D, and D. The initial job is A, followed by intermediate jobs B, C and D and further finishing work by D.

In networks of the "tops-events" type, all jobs or actions are represented by arrows, and events - by circles (Fig. 2). This network graph depicts a simple production process with six interrelated events: 0, 1, 2, 3, 4, and 5. In this case, the initial event is the zero event, the final event is the fifth, and all others are intermediate.

Network schedules are used not only for planning various works, but also for their coordination between managers and executors of projects, as well as for the rational use of production resources.

Network planning is successfully applied in various areas of business and production activities, such as:

Marketing research;

Research work;

Development design;

Implementation of organizational and technological projects;

Mastering the pilot and serial production of products;

Construction and installation of industrial facilities;

Repair and modernization of technological equipment;

Development of business plans for the production of new goods;

Restructuring of existing production in market conditions;

Training and placement of various categories of personnel;

Management of innovation activities, etc.

The use of network planning in modern production contributes to the solution of strategic and operational tasks. Network planning allows you to:

1) reasonably choose the development goals of each division of the enterprise, taking into account the existing market requirements and the planned end results;

2) clearly establish detailed tasks for all divisions and services of the enterprise on the basis of their interconnection with a single strategic goal in the planning period;

3) involve experienced and highly qualified performers of the forthcoming work in the preparation of project plans;

4) more efficiently distribute and efficiently use the resources of the enterprise;

5) predict the progress of the main stages of work, and timely adjust the timing;

6) carry out a multivariate economic analysis of various technological methods and the sequence of ways of performing work, as well as resource allocation.

7) promptly receive the necessary planned data on the actual state of the progress of work, costs and production results.

8) link in the process of planning and managing the work of the long-term general strategy and short-term specific chains of the enterprise.

The most important stages of network planning of production

Breakdown of the work package into separate components and their

assignment to responsible executors;

Identification and description by each performer of events and works necessary to achieve the goal;

Construction of primary network diagrams and clarification of the content of the planned work;

Stitching of private networks and building a consolidated network schedule for the implementation of a set of works;

Justification or clarification of the execution time of each work in the network schedule.

The breakdown (subdivision) of the complex of planned works is carried out by the project manager. In the course of network planning, two methods of distribution of work performed are used: division of functions between performers (horizontal distribution); building a project management level diagram (vertical distribution). In the first case, a simple system or object is subdivided into separate processes, parts or elements, for which a coarse network diagram can be built. Then each process is divided into operations, techniques and other calculated actions. A network schedule is created for each component of the work package. In the second case, a complex designed object is divided into separate parts by building a known hierarchical structure of the corresponding levels of project management.

Networking at each level is done by their supervisors or executives. Each of neither in the network planning process:

o draws up a primary network schedule for a given amount of work;

o assesses the progress of the work assigned to him and provides the necessary information to his management;

o participates jointly with employees of production departments or functional bodies in the preparation of planning and management decisions;

o ensures the implementation of the decisions made.

Primary network schedules, built at the level of responsible performers, should be detailed in such a way that they can reflect both the entire set of work performed and all existing relationships between individual works and events. First, it is necessary to identify what events will characterize the complex of work entrusted to the responsible executor. Each event should establish the completeness of the previous actions, for example: the goal of the project is chosen, the design methods are justified, the indicators of competitiveness are calculated, etc. It is recommended to list all events and works included in a given complex in the order of their execution.

The stitching of the network schedule is carried out by the responsible executor on the basis of the established list of works.

The final stage of network planning is the determination of the duration of individual work or cumulative processes. In deterministic models, the duration of the work is considered constant. In real conditions, the execution time for various jobs depends on a large number of factors (both internal and external) and therefore is considered a random variable. To establish the duration of any work, you must first of all use the appropriate standards or norms of labor costs. In the absence of the initial regulatory data, the duration of all processes and works can be established by various methods, including the use of expert assessments.

The duration of the planned process should be assessed by the most experienced experts, managers or responsible executors of the work. When choosing an assessment, it is necessary to make the most of the reference and regulatory materials available in production.

The resulting estimate should be considered as a time benchmark or a possible option for the duration of the work. If the design conditions change, the established estimates must be adjusted during the implementation of the network schedules.

In the process of network planning, expert estimates of the duration of the upcoming work are usually established by the responsible executors. For each job, as a rule, several time estimates are given: the minimum T min, maximum T tyakh and the most likely T iv. If the duration of work is determined by only one estimate of time, then it may turn out to be far from reality, which will lead to a violation of the entire course of work on the network schedule. Estimated work duration is expressed in man-hours, man-days, or other units of time.

Minimum time - this is the smallest possible working time of the designed processes. The likelihood of completing the work in such a time is small. Maximum time- this is the longest time to complete work, taking into account the risk and extremely unfortunate set of circumstances. Most likely time- this is a possible or close to real conditions time of work execution.

The obtained most probable estimate of time cannot be taken as a standard indicator of the expected time of work execution, since in most cases this estimate is subjective and largely depends on the experience of the responsible executor of the work. Therefore, in order to determine the expected execution time for each work, expert estimates are subjected to statistical processing.

In the practice of network planning, the most common method of the critical path (a network of the "vertex-event" type), in which the nodes represent the beginning or end of the final event of the work process and are depicted by circles, and the works themselves - by arrows.

The practical structuring of the project begins with the compilation of a list of works, in which all types of work are given with the appropriate conventions. It is rather difficult to define and thus differentiate between types of work. It is important to maintain the appropriate level of detail for the problem. The list of works contains the characteristics of the materials and capacities required for their implementation by type (personnel, machines, tools), terms and volumes.

In conclusion, the causal relationships between the works are consistently established. This is done either by setting the parameters of some jobs that immediately precede other jobs, or by specifying directly following works... After that, an appropriate network plan is drawn up.

Based on the marketing function (organization of the production process), the search for more effective ways to plan complex processes led to the creation of fundamentally new methods of network planning and management (STM).

The system of SPU methods is a system of planning and management methods for the development of large national economic complexes, scientific research, design and technological preparation of production, new types of products, construction and reconstruction, overhaul of fixed assets by using network diagrams.

SPU is based on modeling a process using a network diagram and is a set of calculation methods, organizational and control measures for planning and managing a complex of works.

The SPU system allows:

form a schedule for the implementation of a certain set of works;

identify and mobilize reserves of time, labor, material and financial resources;

to manage the complex of works on the principle of "leading link" with forecasting and prevention of possible disruptions in the course of work;

to increase the efficiency of management as a whole with a clear distribution of responsibilities between managers of different levels and performers of work.

6.2. The network model and its main elements

Network model is a plan for the implementation of a certain complex of interrelated works (operations), given in a specific form of a network, a graphical representation of which is called network schedule. A distinctive feature of the network model is a clear definition of all the temporal relationships of the upcoming work.

The main elements of the network model are developments and work.

Work- a time-consuming process that requires resources (for example, assembling a product, testing a device, etc.). Each valid work must be specific, clearly described and have a responsible executor.

Event- it is the moment of completion of a process, reflecting a separate stage of the project. An event can be a particular result of a single work or the summarized result of several activities. The event can happen only when all the work that preceded it is finished. Subsequent work can begin only when the event occurs. From here dual the nature of the event: for all immediately preceding works, it is final, and for all immediately following it - initial. Wherein it is assumed that the event has no duration and occurs as if instantly. Therefore, each event included in the network model must be fully, accurately and comprehensively defined, its formulation must include the result of all immediately preceding work.