Annotation: Structural planning. Calendar planning. Operational management. Practical classes on structural and calendar planning. Tasks for testing.

2.1. Theoretical course

2.1.1. Structural planning

Structural planning includes several stages:

1. the division of the project on the set of individual works, the execution of which is necessary for the implementation of the project;
2. construction of a network graph describing a sequence of work;
3. estimation of the time characteristics of the work and analysis of the network schedule.

The main role at the Structural Planning Stage is played by a network schedule.

Network graph - This is an oriented graph in which the vertices indicate the work of the project, and arcs are temporary interconnection of work.

Network schedule must satisfy the following properties.

1. Each work corresponds to one and only one vertex. No work can be represented on the network schedule twice. However, any work can be divided into several separate works, each of which will correspond to a separate summit of the schedule.
2. No work can be started before all the work directly by it will end. That is, if there are arcs in some vertex, then work can begin only after the end of all works, of which these arcs come out.
3. No work that directly follows some work can begin until its end. In other words, if there are several arcs from work, then none of the works in which these arcs enter cannot begin until the end of this work.
4. The beginning and end of the project are indicated by work with zero duration. Such works are called milestones And indicate the beginning or end of the most important stages of the project.

Example. As an example, consider the project "Development of the software package". Suppose the project consists of works, the characteristics of which are shown in Table 2.1.

Table 2.1.

Number of work	Job title	Duration
1	Start the project implementation	0
2	Formulation of the problem	10
3	Interface development	5
4	Development of data processing modules	7
5	Development of the database structure	6
6	Filling a database	8
7	Debugging software package	5
8	Testing and correcting errors	10
9	Drawing up software documentation	5
10	Completion of the project	0

Network graph for this project is depicted in Fig.2.1. On it tops corresponding to ordinary work, circled with a thin line, and the thickline of the project is circled by a thick line.

Fig. 2.1.

Network graph allows for the specified values \u200b\u200bof work durations to find the critical work of the project and its critical path.

Critical This work is called for which the delay of its start will lead to a delay in the end of the project as a whole. Such works do not have time stock. Non-critical works have some reserve of time, and within the limits of this stock, their beginning can be detained.

Critical Path - This is the way from the initial to the final top of the network graph, passing only through critical work. The total duration of the critical path work determines the minimum project implementation time.

Finding a critical path is reduced to finding critical works and is performed in two stages.

1. Calculation early start Each project work. This value shows the time before which the work cannot be started.
2. Calculation late start Each project work. This value shows the time later, the work cannot be started without increasing the duration of the entire project.

Critical works have the same value early and late start.

Denote - the time of performing work, - early start time, - late start time. Then

where - many works, directly preceding work. The early initial work time of the project is taken equal to zero.

Since the latest project work is a zero duration, early time it began to coincide with the duration of the entire project. Denote this magnitude. Now it is accepted in the late start of the last work, and for the rest of the work a later start time is calculated by the formula:

Here is a lot of work, directly following work.

Schematically calculations of the early and late start of the beginning are depicted, respectively, in Fig. 2.2 and Fig.2.3.

Fig. 2.2.

Fig. 2.3.

Example. We will find critical work and a critical path for the project "Development of the software package", which is shown in Fig. 2.1, and the duration of work is calculated for days and are specified in Table 2.1.

First calculate the early start of each work. Calculations start from the initial and end in the final work of the project. The process and results of calculations are shown in Fig.2.4.

The result of the first stage, in addition to early start of work, is the total project duration .

At the next stage, we calculate the time starting time. The calculations begin in the latter and end in the first work of the project. The process and results of the calculations are shown in Figure 2.5.

Fig. 2.4.

Fig. 2.5.

Consolidated calculation results are shown in Table 2.2. It is highlighted in pouring critical work. The critical path is obtained by connecting critical work on the network graphics. It is shown by dotted arrows in Fig.2.6.

Table 2.2.

Work	1	2	3	4	5	6	7	8	9	10
Early start time	0	0	10	16	10	16	24	29	29	39
Later, start time	0	0	12	17	10	16	24	29	34	39
Time Reserve	0	0	2	1	0	0	0	0	5	0

Introduction

Chapter I. Concept and Essence network planning and management

1.1. Essence of network planning and management methods

1.2. Elements and types of network models

Chapter II. Practical application of network planning and management models

2.1. Network Planning and Management Methods

2.2. Network graph

Conclusion

Literature

Introduction

IN modern conditions Socio-economic systems are becoming increasingly complex. Therefore, decisions made on the rationalization of their development should receive a strict scientific basis on the basis of mathematical and economic modeling.

One of the scientific analysis methods is network planning.

In Russia, work on network planning began in 1961-1962. And quickly got widespread. The works of Antonavichus K. A., Afanasyev V. A., Rusakova A. A., Leibman L. Ya, Mikhelson V. S., Pankratova Yu. P., Rybalksky V.I., Smirnova T. I. , Tsaya T. N. and others. ,,

From numerous studies of individual aspects of network methods for planning and management, a transition to the system use of a new planning methodology was carried out. In literature and practice, the attitude towards network planning is increasingly widespread. Not only as an analysis method, but also as a developed planning and management system adapted for a very wide range of problems.

For years practical use In Russia and abroad, network planning has shown efficiency in a wide variety of spheres of economic and organizational analysis.

The need to use network planning methods in the management of management systems is explained by many variety of planning models: graphics and tables, physical models, logical and mathematical expressions, machine models, simulation models.

Of particular interest is the network method for a formalized presentation of control systems, which is reduced to building a network model to solve a comprehensive management task. The basis of network planning is the information dynamic network model in which the entire complex is dismembered into separate, well-defined operations (operation) located in a strict technological sequence of their execution. When analyzing the network model, a quantitative, temporary and value assessment of the work performed is performed. Parameters are specified for each work included in the work network based on regulatory data or its production experience.

With imitation dynamic modeling A model is built, adequately reflecting the internal structure of the simulated system; Then the behavior of the model is checked on a computer at an arbitrarily a long time. This makes it possible to investigate the behavior as a system as a whole and its components. Simulation dynamic models use a specific apparatus, which makes it possible to reflect the causal relations between the elements of the system and the dynamics of changes in each element. Models of real systems typically contain a significant number of variables, so their imitation is carried out on the computer.

Thus, the topic of study of network planning methods is relevant, because A graphical representation not only gives an idea of \u200b\u200ba complex process, but also allows you to carry out a versatile study of the project management system.

Based on the above arguments of the relevance and theme of work, it is possible to formulate the purpose of the work - the coverage of network planning and management methods in the study of socio-economic and political processes.

To achieve the goal, the following tasks are set and solved:

1. The analysis of network planning and management.

2. Revealed the essence of network planning and management methods

3. The types of network planning and management methods, the scope of their application has been studied.

4. The basis of the practical application of network planning and management methods is considered.

The subject of the study of my course work is the methodology of network planning and management.

The object of my course work is the scope of application of network planning and management methodology.

Chapter I. . The concept and essence of network planning and management

1.1. Essence of network planning methods

Network planning - This is a complex of graphic and settlement methods of organizational events that provide modeling, analysis and dynamic restructuring of a plan for comprehensive projects and developments, such as:

· Construction and reconstruction of any objects;

· Implementation of research and design work;

· Preparation of production to product production;

· Re-equipment of the army.

A characteristic feature of such projects is that they consist of a number of individual, elementary work. They cause each other so that the performance of some works can not be started earlier than some others have completed.

Basic target Network planning and management is a reduction to a minimum of the project duration.

A task Network planning and management is to graphically, clearly and systematically display and optimize the sequence and interdependence of work, actions or activities that ensure timely and systematic achievement of the final goals.

To display and algorithm for certain actions or situations, economic and mathematical models are used, which are customary to call network models, the simplest of them are network graphics. With the help of the network model, the work manager or operation has the ability to systematically and largely represent the entire course of work or operational activities, to manage the process of their implementation, as well as maneuver resources.

In all network planning systems, the main object of modeling serves a variety of complexes of upcoming work, such as socio-economic research, design developments, development, production of new products and other planned activities.

SPU system allows:

· To form a calendar plan for the implementation of some complex of work;

· Identify and mobilize time reserves, labor, material and money resources;

· Implement a complex of work on the principle of "leading link" with predicting and preventing possible disruptions during the work;

· Improve the effectiveness of the management as a whole with a clear distribution of liability between the leaders of different levels and performers;

· Clearly display the volume and structure of the problem being solved, to identify with any required degree of work detail, forming a single complex of the problem of solving the problem; identify events that are required to achieve the targets;

· To identify and comprehensively analyze the relationship between the works, since in the most methods for constructing a network model, an accurate reflection of all dependencies due to the state of the object and the conditions of the external and internal environment are laid;

· Widely use computing techniques;

· Quickly process large amounts of reporting data and provide guidance timely and comprehensive information on the actual status of the program;

· Simplify and unify reporting documentation.

The range of applications is quite wide: from the tasks relating to the activities of individuals to projects in which hundreds of organizations and tens of thousands of people participate.

The network model is a description of a complex of work (complex of operations, project). Under it is understood every task, to perform which it is necessary to implement enough a large number of A variety of actions. This may be the creation of any complex object, the development of its project and the process of building project implementation plans.

The use of network planning methods contributes to a reduction in the timing of creating new objects by 15-20%, to ensure rational use labor resources and technology.

The most effective areas of application of network methods for planning and management are the management of major target programs, scientific and technical developments and investment projects, as well as complex complexes of social, economic and organizational and technical measures at the federal and regional levels.

1.2. Elements and types of network models

Network models consist of three following elements:

· Work (or task)

· Event (milestones)

· Communication (dependence)

Work ( A. ctivity) - This is a process that needs to be performed to obtain a specific (specified) result, as a rule, which makes it possible to proceed to subsequent actions. The terms "task" (task) and "work" can be identical, but in some cases the tasks are made to be called the implementation of actions beyond the scope of direct production, such as "project documentation examination" or "negotiations with the customer". Sometimes the concept of "task" is used to display works by low level hierarchy.

The term "work" is used in the broad sense of the word, and may have the following values:

· valid work , that is, the labor process that requires the cost of time and resources;

· expectation - process requiring time, but not consuming resources;

· addiction or "fictitious work" - work that does not require time and resources, but indicating that the possibility of the beginning of one work directly depends on the results of the other.

International University of Nature, Society and Man
"Dubna"

Department system analysis and management

Abstract on discipline

"Development management solutions»

"Network management
and planning "

Is done by a student
Shadrov K.N., gr. 4111.

Checked:
Bugrov A.N.

Introduction

Relevance This work is due to the need for competent management of large national economic complexes and projects, research, design and technological preparation of production, new types of products, construction and reconstruction, overhaul of fixed assets by applying network models.

purpose Works - describe and assimilate that, in general, is network planning and management (SPU).

To achieve the goal, the following should be solved tasks:

Ø Light the History of SPU,

Ø Show, what is the essence and purpose of SPU,

Ø to define the main elements of SPU,

Ø Specify the rules for building and streamlining network graphs,

Ø Describe SPU temporary indicators

Ø to optimize network graphics,

Ø Show construction of network graphics on time.

History of network planning and management

Network planning techniques were developed in the late 50s in the United States. In 1956, M. Walker from the company "DUPON", exploring the possibilities of more efficient use by the UNIVAC computing car, combined his efforts from D. Kelly from the planning group of the Capital construction of Remington Rand. They tried to use the computer to draw up schedules of large complexes of work on the modernization of Dupont factories. As a result, a rational and simple method for describing the project using a computer was created. Initially, he was named by Walker Celly, and later received a name method of critical path - MCP (or CPM - Critical Path Method).

In parallel and independently in the US naval forces, the method of analysis and evaluation of PERT programs was created (Program Evaluation and Review Technique). This method was developed by Lockhid and the Consulting Firm "Buz, Allen and Hamilton" to implement the project to develop a Polaris Rocket System, which combines about 3,800 main contractors and consisting of 60 thousand operations. The use of the PERT method allowed the program management to know exactly what to do at every moment of time and who exactly should do it, as well as the likelihood of timely completion of individual operations. The program management turned out to be so successful that the project managed to complete two years before the planned term. Thanks to this successful start, this management method soon began to be used to plan projects in all US Armed Forces. The technique has proven itself in the coordination of works performed by various contractors within large projects for the development of new types of weapons.

Large industrial corporations began to apply such a management technique almost simultaneously with the military to develop new types of products and modernization of production. The general application of the work planning methodology based on the project was in construction. For example, to control the project of a hydroelectric power station on the Churchill River in Newfoundland (Labrador Peninsula). The cost of the project amounted to 950 million dollars. The hydroelectric power station was built from 1967 to 1976. This project included more than 100 construction contracts, and the cost of some of them reached $ 76 million. In 1974, the progress of work on the project was ahead of the schedule for 18 months and was placed in the planning estimate of costs. The Customer of the project was Churchill Falls Labrador Corp., which has hired ACRESS CANADIAN BETCHEL to develop a project and management of construction.

Essentially, a significant time gain was formed from the use of accurate mathematical methods in the management of complex work complexes, which was made possible by the development of computing technology. However, the first computers were roads and are available only to large organizations. Thus, historically, the first projects were represented from themselves grand scale, the number of performers and investments state programs.

Initially, large companies Implemented software development software to support their own projects, but soon the first project management systems appeared in the software market. Systems stood at the sources of planning were designed for powerful large computers and mini-computer networks.

The main indicators of the systems of this class were their high power and, at the same time, the ability to describe projects in sufficient detail using complex methods Network planning. These systems were focused on highly professional managers who manage the development of largest projects that are familiar with network planning algorithms and specific terminology. As a rule, the project development and advice on project management was carried out by special consulting firms.

Stage The most rapid development of systems for project management began with the advent of personal computers, when the computer became a working tool for a wide range of managers. Significant expansion of the circle of users of managerial systems generated the need to create systems for managing new type projects, one of the most important indicators Such systems were easy to use. The new generation management systems were developed as a project management tool understandable to any manager, which does not require special training and ensuring easy and fast inclusion in the work. Time Line belongs to this class of systems. Developers of new versions of the systems of this class, trying to preserve the external simplicity of systems, invariably expanded their functionality and power, and at the same time they retained low priceswho have made systems available to the firms of almost any level.

Currently there are deep traditions of using project management systems in many areas of vital activity. Moreover, the main share among planned projects make up small projects. For example, the studies conducted by the InfoWorld weekly showed that fifty percent of users in the United States requires systems to maintain plans consisting of 500-1,000 works and only 28 percent of users develop schedules containing more than 1,000 work. As for resources, 38 percent of users have to manage 50-100 types of resources within the project, and only 28 percent of users need to control more than 100 types of resources. As a result of the research, the average sizes of project schedules were also identified: for small projects - 81 work and 14 types of resources, for averages - 417 works and 47 types of resources, for large projects - 1.18 works and 165 types of resources. These figures can serve as a starting point for the manager, which is considering the usefulness of the transition to the design form of managing the activities of its own organization. As we see, the application of the project management system in practice can be effective for very small projects.

Naturally, with the expansion of the circle of users of project management systems, the methods and methods of their use occur. Western industry journals regularly publish articles on project management systems, including tips to users of such systems and an analysis of the use of network planning techniques to solve problems in various management spheres.

In Russia, network management work began in the 60s. Then the methods of SPU were used in construction and scientific research. In the future, the network methods began to be widely applied in other areas of the national economy.

Essence and appointment of network planning and management

The more difficult and more planned work or project, the more difficult tasks of operational planning, control and management. Under these conditions, the application of the calendar graph cannot always be sufficiently satisfactory, especially for a large and complex object, because it does not allow to reasonably and promptly plan, choose the optimal version of the duration of the work, use reserves and adjust the schedule during activities.

The listed shortcomings of the linear calendar graph are largely eliminated when using a network models that allow you to analyze the schedule, identify the reserves and use electronic computing techniques. The use of network models provides a thoughtful detailed organization of work, creates conditions for effective manual.

The whole process is reflected in the graphic model called the network schedule. In the network chart, all the design work is taken into account before commissioning, the most important, critical work is determined, from the execution of the end of the project. During the activity, it is possible to adjust the plan, make changes, ensure continuity in operational planning. Existing methods for analyzing a network schedule make it possible to estimate the degree of influence of changes made to the implementation of the program, predict the status of work for the future. The network schedule accurately indicates works on which the program is depends on.

Basic network planning and management elements

Network planning and management - This is a combination of settlement methods, organizational and control measures for planning and managing a complex of work using a network graph (network model).

Under complex of work We will understand all the task, to fulfill which it is necessary to carry out a sufficiently large number of diverse works.

In order to compile a plan for the implementation of large and complex projects consisting of thousands of individual studies and operations, it is necessary to describe it with a certain mathematical model. This means of describing projects is a network model.

Network model - This is a plan for performing some complex of interrelated work specified in the form of a network, which is called the graphic image network graph.

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

The term work in SPU has several values. First, it is valid work - the process extended in time, requiring resource costs (for example, a product assembly, instrument test, etc.). Each valid work must be concrete, clearly described and have a responsible performer.

Secondly, it expectation - the process extended in time, which does not require labor costs (for example, the drying process after painting, aging of metal, hardening concrete, etc.).

Thirdly, it is addiction, or fictive work - Logic connection between two or several works (events) that do not require labor costs, material resources or time. It indicates that the possibility of one job directly depends on the results of the other. Naturally, the duration of the fictitious work is taken equal to zero.

Event is the moment of completion of a process, reflecting a separate stage of project execution.. The event may be a private result of a separate work or a total result of several works. The event can be accomplished only when all the works will end, it is preceding. Subsequent works can start only when the event is accomplished. From here the dual character of the event: For all the work directly, it is the final, and for all directly following it - initial. It is assumed that the event has no duration and is accomplished as if instantly. Therefore, each event, included in the network model, must be fully, accurately and comprehensively determined, its formulation should include the result of all the work previously preceding it.

Picture1 . The main elements of the network model

When drawing up network graphs (models) use legend. Events on network graphics (or, as they say, on the grade) are depicted with circles (vertices of the graph), and work - arrows (oriented arcs):

¡- Event,

Work (process),

Fictive work - applied to simplify network graphs (duration is always equal to 0).

Among the network models, the original and final events allocate. The initial event has no preceding work and events relating to the workflow presented in the model. The final event does not have subsequent work and events.

There is another principle of building networks - without events. In such a network of the vertex, the graph means certain works, and the arrows are the dependencies between the works that determine their execution. The network schedule of "jobs", unlike the "event-work" schedule, has well-known advantages: does not contain fictitious works, has more simple technique Building and restructuring, includes only a well-known performer's concept of work without the less familiar concept of an event.

At the same time, the network without events are significantly more cumbersome, as events are usually significantly less than work ( network complexity rateequal to the ratio of the number of work to the number of events, as a rule, is significantly more than one). Therefore, these networks are less effective in terms of complex management. This explains the fact that now the highest distribution was the network charts of "Event Works".

If there are no numerical estimates in the network model, then such a network is called structural. However, in practice, networks are most often used, in which estimates of the duration of work, as well as estimates of other parameters, for example, complexity, cost, etc.

Order and rules for building network graphs

Network graphics are compiled at the initial planning stage. Initially, the planned process is divided into separate work, a list of works and events is drawn up, their logical connections and a sequence of execution are thought out, work is confined for responsible performers. With their help and with the help of standards, if such exist, the duration of each work is estimated. Then compiled ( stitched) Network graph. After streamlining the network graph, the parameters of events and work are calculated, time reserves are determined and critical Path. Finally, the analysis and optimization of the network graphics are carried out, which, if necessary, is drawn up to recalculate the parameters of events and work.

When building a network graph, you must follow the rules.

1. There should be no "dead-up" events in the network model, that is, events from which no work does not come out, with the exception of the final event. Here, either the work is not needed and it is necessary to cancel, or the need for a certain work following the event is not noticed to achieve any subsequent event. In such cases, it is necessary to carefully study the relationship between events and work to correct the misunderstanding.

2. In the network chart should not be "tail" events (except for the initial), which are not preceded by at least one job. Finding such events on the Web, it is necessary to identify the performers of the previous works and include these work on the network.

3. There should be no closed contours and loops on the network, that is, paths connecting some events with themselves. If the circuit occurs (and in complex networks, that is, in networks with a high rate of complexity, it is found quite often and detected only with the help of a computer) it is necessary to return to the initial data and the revision of the composition of work to achieve its elimination.

4. Any two events should be directly related to no more than one work-arrow.. Violation of this condition occurs when an image of parallel works. If you leave these works, it will be confused due to the fact that two different works will have the same designation. However, the content of these works, the composition of the convicted performers and the number of resources spent on the work may differ significantly.

In this case, it is recommended to enter fictive event and fictive workAt the same time, one of the parallel works closes this fictitious event. Fictive work is depicted on the graph of dotted lines.

Figure 2. Examples of the introduction of fictitious events

Fictive work and events must be administered in a number of other cases. One of them is a reflection of the dependence of events that are not related to real works. For example, work A and B (Figure 2, a) can be performed independently of each other, but under the terms of production, work would not begin earlier than the work of the work of A. This circumstance requires the introduction of fictitious work S.

Another case is an incomplete dependence of the work. For example, work with requires it to start the completion of works A and B, on the work of D is connected only with the work of B, and from work and does not depend. Then the introduction of fictitious work f and a fictitious event 3 'is required, as shown in Figure 2, b.

In addition, fictitious works can be administered to reflect the real delay and expectations. In contrast to the previous cases, the fictitious work is characterized here in time.

If the network has one end target, the program is called monocelter. A network schedule having several final events is called multipurpose and the calculation is carried out relative to each end target. An example is the construction of a residential microdistrict, where the entry of each house is the final result, and in the graph on the construction of each house its critical path is determined.

Streamlining network graphics

Suppose that when compiling some project, 12 events are allocated: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 24 binding their works: (0, 1), (0, 2 ), (0, 3), (1, 2), (1, 4), (1, 5), (2, 3), (2, 5), (2, 7), (3, 6), (3, 7), (3, 10), (4, 8), (5, 8), (5, 7), (6, 10), (7, 6), (7, 8), (7 , 9), (7, 10), (8, 9), (9, 11), (10, 9), (10, 11). Calculated the original network graph 1.

The ordering of the network graph is in this location of events and works, in which the Event preceding it is located to the left and has a smaller number compared to the event that finalizes this operation.. In other words, in an ordered network chart, all work-arrows are directed from left to right: from events with smaller numbers to events with large numbers.

We separate the original network schedule for a few vertical layers (we supply them with dashed lines and denote Roman numbers).

Having placed the initial event 0 in the first layer, mentally cross out from the chart this event and all overlooking it work-arrows. Then, without incoming arrows, an event 1 will remain, forming II layer. Having shutting up a mentally eventful event 1 and all the work out of it, we will see that events 4 and 2 remain without incoming arrows, which form the III layer. Continuing this process, we get a network graph 2.

Network Chart 1. Disordered Network Schedule

Network Schedule 2. Ordering a network graph with a layer

Now we see that the initial numbering of events is not entirely correct: so, the event 6 lies in the VI layer and has a number smaller than an event 7 from the previous layer. The same can be said about events 9 and 10.

Network Chart 3. Ordered Network Schedule

Change the numbering of events according to their location on the graph and obtain an ordered network graph 3. It should be noted that the numbering of events located in one vertical layer does not have a fundamental value, so that the numbering of the same network graphic may be ambiguous.

Concept of way

One of the most important concepts of network graphics is the concept of the path. The path is any sequence of work in which the final event of each work coincides with the initial event of the next job. Among different paths Network graphics is the greatest interest full way- Any way, the beginning of which coincides with the source event of the network, and the end - with the final.

The most prolonged full path in the network chart is called critical. Critical is also called work and events on this path.

On the network graph 4, the critical path passes through the works (1; 2), (2; 5), (5; 6), (6; 8) and equal to 16. This means that all work will be completed for 16 times of time. The critical path is of particular importance in the SPU system, since the work of this path will determine the overall cycle of completion of the entire complex of work planned using a network schedule. Knowing the start date of work and the duration of the critical path, you can set the end date of the entire program. Any increase in the duration of work on the critical path will delay the execution of the program.

Network Schedule 4. Critical Path

At the stage of management and control over the progress of the program, the focus is on the work at the critical path or by virtue of the lag behind the critical path. To reduce the duration of the project, it is primarily necessary to reduce the duration of work under the critical path.

Time Parameters of Network Graphs

Early (or expected) Determined by the duration of the maximum path preceding this event.

The delay in the accomplishment of an event in relation to its early term will not affect the term of the completion of the final event (and therefore on the period of execution of the work complex): as long as the amount of the achievement of this event and duration (length) of the maximum of the following paths will not exceed Critical path lengths.

therefore late (or limit) Death Determination Event It is equal to the difference in the maximum occurrence of the subsequent work of the event and the time of work before this (future) event.

Event time reserve Determined as the difference between the late and early deadlines for its accomplishment.

The event time reserve shows for which permissible period of time you can delay the onset of this event, without causing an increase in the period of execution of the complex of work.

Critical events of time reserves do not have, since any delay in the accomplishment of an event lying on the critical path will cause the same delay in the accomplishment of the final event.

It follows from this that in order to determine the length and topology of the critical path, it is not necessary to sort out all the full paths of the network schedule and determine their lengths. By defining the early term of the onset of the end of the network, we thus define the length of the critical path, and, identifying events with zero time reserves, we determine its topology.

If the network schedule has a single critical path, then this path passes through all critical events, that is, events with zero time reserves. If there are several critical paths, then the detection of them using critical events may be difficult, since through part of critical events, both critical and non-critical paths can be held. In this case, to determine the critical paths it is recommended to use critical work.

Separate work can begin (and end) in early, late or other interimatons. In the future, when optimizing the graph, any placement of work in a given interval is called, called workpiece.

It's obvious that early life Coincides with an early occurrence of the previous event.

Early deadline Coincides with an early deprivation of the subsequent event.

Late start of work Coincides with the late events of the previous event.

Late deadline Coincides at a late occurrence of the subsequent event.

Thus, in the framework of the network model, the starting and ending moments are closely related to neighboring events with relevant restrictions.

If the path is not critical, then it has Time Reserve, defined as the difference between the critical path length and the considered. It shows how long the duration of all works belonging to this path can be increased. From here we can conclude that any of the work paths on its site, which does not match the critical way (closed between the two events of the critical path), has a time reserve.

Among the work time reserves, four varieties are distinguished.

Full time reserve Work shows how much time you can increase the execution time of this work, provided that the deadline for execution of the work complex will not change.

A complete reserve of work time is equal to the reserve of maximum from paths passing through this work. This reserve can be placed when performing this work, if its initial event is accomplished on the earliest period, and one can admit the achievement of the final event in its latest term.

An important property of the full time reserve is the fact that it belongs not only to this work, but also with all the full ways passing through it. When using a full time reserve, only for one work reserves of the remaining works lying on the maximum path passing through it will be completely exhausted. Reserves of work time lying on other (neximum duration) paths passing through this work will be reduced by the value of the used reserve, respectively.

The remaining reserves of work time are parts of its full reserve.

Private reserve of the first type of time There is a part of the full time reserve to which you can increase the duration of work without changing the late period of its initial event. This reserve can be placed when performing this work under the assumption that its initial and final events are accomplished in their most late time.

Private time reserve of the second type, or free time reserve The work represents a part of the full time reserve on which you can increase the duration of work without changing the early period of its final event. This reserve can be placed when performing this work under the assumption that its initial and final events are accomplished in its earlier time.

A free time reserve can be used to prevent accidents that may arise during work. If you plan to work on the early periods of their start and end, it will always be possible if necessary to switch to the late periods of start and end of work.

Independent time reserve Works - part of the full time reserve obtained for the case when all previous works are completed at the later dates, and all subsequent works begin in early terms.

The use of an independent time reserve does not affect the value of other work reserves. Independent reserves seek to use when the end of the previous work occurred in the late permissible period, and the subsequent works want to fulfill in early terms. If the value of an independent reserve is zero or positive, then such an opportunity is. If this value is negative, then this possibility is not, since the previous work does not end yet, and the subsequent must begin. I.e negative meaning This magnitude has no real meaning. In fact, the independent reserve has only those works that do not lie on the maximum paths passing through their initial and end events.

Thus, if a private reserve of the first type of time can be used to increase the duration of this and subsequent work without the cost of the time of the preceding work, and the free reserve of times - to increase the duration of this and preceding work without disrupting the time reserve for subsequent work without disrupting the time reserve The independent time spent can be used to increase the duration of this work only.

Works lying on the critical path, as well as critical events, have no time reserves.

Figure 3. Key to calculate the sector method

It should be noted that in the case of sufficiently simple network graphs except the table method for calculating network graphs, can be applied sectoral view Time parameters, that is, the calculation of the parameters can be produced on the graph. Each event for this is divided into four sectors. In the left sector, the events write down the early start of work, in the right - later the end, in the upper - the number of this event, in the lower - the number of the previous event, from which the maximum duration goes to this event. There is a place when the event number is set in the lower sector and the upper sector is not filled. Certain time reserves are recorded under the arrow in the form of a fraction: in a numerator, a common reserve, and in the denominator a private reserve.

Network graph 5. Sector representation of temporary parameters

In practice, the duration of work, the actual state may change. This may vary and the expected time of the event, the end of the work and the critical path. Knowing the critical way, the management can focus on those works that are decisive in terms of the deadlines of the end of all works.

Analysis and optimization of network graphics

After finding a critical path and reserves of work time and evaluating the likelihood of a project for a specified period, a comprehensive analysis of the network schedule must be carried out and measures taken to optimize it. This very important stage in the development of network graphs reveals the basic idea of \u200b\u200bSPU. It consists in bringing a network schedule in accordance with the specified deadlines and the possibilities of the organization developing the project.

Optimization of the network graph, depending on the completeness of the solid tasks, can be conditionally divided into private and complex. See private optimization Network graphics are: minimizing the time of execution of a complex of work at a given value; Minimizing the cost of a complex of work at a given time of project execution. Comprehensive optimization It is the foundation of the optimal ratio of the values \u200b\u200bof the value and the timing of the project, depending on the specific purposes that are applied during its implementation.

First, consider the analysis and optimization of calendar networks, in which only the duration of work is given.

An analysis of the network graph begins with the analysis of the network topology, which includes controlling the construction of a network schedule, the establishment of the feasibility of choosing work, the degree of dismemberment.

Then the classification and grouping of reserve values \u200b\u200bare carried out. It should be noted that the value of the full time reserve is far from always can accurately characterize how intense is the implementation of one or another work of the non-critical path. It all depends on how the sequence of work is subject to the calculated reserve, what is the duration of this sequence.

It is possible to determine the degree of difficulty of execution on the term of each group of work of the non-critical path using the voltage coefficient of work.

The voltage coefficient of work It is called the ratio of the duration of the inconsistent, but prisoners between the same events, segments of the path, one of which is the path of maximum duration passing through this work, and the other is a critical way.

This coefficient can vary in the range from 0 (for work, in which the segments of the maximum of the paths that do not coincide with the critical way, consist of fictitious work of zero duration) to 1 (for the work of the critical path).

We draw attention to the fact that a larger full reserve of one work (compared to the other) does not necessarily indicate a lesser degree of its strength. This is due to the different specific weighing of full reserves of work in the length of segments of maximum paths that do not coincide with the critical way.

The calculated voltage coefficients allow you to further classify work on zones:

Ø Critical to\u003e 0.8,

Ø Podcritical 0.6< К < 0,8,

Ø Reserve K.< 0,6.

Optimization of a network graph represents the process of improving the organization of the execution of a complex of work, taking into account the period of its implementation. Optimization is carried out in order to reduce the length of the critical path, aligning the coefficients of working voltage, rational use of resources.

First of all, measures are taken to reduce the duration of work on the critical path. This is achieved:

Ø by the redistribution of all types of resources, both temporary (the use of reserves of non-critical pathways) and labor, material, energy, while the redistribution of resources should take, as a rule, from zones, less tense, in zones that combine the most stressful work.

For example, it is possible to increase the replacement of work on the "narrow" sites of construction. This event is most efficient because it allows you to achieve the desired result with the same leading machines (excavator, machine, etc.), only increasing the number of workers.

Ø reduction in the time consideration of critical work due to the transfer of part of work on other ways that have time reserves;

Ø Revision of network topology, change in the composition of the work and network structure.

Ø to ensure the holding of parallel (combined) works;

Ø divide the wide front of work on smaller captures or sections;

Ø Reduce the duration of the program can be changed by changing the technology used, for example, in the construction, replacement of monolithic reinforced concrete structures with prefabs, other prefabricated elements manufactured at the factory.

By adjusting the graphics, it should be borne in mind that the workers are saturated with resources to a certain limit (so that each worker is provided with a sufficient front of the work and has the opportunity to comply with safety regulations).

In the process of reducing the duration of work, the critical path may change, and in the future the optimization process will be aimed at reducing the duration of the work of the new critical path and will continue until a satisfactory result is obtained. Ideally, the length of any of the full paths can be equal to the length of the critical path or at least the path of the critical zone. Then all the work will be carried out with equal stress, and the deadline for completion of the project will be significantly reduced.

The most obvious version of the private optimization of a network schedule, taking into account the cost implies the use of work time reserves. The duration of each work that has time reserves increases until this reserve is exhausted, or the top value will not be reached. The duration of each work is advisable to increase by the amount of such a reserve, so as not to change the early time of the onset of all network events, that is, the amount of a free time reserve.

In practice, when attempts to effectively improve the plan, an inevitable introduction additionally to estimates of the timing of the cost of the cost of work. The project may require the acceleration of its implementation, which, naturally, will affect the cost: it will increase. Therefore, it is necessary to determine the optimal ratio between the cost of the project and the duration of its implementation.

When using the "Time-value" method, it is assumed that the reduction in the duration of work is proportional to the increase in its value. Increasing value with a decrease in time is called atrates on acceleration.

It is very effective to use the method of statistical modeling based on multiple consistent changes in the duration of work (at specified limits) and "playback" on the computer different options Network graphics with calculations of all its time parameters and coefficients of work voltage.

For example, you can take as an initial plan having minimal values \u200b\u200bof the duration of work and, accordingly, the maximum cost of the project. And then consistently increase the duration of the completion of the complex of work by increasing the duration of work located on non-critical, and then on critical (critical) paths to a satisfactory value of the project cost. Accordingly, it is possible to take a source plan having a maximum duration of work, and then sequentially reduce their duration to such an acceptable value of the project.

The process of "playback" continues until an acceptable version of the plan is obtained or it will not be established that all the existing opportunities for improving the plan are exhausted and the conditions are not fulfilled before the project developer.

Currently, in practice, the network is first corrected in time, that is, leading it to a given period of construction. Then projected the adjustment of the schedule on the distribution criterion of resources, starting with labor resources.

It should be noted that with the linear dependence of the cost of work on their duration, the task of constructing the optimal network graphics can be formulated as a task. linear programmingIn which it is necessary to minimize the cost of project implementation during restriction, firstly, the duration of each work under the established limits, and, secondly, the duration of any full path of the network graphic of no more established period of project execution.

Building a network schedule on time scale

In practice, network graphics drawn up on the scale of time with reference to calendar periods were distributed. When monitoring the work of work, such a schedule will quickly find work performed at a certain period of time, to establish their advance or lag and, if necessary, redistribute resources.

A network schedule, which has a scale of time, makes it possible to build charts of the need for resources and thereby establish correspondence to their actual presence. Building a network graphic across the time scale is made in early origin or late endings of work and goes sequentially from the source event to the final.

Binding a network schedule to a calendar is conveniently performed using a calendar line, into which years, months and numbers are recorded (without days off and holidays). Using the table, you can easily find the calendar date of the beginning or end of work.

Network graph 6. Network schedule on time scale

In cases of changes in the source data and the actual stroke of work, the network schedule compiled in relation to scale causes complications when adjusting it. Therefore, this method is applicable for relatively small network graphs.

Conclusion

Based on the foregoing, it can be argued that the methods of network planning and management provide managers and performers at all areas of work with informed information, which is necessary for them to make decisions on planning, organization and management. And when using computing equipment, SPU is no longer just one of the planning methods, but an automated management method production process.

Used sources

1. webforum.land.ru - Project Management Forum in Russia.

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Network planning - the method of analyzing the timing (early and later) beginning and end of the unrealized parts of the project, makes it possible to link the implementation of various works and processes over time, having received a forecast of the total duration of the entire project.

The method appeared by combining two methods:

The first method is the method of critical path developed in 1956 by a specialist in the field of computational technology from the company "DUPON" M. Walker and D. Kelly, who worked in the planning group of the capital construction of Remington Rad.

The second method is the method for assessing and analyzing programs developed in the US naval forces.

The combined method was called network planning and management method.

Network planning and management contains three main stages:

Structural planning;

Calendar planning;

Operational management.

The purpose of structural planning is to describe the composition and interconnection of technological operations that are required to implement the project. In network planning theory, such operations are called works or tasks. In addition, this step needs to determine the duration of work. The result of structural planning is a network schedule of the project.

The network graph consists of elements of two types - works and events - and allows in a visual form to present the structure of the project from the point of view of work within it. In other words, the network schedule displays the relationship between the works within the project and the procedure for their execution. Network graph allows, first of all, to estimate the temporary characteristics of the project and the works of it. In this regard, the so-called critical work in the construction of the project plan has the most important. The work is considered critical if the delay of its start leads to a delay in the end of the project as a whole. Noncritical work is characterized by the fact that the time interval between its early start and late ending more of its actual duration. The critical path is a continuous sequence of critical work, connecting the original and final network events. To build a critical path, it is necessary to identify all the critical work of the project.

The process of solving problems associated with the purpose and distribution of resources occurs at the next stage of network planning - at the stage of constructing a calendar schedule. The calendar schedule is based on the Ganta chart. The Gantt diagram is a linear schedule that sets the deadlines for the start and end of interrelated work, indicating the resources used for their implementation.

The logical sequence of operations (works) can be illustrated using a graph. There are various types of graphs, but two types obtained the most widely used: the so-called vertex and shooting graphs. However, each of them has its advantages and disadvantages, and the choice of one or another graph is a question of personal preferences or is determined to create and use this graph.

In the arrow type of graphs each work is represented by the arrow. The length of the arrows does not matter. The direction of the arrow reflects the time of time and is usually indicated from left to right. The beginning and end of each work is called events and are depicted on the column with circles or node.

The works are denoted by the letter or word, and the events are a number. Since any work is characterized by a pair of events, it can also be denoted by the numbers corresponding to these events. One node may correspond to (enter or out of it) several operations. The event depicted on the column with the help of a node is not considered to be accomplished until all the works included in it are completed. Work coming out of some node can not start until the initial event is reached, i.e. Until all the works included in the nodal initial event are completed.

The fictitious logical arrow is entered into the graph, if it is necessary to reflect that some event can not appear before another event, and with the help of ordinary arrows corresponding to the work, this cannot be done. The function of the fictitious logical operation is to show the sequence of events.

The fictitious logical work is put in accordance with the zero duration of the execution, and they are usually depicted by a dotted line.

In the vertex type of network graphs of work is represented by the assembly nodes, and the arrows depict their relationship. In such graphs, there is no need to introduce fictitious operations. As in the previous case, the flow of time should be depicted in the direction from left to right.

Each of the described types of graphs has its advantages and disadvantages. It is usually not fundamental importance which of the systems is used. If the shooters have to enter a sufficiently large number of fictitious operations, it is much more preferable.

Conclusions of 1 chapter

There is a wide variety of selection of software tools intended to solve planning, accompaniment and project implementation. They differ by scale scope: project management systems for small and medium enterprises and project management systems for large corporations, enterprises - professional project management systems.

In this term paper It will be about project management systems for small and medium enterprises as systems that are most widely used in our country in connection with the market and more and more enterprises and firms. In particular, we will consider the Microsoft Project project management system.

Microsoft Project is an ideal project management system.

First, the system provides for the majority of the necessary functions.

Secondly, Microsoft Office is the most common office attachment not only in Russia, but also in the world. This is very important for example to integrate applications.

Yet an important detail Project management using autonomous applications is getting competitive advantageWith respect to the response time to changes in projects. Now there is no need to have a strong profile education (it certainly does not prevent), the system itself will solve all the problems that arise during the planning.

Bibliographic Description:

Nesterov AK Network planning [Electronic resource] // Educational encyclopedia website

The main purpose of the network planning methodology in managing to reduce to a minimum of the project duration. With the help of network models, the head can systematically evaluate the current and promising course of planned operations, due to which it is possible to control the project implementation process as a whole. Calendar-network planning also allows you to rationally operate with the resources available.

Purpose and tasks of network planning

The main goal of network planning follows from its purpose: to build a model for implementing a project based on the formation of a complex of work, the tasks of their order, determine required resources And the tasks that must be solved to complete the project. As a result, it is necessary to reduce to a minimum of the project's duration.

The network planning method allows you to coordinate the activities of the project participants, determine the order according to which planned work, operations, actions should be performed. In this case, the basis is the duration of each operation, the actions that should be determined taking into account the needs for material, labor and financial resources.

- This is a method of management based on the mathematical apparatus of the theory of graphs and a systematic approach, pursues the tasks of objective construction of the operation plan for a given period of time due to the algorithmization of interrelated work. Thanks to this approach, the goal is achieved.

The application of the network planning methodology in management involves the formalization of the operational structure in a table form, on the basis of which the operations are structuring on time segments and the grouping of parallel operations to optimally perform the entire project as a whole. On the basis of this, the operation table is built into which all significant data on each operation is reduced in accordance with the formalized structure of operations and groups of parallel operations. The result is the construction of a network diagram, which is subject to adjustment in the event of a non-compliance of the planned actions by the total period of their execution, or certain periods of time within the total temporary structure of the project.

Network Planning Tasks:

1. Determine the list of critical works or operations (i.e. such operations that have the greatest impact on the total duration of the project);
2. Build a network project plan in such a way that all planned work and operations are made in compliance with the specified time and minimum cost.

The unit of such a network model is an operation (operation or task), which means any activity as a result of which certain results will be achieved.

The result of network planning is a graphical display of the sequence of operations, the execution of which will lead to the achievement of the ultimate goal of the project. The main method of mapping is network economic and mathematical models. For management activities are most suitable. Using the network model, the possibility of system presentation of all operations and the conditions for managing the project implementation process is formed. If necessary, the network planning method allows you to maneuver resources within the model to achieve the ultimate goal.

Often, the leaders tend to rely only on personal experiencewhich is limited and subjective. Such a limited level of competence rarely helps in a dynamic environment, and sometimes it can bring direct damage.

Network planning makes it possible to eliminate the impact of subjective factors for project management, contributing to a reduction in the implementation of the project's implementation of a minimum by 15-20%, rationalization of the use of available resources and optimizing costs. In this case, individual operations are considered as separate elements of the holistic system, and the performers act as links of this system.

Network planning methods

Using (network graph, pert diagram), the following aspects should be taken into account:

• the network diagram reflects a full range of works and project steps;
• the network graph should be established between operations;
• network graphics are not flowcharts;
• network diagrams contain only operations and logical dependencies between them (there are no inputs, processes, outputs, etc.);
• network models do not allow recurring cycles, steps, "loops" of operations.

Network planning is focused on a reduction to a minimum of the project duration, two methods can be applied for the extreme:

1. Critical path method
2. The method of assessment and revision of plans.

"The maximum duration of the full path in the network is called critical; the works lying on this path are also called critical. It is the duration of the critical path that determines the smallest overall duration of the project as a whole." Increasing or reducing the time of the critical path operations leads to an increase and decrease in the duration of the project, respectively. The method of the critical path involves the calculation of work schedules, the duration of each work to determine the critical path of the project, and then take measures to reduce it.

The method of assessment and revision of the plans is to comply with the design schedules, production, organization of work and other established deadlines. According to this technique, the entire project is "breaking" to a number of subtasks, and the time required for its execution is estimated for each task, the priority of execution is also assigned. Depending on the priority of the task and its influence on the project, measures are taken to optimize its implementation to reduce the duration of the project.

Thus, the process of network planning is to describe a specific project or action plan for a given period in the form of a certain set of events, tasks, measures, procedures or works.

This monitors the object relationship between all procedures and operations that are included in the project structure or action plan for a given period. The development of project management techniques at the beginning of the 21st century led to the fact that in the event of a non-compliance with the real technology of performing work, network planning turns into a "formal check mark", as a result, the very idea of \u200b\u200busing calendar-network planning technologies is discredited.

Methods of building network models

Network diagrams reflect a network model of a specific project or action plan for a given period in the form of a plurality of vertices that are scheduled to be scheduled within the framework of this plan operations and procedures. Each vertex is connected to the preceding and next vertices by logic lines representing the relationship between operations. The exception is the initial and final vertex corresponding to the first and last operation as part of a particular project or action plan at a given period.

Before the direct construction of the network diagram, work is carried out on the formation of operations within a specific project or action plan for a given period. The formalized structure of operations in tabular form is preformed.

Based on the formalized structure of operations, the calendar time of implementation of the action plan is calculated, which is carried out by the calendar of the corresponding year and the period in which these operations are planned. If the planned operations must be performed in a certain calendar period, for example, a month, then the calculation is carried out on the basis of working days.

For example, from 01.09.2018 to 09/30/2018, each working week includes 5 working days, therefore, the calculation must be implemented on the basis of the presence of 20 days to fulfill all planned operations.

The distribution of performers within the framework of a formalized structure of operations in network planning is carried out on the basis of their functional duties in compliance with the three principles:

1. Each department or a specific employee fulfills only those operations that are provided for by its functional duties. Attract specialists to inappropriate its powers and duties work.
2. Regular and mandatory types of work are included in the project or action plan for a given period in accordance with their defined frequency, for example, weekly. Ignoring them within the framework of the Operation Plan is fraught with non-compliance with the scheduled period.
3. Parallel works are grouped in the entire project or action plan for a given period, or at certain time interim. For example, if the project is designed for one calendar month, then it is advisable to group parallel works within the framework of working weeks in the presence of such an opportunity.

Based on the work done on calculating the calendar time of the project implementation or action plan for a given period, structuring of operations on weeks and grouping parallel works is drawn up.

Building a network diagram

After structuring operations, the primary planning and construction of the network model is carried out in accordance with the planned operations. This contains a form of operations in the form of a table, which contains the following data:

• a consistent list of all operations to be made in the framework of the project or action plan for a given period;
• for each operation, its duration and number of performers are specified, which are involved in its implementation;
• each operation, except the initial, must correspond to the previous operations.

An example of a table of operations on the project for a competition for the choice of the best school of the city is given in the table.

An example of a table of operations

	the name of the operation	Previous operations	Continue, days	Number of performers, people
	Signing a Competition
	School registration
	Search for premises for a competition
	Personnel selection for competition
	Preparation of the room
	Development of a competition plan
	Instructing personnel
	Arrangement of the room before holding a competition
	Conduct competition
	Summing up the competition

In accordance with the formalized structure of operations and operations table, it is necessary to build a network model.

We use data on operations from the table and imagine a networking data chart.

An example of building a network diagram

In this network model, the peak is a specific operation, and the lines are the relationship between them. In this diagram in each vertex, the upper digit indicates the operation number, the lower indicates the duration of this operation in days, weeks or other units. This approach is also called the construction of the preceding and following diagram and is the most common representation of network models in planning.

The construction of network models in the type "Top-work" is most common in the practice of management and is actively applied in the field of state and municipal management, in planning on industrial, manufacturing and commercial enterprises of various sectors of the economy.

The critical path, as seen from the figure, make up the following operations: 1, 2, 6, 9 and 10.

Consequently, the length of the critical path is:

1 + 4 + 8 + 1 + 1 \u003d 15 days.

According to the results of the planning and construction of the network model, one of two conclusions can be made:

1. If the network model and the length of the critical path indicate that the entire set of duration operations is laid at a specified period, it is believed that the project implementation or a specified action plan will be made correctly.
2. In the event that the project implementation or a specified action plan is not stacked in the period allotted for this, the network model is adjusted.

Network model adjustment

The adjustment of the network model can be carried out in the first case, if it is possible to improve the efficiency of the planned operations.

In the network planning, there are three ways to adjust the model:

1. changing the timing of critical operations by attracting additional resources, which can be cash, materials or human resources;
2. changing the timing of critical operations by attracting performers employed on other operations while maintaining the initial parameters of resources;
3. changing the timing of operations by combining their execution.

In the first case, the adjustment of the network model is carried out without changing the network diagram. This approach is most often practiced in cases where free resources are not involved in other operations remain for operations.

In the second case, the network diagram also remains unchanged. This approach is used in cases where it is possible to increase the period for performing operations that do not belong to the critical path.

The third case is applied if it is impossible to use additional resources and implies the re-constructing of the network diagram.

After adjustment, an alternative network model is constructed.

It should be noted that in the adjustment of the network model it is the fundamental assignment of network planning. Thanks to the construction of network models already on early stage Planning can identify conditions indicating that the project cannot be implemented in the draft directivity time. Therefore, it is possible to correct the schedule of operations on the principle of changing the duration of critical operations from the point of view of the target draft purposes. Thus, if the project or the specified action plan does not fit into the policy time, then an attempt is made to reduce the timing of critical operations due to changes in their dependence on the initially specified parameters of their execution.

Literature

1. Chernyak Vz, Dovdienko I.V. Methods of making management decisions. - M.: Academy, 2013.
2. Mazur I.I., Shapiro V.D., Olderogge N.G., Polkovnikov A.V. Project management. - M.: Omega-L, 2012.
3. Novysh B.V., Shesholdko V.K., Shastitko D.V. Economic and mathematical methods of decision-making. - M.: Infra-M, 2013.
4. Ovubkov A.R., Fedotov I.V. Methods and models of management solutions. - M.: Publishing House Anch, 2011.
5. Sukhachev K.A., Kolosova E.S. The practice of applying calendar-network planning technologies. // Oil and gas vertical. - 2010. - №11 (240), June 2010. - P. 28-30.