Network planning in a project management system. On the load graph, time is plotted along the horizontal axis, for example in days, while the vertical axis shows the number of people working on each specific day.

Basic elements of network planning and management

Network planning and management is a set of calculation methods, organizational and control measures for planning and managing a set of works using a network diagram (network model).

Under complex of works we will understand any task for which it is necessary to carry out a sufficiently large number of varied works.

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

Network model- this is a plan for the implementation of a certain set of interrelated works, specified in the form of a network, the graphical representation of which is called network diagram.

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

The term work in SPU has several meanings. Firstly, this actual work- a time-consuming process that requires resources (for example, assembling a product, testing a device, etc.). Each actual job must be specific, clearly described and have a responsible person.

Secondly, this expectation- a long-term process that does not require labor (for example, the drying process after painting, aging of metal, hardening of concrete, etc.).

Thirdly, this 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 directly depends on the results of another. Naturally, the duration of the fictitious work is assumed to be zero.

An event is the moment of completion of a process, reflecting a separate stage of the project.. An event can be a partial result of a separate work or the total result of several works. An event can only happen when all the work preceding it is completed. Subsequent work can begin only when the event occurs. From here dual nature of the event: for all works immediately preceding it it is final, and for all immediately following it it is initial. 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 work immediately preceding it.

Figure 1. Basic elements of the network model

When drawing up network diagrams (models), symbols are used. Events on the network diagram (or, as they also say, on the graph) are depicted by circles (vertices of the graph), and works - by arrows (oriented arcs):

Event,

Work (process),

Dummy work - used to simplify network diagrams (duration is always 0).

Among the events of the network model, initial and final events are distinguished. The initial event does not have previous works and events related to the set of works presented in the model. The ending event has no next works and events.

There is another principle for building networks - without events. In such a network, the vertices of the graph represent certain jobs, and the arrows represent dependencies between jobs that determine the order of their execution. The “work-connection” network graph, in contrast to the “event-work” graph, has certain advantages: it does not contain fictitious work, has a simpler construction and restructuring technique, and 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 significantly fewer events than jobs ( network complexity indicator, equal to the ratio of the number of jobs to the number of events, is usually significantly greater than one). Therefore, these networks are less effective from the point of view of complex management. This explains the fact that at present, “event-work” network graphs are most widespread.

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 are specified, as well as estimates of other parameters, such as labor intensity, cost, etc.

The procedure and rules for constructing network graphs

Network diagrams are drawn up at the initial planning stage. First, the planned process is divided into separate works, a list of works and events is compiled, their logical connections and sequence of execution are thought out, and the work is assigned to responsible performers. With their help and with the help of standards, if they exist, the duration of each job is estimated. Then it is compiled ( stitched) network diagram. After streamlining the network schedule, the parameters of events and work are calculated, time reserves are determined and critical path. Finally, the network diagram is analyzed and optimized, which, if necessary, is drawn again with recalculation of the parameters of events and work.

When constructing a network diagram, a number of rules must be followed.

In the network model there should be no “dead-end” events, that is, events from which no work comes out, with the exception of the termination event. Here, either the work is not needed and must be canceled, or the need for certain work following the event in order to accomplish some subsequent event is not noticed. In such cases, a thorough study of the relationships between events and work is necessary to correct the misunderstanding that has arisen.

There should be no “tail” events in the network diagram (except for the initial one) that are not preceded by at least one job. Having discovered such events in the network, it is necessary to determine the performers of the work preceding them and include these works in the network.

The network should not have closed circuits and loops, that is, paths connecting certain events to themselves. When a loop occurs (and in complex networks, that is, in networks with a high complexity index, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the original data and, by revising the scope of work, achieve its elimination.

Any two events must be directly connected by at most one arrow job. Violation of this condition occurs when depicting parallel work. If these works are left as they are, then confusion will occur due to the fact that two different works will have the same designation. However, the content of these works, the composition of the involved performers and the amount of resources spent on the work may differ significantly.

In this case, it is recommended to enter fictitious event And fictitious work, while one of the parallel jobs is closed on this fictitious event. Fictitious jobs are depicted on the graph as dotted lines.

Figure 2. Examples of introducing fictitious events

Fictitious jobs and events need to be introduced in a number of other cases. One of them is a reflection of the dependence of events not related to real work. For example, work A and B (Figure 2, a) can be performed independently of each other, but according to production conditions, work B cannot begin before work A is completed. This circumstance requires the introduction of fictitious work C.

Another case is incomplete dependency of jobs. For example, work C requires the completion of work A and B to begin, work D is connected only with work B, and does not depend on work A. Then the introduction of fictitious work Ф and fictitious event 3’ is required, as shown in Figure 2, b.

In addition, fictitious work may be introduced to reflect real delays and waits. Unlike previous cases, here the fictitious work is characterized by its duration in time.

If the network has one final goal, then the program is called single-purpose. A network diagram that has several final events is called multi-objective and the calculation is carried out relative to each ultimate goal. An example could be the construction of a residential neighborhood, where the commissioning of each house is the final result, and the construction schedule for each house defines its own critical path.

Organize your network diagram

Suppose that when drawing up a certain project, 12 events are identified: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 24 works connecting them: (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). Created the initial network diagram 1.

The ordering of the network diagram consists in such an arrangement of events and activities in which for any activity the event preceding it is located to the left and has a lower number compared to the event that completes this activity. In other words, in an ordered network diagram, all arrow jobs are directed from left to right: from events with lower numbers to events with higher numbers.

Let's divide the original network diagram into several vertical layers (circle them with dotted lines and denote them with Roman numerals).

Having placed the initial event 0 in layer I, we mentally delete this event and all the arrow jobs coming out of it from the graph. Then, without incoming arrows, event 1 will remain, forming layer II. Having mentally crossed out event 1 and all the work coming out of it, we will see that events 4 and 2, which form the III layer, remain without incoming arrows. Continuing this process, we obtain network diagram 2.

Network 1. Unordered network

Network 2: Organize your network using layers

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

Network Diagram 3. Ordered Network Diagram

Let's change the numbering of events in accordance with their location on the graph and get an ordered network diagram 3. It should be noted that the numbering of events located in the same vertical layer is not of fundamental importance, so the numbering of the same network diagram may be ambiguous.

The concept of the path

One of the most important concepts in a network diagram is the concept of path. Path - any sequence of activities in which the final event of each activity coincides with the initial event of the activity following it. Among the various network paths, the most interesting is full path- any path whose beginning coincides with the initial network event, and the end with the final one.

The longest complete path in a network diagram is called critical. Works and events along this path are also called critical.

In network diagram 4, the critical path passes through activities (1;2), (2;5), (5;6), (6;8) and is equal to 16. This means that all activities will be completed in 16 units of time. The critical path is of particular importance in the control system, since the work on this path will determine the overall completion cycle of the entire set of works planned using the 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 activities on the critical path will delay the execution of the program.

Network diagram 4. Critical path

At the stage of management and control over the progress of the program, the main attention is paid to work that is on the critical path or, due to a lag, on the critical path. To reduce the duration of a project, it is necessary to first reduce the duration of activities on the critical path.

The material was prepared using the work: webforum. land. ru.

Techniques network planning were developed in the late 50s in the USA.

However, the first computers were expensive and available only to large organizations. Thus, historically, the first projects were state programs that were grandiose in terms of the scale of work, the number of performers and capital investments.

Currently, there are deep traditions of using project management systems in many areas of life.

The essence and purpose of network planning and management

The disadvantages of a linear calendar schedule are largely eliminated by using a system of network models that make it possible to analyze the schedule, identify reserves and use electronic computer technology.

The entire process is reflected in a graphical model called a network diagram. The network diagram takes into account all work from design to commissioning, identifying the most important, critical works, the implementation of which determines the completion date of the project. In the process of activity, it becomes possible to adjust the plan, make changes, and ensure continuity in operational planning. Existing methods for analyzing a network diagram make it possible to assess the degree of influence of changes made on the progress of the program, and to predict the state of work for the future. The network schedule accurately indicates the activities on which the program completion period depends.

Basic elements of network planning and management

Network planning and management is a set of calculation methods and control measures for planning and managing a set of works using a network diagram.

Network model- this is a plan for the implementation of a certain set of interrelated works, specified in the form of a network, the graphical representation of which is called network diagram.

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

An event is understood as the moment of start and end of work. The event has no time duration.

An event can only happen when all the work preceding it on the network schedule is completed. For all work immediately preceding the event, it is final, and for all immediately following it, it is initial.

Each event included in the network model must be fully, accurately and comprehensively defined, and its formulation must include the result of all work immediately preceding it.

Work is understood as a process that has a temporary duration.

Firstly, this actual work- a time-consuming process that requires costs. Each actual job must be specific, clearly described and have a responsible person. Secondly.

Secondly, this expectation- a time-consuming process that does not require labor.

Thirdly, this addiction, or fictitious work- a logical connection between two or more works. She points out that the possibility of one job directly depends on the results of another. Fictitious work only reflects the fact that one job cannot be started before another job finishes. The duration of the fictitious work is assumed to be zero.

The network model of the network diagram can be specified in two interpretations:

in the form of an event graph (event-based graph; CRM diagram);

in the form of a vertex graph (work-based graph; PERT diagram).

Network diagrams are drawn up at the initial planning stage. First, the planned process is divided into separate works, a list of works and events is compiled, their logical connections and sequence of execution are thought out, and the work is assigned to responsible performers. With their help and with the help of standards, if they exist, the duration of each job is estimated. Then it is compiled ( stitched) network diagram. After streamlining the network schedule, the parameters of events and work are calculated, time reserves are determined and critical path. Finally, the network diagram is analyzed and optimized, which, if necessary, is drawn again with recalculation of the parameters of events and work.

Formation of an event graph.

When forming an event graph, the following notations are used.

Events in the event graph are represented by circles (vertices of the graph) indicating the event number. All vertices within the graph must have different numbers. You can number vertices in any order without skipping numbers, starting from 1. An example of an event vertex is shown in Fig. 5.11.

Rice. 5.11. An example of an event graph vertex

Activities in the event graph are represented by unidirectional arrows. Fictitious work is represented by a dotted line. In graph theory, these lines are called edges, and such a graph is called a directed graph. Next to the edge you must indicate the duration of the work.

When generating an event graph, certain requirements must be met:

the graph must have only one initial vertex;

the graph must have only one end vertex;

the graph should not have loops, i.e., edges with beginning and end at the same vertex;

there should be no cycles in the graph, i.e. the path from the initial vertex of the graph along the arrows and any path always leads to the final vertex of the graph;

any two vertices, i.e., two events, should preferably have only one edge, i.e., one job. This condition is not mandatory.

The most common mistake made in a complex graph structure is with cycles. This error cannot be detected on a computer and therefore the graph must be prepared very carefully. If there are cycles in the graph, then network planning programs will simply either go into cycles or produce incorrect results.

An example of an event graph is shown in Fig. 5.12.

Rice. 5.12. Example of an event graph

An example of an incorrect graph with a cycle is shown in Fig. 5.13.

Rice. 5.13. Erroneous graph with a cycle

Network graphs based on the event graph are most widespread. This is primarily due to a very good mathematical study of network planning based on these graphs. Such graphs are most understandable to professional mathematicians.

In practice, a graph image is used without specifying node numbers and work durations. If there are no numerical estimates in the network model, then such a network is called structural. However, for calculations it is necessary to use networks in which estimates of the duration of work are specified, as well as estimates of other parameters, such as labor intensity, cost, etc.

If a network has one end goal, then the network is called single-purpose. A network diagram that has multiple terminating events is called multi-purpose. Networks are multi-purpose and cannot be calculated using a single algorithm. The calculation here is carried out in relation to each final goal. An example could be the construction of a residential neighborhood, where the commissioning of each house is the final result, and the construction schedule for each house defines its own critical path. However, with separate calculations for each final goal, there may be critical paths that do not coincide in the general part of the graph. In this regard, if the project is single, then the end nodes of such a graph need to be connected by fictitious works. The direction of the fictitious work edge is specified arbitrarily and the result of network planning does not depend on this direction.

There is no need to indicate work-wait in the event graph. If there is an urgent need for its indication, then such work is indicated as ordinary work. Specifying work-wait may be possible in a graph with multiple starts and known time intervals between those starts.

Formation of a vertex graph.

The event graph does not receive attention among professional economists, because it is less understandable to them than the vertex graph.

The vertex graph is built based on the interaction of jobs with each other. The vertex in this graph is the job, and the edge is the connection of one job to another. For economists, this structure is understandable because it is necessary to establish connections between one job and another.

Work in a vertex graph is specified by the vertex of the graph, i.e. in the form of a circle, as in an arrow graph. All vertices are numbered starting from 1 and without skipping numbers. The graph must not have vertices with the same numbers. Next to the vertex the duration of the work is indicated. Dummy jobs in the vertex graph are not specified, since this does not make sense here.

The connection of one job with another is specified by a directed edge of the graph. The edge of such a graph reflects only the fact of connection between two jobs and, therefore, no duration is indicated on the edge and the edges are not numbered.

An example of a vertex graph corresponding to the event graph in Fig. 5.12, shown in Fig. 5.14.

Rice. 5.14. Vertex graph example

It is noteworthy that the vertex graph is easy to obtain based on the event graph. To do this, you need to mentally represent an edge in the event graph as a point and draw the interaction of the resulting points based on the event graph. On the contrary, obtaining an event graph based on a vertex graph is not very easy. In this regard, it is best to draw the event graph first.

A vertex graph can have several starting and ending job vertices. The only condition for the correctness of the graph is the zero start time of all initial work and one time for completion of all final work. It is impossible to define a multi-purpose vertex graph, unlike an event graph, without additional verbal explanations. This fact is demonstrated in Fig. 5.15.

Rice. 5.15. An example of a multi-objective event graph and corresponding vertex

As follows from Fig. 5.15, in the vertex graph there is no uniqueness in the non-simultaneous completion of all jobs and, therefore, it will be considered that the jobs finish simultaneously.

Network planning based on a vertex graph has a more complex mathematical implementation in the general case. Calculating the critical path of a network diagram, on the one hand, has a simpler implementation algorithm. On the other hand, calculating early and late start and end times in a vertex graph is implemented with a much more obscure and complex algorithm.

Job-based networks turn out to be much more cumbersome, since there are usually significantly fewer events than jobs ( network complexity indicator, equal to the ratio of the number of jobs to the number of events, is usually significantly greater than one). Therefore, these networks are less effective from the point of view of complex management.

Network planning is one of the forms of graphical reflection of the content of work and the duration of implementation of strategic plans and long-term complexes of design, planning, organizational and other types of enterprise activities. Along with line graphs and tabular calculations network planning methods are widely used in the development of long-term plans and models for the creation of complex production systems and other objects of long-term use. Network work plans of enterprises to create new competitive products contain not only the total duration of the entire complex of design, 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, production process schedules were used in American companies by G. Gantt. On linear or strip graphs, the duration of work at all stages of production is plotted along the horizontal axis on a selected time scale. The content of work cycles is depicted along the vertical axis with the necessary degree of their division into separate parts or elements. Cyclic or line graphs are usually used at domestic enterprises in the process of short-term or operational planning production activities. The main disadvantage of such schedules is the lack of possibility of close interconnection individual works into a single production system or general process achieving the planned final goals of the enterprise (company).

Unlike linear graphs, network planning serves as the basis for economic and mathematical calculations, graphical and analytical calculations, organizational and management decisions, operational and strategic plans, providing not only images, but also modeling, analysis and optimization of projects for the implementation of complex technical objects and design developments and etc. Under network planning It is customary to understand a graphical representation of a certain set of works being performed, reflecting their logical sequence, existing relationships and planned duration, and ensuring subsequent optimization of the developed schedule based on economic-mathematical methods and computer technology for the purpose of using it for ongoing management of the progress of work. The network model of the complex is called a directed graph. It represents many interconnected elements to describe the technological dependence of individual works and stages of upcoming projects. Network models or graphs are intended for the design of complex production facilities, economic systems and all kinds of work consisting of large number various elements. For simple work, linear or cyclic graphs are usually used.

Network diagrams serve not only for planning a variety of long-term work, but also for their coordination between project managers and executors, as well as for determining the necessary production resources and their rational use. Network planning can be successfully applied in various areas of production and entrepreneurial activity, such as:

• performing marketing research;
• carrying out research work;
• design of experimental developments;
• implementation of organizational and technological projects;
• development of pilot and serial production of products;
• construction and installation of industrial facilities;
• repair and modernization 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 innovative activities of the enterprise, etc. Application of network planning in modern production contributes to the achievement of the following strategic and operational objectives:
  • 1) reasonably select the development goals of each division of the enterprise, taking into account existing market requirements and planned end results;
  • 2) clearly establish detailed tasks for all divisions and services of the enterprise based on their interconnection with a single strategic goal in the planning period;
  • 3) involve future direct executors of the main stages of the upcoming work, who have production experience and high qualifications, in drawing up project plans;
  • 4) more effectively distribute and rationally use the limited resources available at the enterprise;
  • 5) predict the progress of the main stages of work focused on the critical path, and timely take the necessary planned and management decisions on adjusting deadlines;
  • 6) carry out multivariate economic analysis various technological methods and sequential ways of performing work, as well as allocating resources in order to achieve planned results;
  • 7) make the necessary adjustments to work schedules taking into account changes in the external environment, internal environment and other market conditions;
  • 8) use modern computer technology to process large amounts of reference information, perform current calculations and build network models;
  • 9) promptly receive the necessary planned data on the actual state of progress of work, costs and production results;
  • 10) ensure the interaction of the long-term general strategy with short-term ones in the process of planning and managing work specific goals enterprises.

Thus, the use of a network planning system contributes to the development optimal option strategic plan for the development of the enterprise, which serves as the basis operational management complex of works during its implementation. The main planning document in this system is a network diagram, or simply a network, representing an information-dynamic model that reflects all the logical relationships and results of the work performed necessary to achieve the final goal of strategic planning. The network diagram depicts with the required degree of detail what work, in what sequence and for what time, needs to be completed in order to ensure the completion of all types of activities no later than the specified or planned period.

Network modeling is based on the image of the planned set of works in the form of a directed graph. Count - This is a conditional diagram consisting of given points(vertices) connected to each other by a certain system of lines. The segments connecting the vertices are called edges (arcs) of the graph. A graph is considered directed if arrows indicate the directions of all its edges, or arcs. Graphs are called maps, labyrinths, networks and diagrams. The study of these schemes is carried out using the methods of a theory called “graph theory”. It operates with such concepts as paths, contours, etc. Path - this is a sequence of arcs, or works, when the end of each previous segment coincides with the beginning of the next one. Circuit means a finite path whose initial vertex or event coincides with the final one. In other words, a network graph is a directed graph without contours, arcs, or edges of which have one or more numerical characteristics. On the graph, the edges are considered to be jobs, and the vertices are events.

Works refers to any production processes or other actions leading to the achievement of certain results or events. Possible waiting for the start of subsequent processes, associated with interruptions or additional time costs, should also be considered work. Work-waiting usually requires the expenditure of working time without the use of resources, for example, cooling of heated workpieces, hardening of concrete, natural “aging” of body parts, etc. In addition to actual jobs and wait jobs, there are dummy jobs or dependencies. Fictitious work a logical connection or dependence between some finite processes or events that does not require time is considered. On the graph, fictitious work is represented by a dotted line.

Events the final results of previous work are considered. An event records the fact that work has been completed, specifies the planning process, and eliminates the possibility different interpretations results of various processes and work. Unlike work, which usually has its own duration in time, an event represents only the moment of completion of a planned action, for example, a goal is chosen, a plan is drawn up, goods are produced, products are paid for, money is received, etc. Events can be initial or initial, final or final, simple or complex, as well as intermediate, preceding or subsequent, etc.

There are three main ways to depict events and activities on network graphs: “vertex-activities”, “vertex-events” and mixed networks.

In networks like "tops-of-work" all processes or actions are presented in the form of rectangles following one another, connected by logical dependencies (Fig. 4.1).

Rice. 4.1.

As can be seen from the network diagram, it shows simple model, or a network consisting of five interconnected jobs: A, B, C, D and E. The initial, or initial, job is A, followed by intermediate jobs - B, C and D, and then the final job D.

In networks like "vertex-events" all jobs or actions are represented by arrows, and events by circles (Fig. 4.2).

Rice. 4.2.

This network diagram shows a simple production process involving six interconnected events: 0, 1,2, 3,

4 and 5. The initial one in this case is the zero event, the final one is the fifth one, all the rest are intermediate. Between each of the two events there is one actual work, depicted as a solid line-arrow. Events 2 and 3 are connected by fictitious work, which means that there is a time dependence or logical connection between them. In other words, event 3 cannot be completed before event 2 finishes.

In the practice of network planning at domestic enterprises, models of the “vertex-event” type have become more widespread (see Fig. 4.2). However, many American firms are now also using node-to-work networks (see Figure 4.1). Their main advantage is as follows.

• 1. Working in such network models looks more natural, since it is represented schematically workplace performer or specialist.
• 2. The graphical representation of the network model also seems more convenient, since it is possible to first draw all the work, and then arrange the necessary logical dependencies.
• 3. Writing application programs for these networks is also a simpler and less labor-intensive activity.
• 4. Network graphs of the “vertex-work” type are more adapted to existing standards in project management.

In all network graphs, an important indicator is the path that defines the sequence of activities or events in which the final process, or result, of one stage coincides with the initial indicator of the next phase. In any graph it is customary to distinguish several paths:

• ? full path from the initial to the final event;
• ? path, previous to this event from the initial one;
• ? the path next after this event until the final one;
• ? path between several events;
• ? critical path from the initial to the final event of maximum duration.

Network models can be very diverse both in organizational structure production system, and according to the purpose of network diagrams, as well as the normative data and information processing tools used. By organizational structure distinguish intra-company or industry models of network planning, according to purpose- single and continuous action. Network models can be deterministic, probabilistic and mixed. IN deterministic network diagrams, all the work of a strategic project, their duration and interconnection, as well as the requirements for expected results are predetermined. In probabilistic models, many processes are random in nature. In mixed networks, one part of the work is certain and the other part is uncertain. Models can also be single-purpose And multi-purpose.

When constructing network diagrams, it is necessary to take into account all existing real conditions and specific characteristics of work at each enterprise.

Concept, rules of construction and directions of application of network planning. Features of critical path methods, statistical tests (Monte Carlo method), evaluation and revision of plans and graphical analysis. Principles of constructing a Gantt chart.

INTRODUCTION

1. Network planning

1.1 Concept of network planning

1.2 Basic concepts of network planning

1.3 Rules for constructing network models

2. History of network planning

2.1 Foreign experience

2.2 Network planning in Russia

3. Network planning methods

3.1 Gantt chart

3.2 Critical path method (CPM)

3.3 Statistical test method (Monte Carlo method)

3.4 Method of evaluation and revision of plans (PERT, PERT)

3.5 Graphical Evaluation and Analysis Technique (GERT)

3.6 Additional methods for calculating a network diagram

Conclusion

Used literature and sources

Applications

INTRODUCTION

My theme course work- analysis of methods for network planning of project work.

Planning and managing a set of project activities is a complex and, as a rule, contradictory task. The assessment of the time and cost parameters of the functioning of the system, carried out within the framework of this task, is carried out using various methods. Among existing great importance has a network planning method.

Network planning methods can be widely and successfully used to optimize the planning and management of complex, branched sets of work that require the participation of a large number of performers and the expenditure of limited resources.

It should be noted that the main goal of network planning is to reduce the duration of the project to a minimum, thus, the use of network models is due to the need for competent management of large national economic complexes and projects, scientific research, design and technological preparation of production, new types of products, construction and reconstruction, major repairs fixed assets, etc.

Using a network model, the manager of a work or operation can systematically and on a large scale represent the entire progress of work or operational activities, manage the process of their implementation, and also maneuver resources.

The purpose of my course work is to examine network planning methods.

The following tasks can be distinguished:

1) Consider the concept of network planning.

2) Highlight the basic concepts of network planning.

3) Study the rules for constructing network models.

4) Determine the areas of application of network planning.

5) Study the history of network planning, as in foreign countries, and in Russia

6) Analyze such network planning methods as the Gantt chart, the critical path method, the Monte Carlo method, the plan evaluation and revision method (PERT), the graphical evaluation and analysis method (GERT), as well as additional methods for calculating the network schedule.

1 . WITHetevoe planning

1.1 Network planning concept

Network planning- a control method that is based on the use of the mathematical apparatus of graph theory and systematic approach to display and algorithmize complexes of interrelated work, actions or activities to achieve a clearly defined goal.

Network planning allows you to determine, firstly, which of the many works or operations that make up the project are “critical” in their impact on the overall calendar duration of the project and, secondly, how to build the best plan for carrying out all work on this project with in order to meet specified deadlines at minimal cost.

Network planning is based on the Critical Path Method (CPM) and the PERT (Program Evaluation and Review Technique) method, developed almost simultaneously and independently.

Network planning methods are used to optimize the planning and management of complex, branched sets of work that require the participation of a large number of performers and the expenditure of limited resources.

The main goal of the network planning - reducing the duration of the project to a minimum.

Network task planning is to graphically, visually and systematically display and optimize the sequence and interdependence of works, actions or activities that ensure the timely and systematic achievement of final goals. To display and algorithmize certain actions or situations, economic and mathematical models are used, which are usually called network models, the simplest of which are network graphs. With the help of a network model, the manager of a work or operation has the opportunity to systematically and on a large scale represent the entire progress of work or operational activities, manage the process of their implementation, and also maneuver resources.

An important feature of SPU (network planning and management) is a systematic approach to issues of organizing management, according to which teams of performers taking part in a set of works and united by the commonality of the tasks assigned to them, despite different departmental subordination, are considered as parts of a single complex organizational system.

The use of network planning methods helps reduce the time required to create new facilities by 15-20%, ensuring the rational use of labor resources and equipment.

Network planning is based on the construction of network diagrams. Network diagram (network, network graph, PERT diagram) is a graphical display of project activities and the dependencies between them. In SPU, the term “network” refers to the full range of work and project milestones with the dependencies established between them.

There are two types of network diagrams - a network model of the “vertex-work” type and the “vertex-event” or “arc-work” type.

Network diagrams of the first type display the network model in graphical form as a set of vertices corresponding to jobs, connected by lines representing the relationships between jobs. This type of diagram is also called a precedence-follow diagram. It is the most common representation of a network ( rice.1 )

Another type of network diagram, a vertex-event network, is used less frequently in practice. With this approach, work is represented as a line between two events (graph nodes), which, in turn, reflect the beginning and end of this work. PERT charts are examples of this type of chart (rice.2 ).

The following network planning methods can be distinguished:

Deterministic network methods

o Gantt chart

o Critical path method (CPM)

· Probabilistic network methods

o Non-alternative

§ Method simulation modeling(Monte Carlo method)

§ Method of evaluation and revision of plans (PERT, PERT)

o Alternative

§ Graphical Evaluation and Analysis Method (GERT).

1.2 Basice concepts of network planning

The following concepts necessary for network planning should be highlighted.

Job - a production process that requires time and material resources and leads to the achievement of certain results.

In its own way physical nature work can be considered as an action (for example, pouring a foundation with concrete, drawing up a request for materials, studying market conditions), a process (for example, aging castings, aging wine, etching circuit boards) and waiting (a process that requires only time and does not consume any resources; is technological (hardening cement screed) or an organizational (waiting for dry weather) break between works performed directly one after another.

Based on the amount of time spent, the work can be:

· real, that is, a process extended over time, requiring the expenditure of resources;

· fictitious (or dependency), which does not require time and represents a connection between any work: transfer of modified drawings from designers to technologists, submission of a report on the technical and economic indicators of the workshop to a higher division.

Event -- this is the fact of the completion of one or more works that are necessary and sufficient for the start of the next work. Events establish the technological and organizational sequence of work. Events limit the work in question and in relation to it can be initial and final. The start event determines the start of work and is the end event for previous work. An initial event is considered to be an event that has no previous activities within the network diagram under consideration. Final - an event that has no subsequent activities within the network schedule under consideration. A boundary event is an event that is common to two or more primary or private networks.

Path is any sequence of work in a network in which the final event of each work of this sequence coincides with the initial event of the work following it. The path from the initial to the final event is called complete. The path from the initial event to this intermediate event is called the path preceding this event. A path connecting any two events, neither of which is the initial or final one, is called a path between these events.

Travel duration is determined by the sum of the durations of its constituent works. The path having maximum length, is called critical.

For a job-vertex type network model, the following notation is used: milestone- a certain key event indicating the end of one stage and the beginning of another; arc- connection between works.

There are different types of connections in the network model:

Initial work;

Final works;

Consecutive works;

Crushing works (operations);

Works (operations) of merger;

Parallel work.

When drawing up network diagrams (models), symbols are used. (Fig. 3)

1.3 Prafork for constructing network models

The network model development process includes defining the project work list; assessment of work parameters; identifying dependencies between jobs.

When constructing a network diagram, a number of rules must be followed.

1) Rule for the sequence of depicting works: network models should be built from beginning to end, i.e. from left to right.

2) Rule for depicting arrows. In a network diagram, arrows indicating activities, expectations or dependencies can have different slopes and lengths, but must go from left to right, without deviating to the left of the y-axis, and always go from the previous event to the subsequent one, i.e. from an event with a lower sequence number to an event with a larger sequence number.

3) Rule of intersection of arrows. When constructing a network graph, you should avoid crossing arrows: the fewer intersections, the more visual the graph.

4) Rule for designating works. In a network diagram, only one arrow can pass between the symbols of two adjacent events.

To display the work correctly, you can enter an additional event and dependency.

5) In the network model there should be no “dead-end” events, that is, events from which no work comes out, with the exception of the terminating event. Here, either the work is not needed and must be canceled, or the need for certain work following the event in order to accomplish some subsequent event is not noticed.

6) The rule for dividing and paralleling work. When constructing a network diagram, you can begin subsequent work without waiting for the complete completion of the previous one. In this case, you need to “split” the previous work into two, introducing an additional event at the place of the previous work where a new one can begin.

7) The rule for prohibiting closed circuits (cycles, loops). In the network model, it is unacceptable to build closed loops - paths connecting some events with themselves, i.e. it is unacceptable for the same path to return to the same event from which it came.

8) No deadlock rule. There should be no dead ends in the network diagram, i.e. events from which no work comes out, with the exception of the finishing event (in multi-objective graphs there are several finishing events, but this is a special case).

9) No tail event rule. There should be no tail events in the network diagram, i.e. events that do not include any work except the start event.

10) Rule for depicting differentiated-dependent works. If one group of activities depends on another group, but at the same time one or more activities have additional dependencies or restrictions, additional events are introduced when constructing the network diagram.

11) Delivery image rule. In the network schedule, deliveries (delivery means any result that is provided “from the outside,” i.e., is not the result of the work of a direct participant in the project) are depicted with a double circle or another sign that differs from the sign of a regular event on this schedule. Next to the delivery circle there is a link to a document (contract or specification) that reveals the contents and terms of delivery.

12) Rule for taking into account immediate connections (dependencies). In the network diagram, only direct connections (dependencies) between activities should be taken into account.

13) Technological rule constructing network diagrams. To build a network diagram, it is necessary to install in the technological sequence:

* what work must be completed before starting this work;

* what work should be started after completion of this work;

* what work needs to be done simultaneously with this work.

14) Rules for encoding network diagram events. To encode network diagrams, you must use the following rules.

1. All events on the schedule must have their own numbers.

2. Events must be encoded using natural numbers without gaps.

3. The number of the subsequent event should be assigned after assigning numbers to the preceding events.

4. The arrow (work) should always be directed from the event with a lower number to the event with a higher number.

1. 4 Directions pApplications of network planning

The most common applications of network planning are:

· targeted research and development of complex objects, machines and installations, in the creation of which many enterprises and organizations take part;

· planning and management of the main activities of development organizations;

· planning a set of works to prepare and master the production of new types of industrial products;

· construction and installation of industrial, cultural and residential facilities;

· reconstruction and repair of existing industrial and other facilities;

· planning the training and retraining of personnel, checking the implementation of decisions made, organizing a comprehensive audit of the activities of enterprises, associations, construction and installation organizations and institutions.

Network planning methods are used when planning complex complex projects, for example, such as:

1. Construction and reconstruction of any objects;

2. Carrying out research and development work;

3. Preparing production for product release;

4. Rearmament of the army;

5. Deployment of a system of medical or preventive measures.

2. History of network planning

2.1 Foreign experience

The first phase of widespread use of network planning was associated with the advent of Gantt charts, which appeared in the early twentieth century. Ganges diagram is handy tool for organizing, planning and managing the execution of a wide variety of processes.

Second phase. Network planning techniques were developed in the late 50s in the USA. In 1956, M. Walker from DuPont, exploring the possibility of more effective use owned by the company computer Univac, joined forces with D. Kelly from the planning group capital construction from Remington Rand. They tried to use a computer to draw up schedules of large complexes of work to modernize DuPont factories. As a result, a rational and simple method for describing a project using a computer was created. It was originally called the Walker-Kelly method and later became known as critical methodesky way-- MCP (or CPM -- Critical Path Method).

In parallel and independently, the US Navy created a method for analyzing and evaluating programs, PERT (Program Evaluation and Review Technique). This method was developed by Lockheed Corporation and the consulting firm Booz, Allen & Hamilton for the Polaris missile system development project, which involved about 3,800 prime contractors and consisted of 60,000 operations. Using the PERT method allowed program management to know exactly what needed to be done at any given time, who should be doing it, and the likelihood of individual activities being completed on time. The project was completed two years ahead of schedule due to successful program management.

This management method began to be used throughout the US military for project planning. This technique was used to coordinate work performed by various contractors as part of large projects to develop new types of weapons.

Also, this management technique has found application for the development of new types of products and modernization of production by large industrial corporations, as well as in construction.

An example of the successful application of network project planning was the construction of the Churchill River hydroelectric dam in Newfoundland (Labrador Peninsula) from 1967 to 1976. In 1974, the project progress was 18 months ahead of schedule and within the planned cost estimate. The client for the project was Churchill Falls Labrador Corp., which hired Acress Canadian Betchel to design the project and manage construction. It should be noted that a significant gain in time was achieved through the use of precise mathematical methods in managing complex sets of work, which became possible thanks to the development of computer technology. At the same time, the first computers were expensive and available only to large organizations. Thus, historically, the first projects were state programs that were grandiose in terms of the scale of work, the number of performers and capital investments.

Third stage is associated both with the improvement of previous project management methods that continued at the end of the twentieth century, and with the emergence of new ones, but at a higher quality level - with the use of modern software and personal computers. At first, software development was carried out by large companies to support own projects, but soon the first project management systems appeared on the software market. The systems at the origins of planning were developed for powerful large computers and minicomputer networks.

With the advent of personal computers, the most rapid development of project management systems began. The range of users of management systems has expanded, which has led to the need to create systems for managing projects of a new type. Moreover, one of the most important indicators of such systems was ease of use. Therefore, during the further development of new versions, the developers tried to maintain the external simplicity of the systems and expanded them functionality and power, and at the same time maintaining low prices, making the systems accessible to companies of almost any level.

Currently, there are deep traditions of using project management systems in many areas of life. An increase in the number of users of project management systems contributes to the expansion of methods and techniques for their use. Western industry magazines regularly publish articles on project management systems, including advice to users of such systems and analysis of the use of network planning techniques to solve problems in various areas of management.

2 . 2 Network planning in Russia

In the USSR, the beginning of work on network planning dates back to 1961. Then network planning methods found application in construction and scientific developments. When creating domestic missile submarines, a specially developed version was used automated system program-targeted management. In subsequent years, network planning in our country has become widely used. Network planning was considered in a broad context, in the form of a developed system for planning and managing complex projects and programs. The goals of network planning were the rational organization of production and other processes; identification of time and material resources; project and program management; prevention and elimination of possible deviations from planned results; improvement of socio-economic and other indicators of the system; clear distribution of responsibilities of managers and performers at various levels; increasing the effectiveness of programs and projects.

Since the 90s of the 20th century, interest in network planning and management in our country has decreased significantly. This happened due to the fact that network planning was associated with the planning and management system that developed in the administrative-command system. There were many shortcomings of this system, which led to the search for other ways to manage socio-economic processes during the transition to market methods management. This conclusion was largely transferred to the possibilities of applying network planning in new economic conditions. In addition, there was a sharp turn and transition from centralized to decentralized methods of economic management. A disdainful attitude towards planning methods that were used in centralized methods management. At the same time, the fact that many ideas of these methods were successfully applied and were developed in foreign practice was largely ignored.

Currently, there is a combination of centralized mechanisms for regulating the economy with market approaches. Socio-economic forecasting and planning play a significant role in increasing the efficiency of social production during the transition to market methods. Wherein important means The implementation of forecasts and plans is again network planning.

3. Network planning methods

Exist different methods network planning.

Models in which the mutual sequence and duration of work are uniquely specified are called deterministic network models. The most popular deterministic models include the Gantt chart method and the critical path method (CPM).

If the duration of some work cannot be unambiguously specified in advance, or if situations may arise in which the previously planned sequence of project tasks changes, for example, there is a dependence on weather conditions, unreliable suppliers or the results of scientific experiments, deterministic models are not applicable. Most often, such situations arise when planning construction, agricultural or research work. In this case, use probabilistic models, which are divided into two types:

· non-alternative - if the sequence of work is recorded, and the duration of all or some of the work is characterized by probability distribution functions;

· alternative - the duration of all or some of the work and the connections between the works are probabilistic.

The most common methods of probabilistic network planning include:

· program evaluation and review method (PERT);

· simulation method or Monte Carlo method;

· graphical evaluation and analysis of programs (GERT).

3.1 Gantt chartand cyclogram

One of the most common ways to visually represent a production process or project over time is a linear or strip calendar chart - Gan diagramthat.

A Gantt chart is a horizontal line chart in which project tasks are represented as long periods of time, characterized by start and end dates, delays, and possibly other time parameters.

A Gantt chart is a graph in which a process is presented in two forms . On the left side the project is presented as a list of tasks (works, operations) of the project in tabular form, indicating the name of the task and the duration of its completion, and often the work preceding a particular task. On the right side Each project task, or rather the duration of its completion, is displayed graphically, usually in the form of a segment of a certain length, taking into account the logic of completing the project tasks. (see Fig. 4)

At the top right of the Gantt chart is a time scale. The length of the segment and its location on the time scale determine the start and end time of each task. Besides, mutual arrangement task segments shows whether tasks follow one another or whether they are executed in parallel.

The Gantt chart was most widely used in construction. The Gantt chart is quite suitable as a work schedule, but when the need arises to change the structure of work, all work has to be reviewed anew, taking into account the variety of possible technological connections between them. And the more complex the work, the more difficult it is to use the Gantt chart. However, even after the advent of network models, the Gantt chart continues to be used as a means of representing the time aspects of work at the final stages scheduling, when the project duration is optimized using network models. The Gantt chart can also be used for basic control of work. It is used to reflect the current state of the project (project status) in terms of meeting deadlines.

Cyclogram is a linear chart of work duration that displays work as an inclined line in a two-dimensional coordinate system, one axis of which depicts time, and the other the volume or structure of work performed.

Cyclograms were actively used until the 80s of the 20th century, mainly in the construction industry, especially when organizing continuous construction. There are cyclograms of rhythmic and non-rhythmic flow. An equal-rhythmic flow is a flow in which all component flows have the same rhythm, i.e. the same duration of work on all grips. (Fig. 5)

Currently, cyclograms are practically not used in management practice, both because of the shortcomings indicated below and because of the irrelevance of continuous construction.

These models are easy to implement and clearly show the progress of work. At the same time, they cannot reflect the complexity of the process being modeled - the form of the model conflicts with its content. The main disadvantages are:

* lack of clearly indicated relationships between individual works (the dependency of the work underlying the schedule is identified only once in the process of drawing up the schedule (model) and is recorded as unchanged; as a result of this approach, the technological and organizational decisions included in the schedule are usually made as permanent and are lost yours practical significance after the start of their implementation);

* inflexibility, rigidity of the structure of the linear schedule, difficulty in adjusting it when conditions change (the need for repeated rescheduling, which, as a rule, cannot be done due to lack of time);

* the impossibility of clearly delineating the responsibilities of managers at various levels (information received about the progress of development contains too much information at any level that is difficult to quickly process);

* complexity of variant development and limited opportunity forecasting the progress of work.

3. 2 Critical path method(MCP)

Critical path method

The method is based on determining the longest sequence of tasks from the beginning of the project to its completion, taking into account their interrelationships. Tasks lying on the critical path (critical tasks) have zero slack and if their duration changes, the timing of the entire project changes. In this regard, when implementing a project, critical tasks require more careful monitoring, in particular, timely identification of problems and risks that affect the timing of their completion and, consequently, the timing of the project as a whole. As the project progresses, the critical path of the project may change because when the duration of tasks changes, some of them may end up on the critical path.

The critical path method is based on the fact that the duration of operations can be estimated with sufficient high degree accuracy and certainty.

The main advantage of the critical path method is the ability to manipulate the deadlines for completing tasks that are not on the critical path.

Scheduling according to MCP requires certain input data. After they are entered, a forward and reverse pass through the network is performed and the output information is calculated. (Fig. 6).

To calculate the calendar schedule using the MCP, the following input data is required:

Set of works;

Dependencies between jobs;

Estimates of the duration of each job;

Project working time calendar (in the most general case, it is possible to set your own calendar for each work);

Resource calendars;

Restrictions on the start and end dates of individual works or stages;

Calendar date for the start of the project.

Direct calculation - determining the minimum possible time for project implementation begins with works that have no predecessors. During it, ES (early start) and EF (early finish) are determined. Early starts and early finishes of work are determined sequentially, from left to right according to the schedule, that is, from the initial network event to the final one.

Formulas used:

EF=ES+Dur (where Dur is duration)

ESi=EFi-1, provided that operation (i) is not a merge operation.

When merging: ESi=maxEFi-1

Reverse calculation. LS (Late Start), LF (Late Finish) and R (Reserve) are determined. Late starts and late finishes are determined in reverse order - from the ending event of the schedule to the outgoing one, that is, from right to left.

provided that (i-1) is not a splitting operation.

When crushing:

With correct calculations, the condition ES?=LS?

Thus, the critical path is a sequence of operations that have no reserve.

Critical path analysis is an effective method for estimating:

· Problems that need to be solved.

· Possibility of parallel execution of work.

· Shortest project completion time.

· Production resources required to complete the project.

· Sequence of work, including scheduling and determining the duration of work.

· Sequence of problem solving.

· Most effective way reducing the duration of the project in case of its urgency.

The effectiveness of critical path analysis can affect the outcome of a project, whether it succeeds or fails. The analysis can also be very useful in assessing the importance of the problem that may be encountered during the implementation of the plan.

3.3 Methodsimulation modeling (Monte Carlo method)

Monte Carlo method(Monte Carlo methods, MMC) is the general name of a group of numerical methods based on obtaining a large number of realizations of a stochastic (random) process, which is formed in such a way that its probabilistic characteristics coincide with similar values ​​of the problem being solved.

The essence this method consists in the fact that the test result depends on the value of some random variable distributed according to a given law. Therefore, the result of each individual test is also random. After conducting a series of tests, a set of partial values ​​of the observed characteristic (sample) is obtained. The obtained statistical data are processed and presented in the form of numerical estimates of quantities of interest to the researcher (system characteristics).

An important feature of this method is that its implementation is almost impossible without the use of a computer.

The Monte Carlo method has two features:

1) simple structure of the computational algorithm;

2) the calculation error is, as a rule, proportional to D/N, where D is some constant, N is the number of tests. This shows that in order to reduce the error by 10 times (in other words, to get another correct decimal place in the answer), you need to increase N (i.e., the amount of work) by 100 times.

It is impossible to achieve high accuracy in this way. Therefore, it is usually said that the Monte Carlo method is especially effective in solving those problems in which the result is needed with low accuracy (5-10%). The way to use the Monte Carlo method is quite simple. To obtain an artificial random sample from a population of values ​​described by some probability distribution function:

1) The limits for changing the implementation time of each operation are set.

2) Specific implementation times are set for each operation using a random number sensor.

3) The critical path and implementation time of the entire project are calculated.

4) Go to operation "2".

The result of applying the Monte Carlo method is:

· A histogram that shows the probability of project completion time. (Fig. 7)

· Criticality index

3.4 Method of evaluation and revision of plans (PERT,PERT)

PERT Plan Evaluation and Review Method is a type of critical path analysis with a more critical assessment of the duration of each stage of the project. When using this method, you need to estimate the shortest possible duration for each job, the most likely duration, and the longest duration in case the job takes longer than expected. The PERT method allows for uncertainty in the duration of activities and analyzes the impact of this uncertainty on the duration of the project as a whole.

This method is used when it is difficult to specify and determine the exact duration for an operation.

A special feature of the PERT method is the ability to take into account the probabilistic nature of the durations of all or some jobs when calculating time parameters on a network model. It allows you to determine the probabilities of completing a project within given periods of time and by given deadlines.

Instead of one deterministic duration value for project activities, three duration estimates are specified (usually by expert means):

· optimistic (the work cannot be completed faster than t a);

· pessimistic (work cannot be completed slower than in t b);

· most probable t n

Then the probabilistic network model turns into a deterministic one by replacing three estimates of the duration of each job with one value called the expected duration t expected and calculated as the weighted arithmetic average of three expert estimates of the duration of a given job:

t expected =(t a + t b + t n)/6

The critical path is determined based on each t expected operation.

The average is determined standard deviation each operation:

T=(t a + t a) /6

Standard deviation of the implementation time of the entire project:

3.5 Graphical evaluation method andanalysis (GERT)

Graphical Evaluation and Analysis Method (GERT Method) used in cases of work organization where subsequent tasks can begin after the completion of only a certain number of previous tasks, and not all tasks represented on the network model must be completed to complete the project.

The basis for using the GERT method is the use of alternative networks, called GERT networks in terms of this method.

Essentially, GERT networks make it possible to more adequately specify complex processes construction production in cases where it is difficult or impossible (for objective reasons) to unambiguously determine which works and in what sequence must be performed to achieve the intended result (i.e. there are many options for project implementation).

It should be noted that the “manual” calculation of GERT networks that simulate real processes is extremely complex, however software for computing network models of this type, unfortunately, is not common today.

3. 6 Additional methodsnetwork diagram calculation

Network diagram calculation diagonal table method(sometimes called the matrix method) is carried out with a focus on events, rather than on work. At the beginning, a square grid is drawn in which the number of lines and the number of columns is equal to the number of events in the graph. (Fig. 8.) Then on the left, from top to bottom, all the numbers of the initial events are entered (index i), and at the top from left to right are the numbers of final events (index j). In the cells at the intersection of the initial and final events, the values ​​of the duration of work (ti-j) are entered.

There is also sector method. It involves depicting a network diagram with enlarged circles divided into six sectors, which can further be divided into subsectors. The event number is indicated in the upper central sector, and the calendar date of the start of work is indicated in the lower sector. The early starts and finishes of work are entered into the two upper side sectors, and the late starts and finishes of work, respectively, into the two lower side sectors. On the left it is customary to record the completion of work included in this event, on the right - the beginning of work emerging from this event. (Fig. 9)

Calculation of schedule indicators is carried out in two passes: direct from the initial event to the final one sequentially along all paths of the schedule, and reverse - from the final event to the initial one. With a direct pass, the early starts and finishes of work are determined. During the return passage - late starts and finishes of work.

There are other methods for calculating a network graph that involve calculating analytical parameters directly on the graph in event circles divided into several sectors. One of these methods - the four-sector method - involves dividing the event circle into four sectors. There are several modifications of the four-sector method.

As mentioned earlier, today there is an expansion of methods and techniques for using network methods.

Conclusion

So, I tried to consider the topic "Analysis of network methods for planning project work."

I realized that today network planning plays a big role. Network planning methods can be widely and successfully used to optimize the planning and management of complex, branched sets of work that require the participation of a large number of performers and the expenditure of limited resources.

It should be noted that network planning is a management method based on the use of the mathematical apparatus of graph theory and a systems approach to display and algorithmize complexes of interrelated work, actions or activities to achieve a clearly defined goal; The main goal of network planning is to reduce project duration to a minimum.

Network planning is based on the construction of network diagrams, which are of two types - the “vertex-work” type and the “vertex-event” or “arc-work” type.

When creating a network diagram, the concepts of "work", "event" and "path" are the basis for constructing a network.

Network planning techniques were developed in the late 50s in the USA. In the USSR, the beginning of work on network planning dates back to 1961. Then network planning methods found application in construction and scientific developments.

There are various network planning methods.

A Gantt chart is a horizontal line chart in which project tasks are represented as time-bound segments characterized by start and end dates, delays, and possibly other time parameters.

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

The method of statistical testing (otherwise called the Monte Carlo method) consists of considering the network as a probabilistic model, on which estimates of the duration of individual jobs can take any values ​​that lie within the extreme (minimum and maximum) limits specified by experts, and even go beyond these limits in to the extent that the laws of probability theory allow this.

The PERT method is an event-based network analysis method used to determine program duration when there is uncertainty in estimating the duration of individual operations. PERT is based on the critical path method, in which activity duration is calculated as a weighted average of optimistic, pessimistic and expected forecasts. PERT calculates the standard deviation of the completion date from the duration of the critical path. The graphical estimation and analysis method (GERT method) is used in cases of work organization where subsequent tasks can begin after the completion of only a certain number of previous tasks, and not all tasks are represented on the network model , must be completed to complete the project.

Currently, there is an expansion of methods and techniques for using network methods.

So, the network model allows you to: · clearly present the structure of a set of works, identify their stages and relationships with any degree of detail; · draw up a reasonable plan for the implementation of a set of works, using resources more efficiently according to a given criterion; · conduct a multivariate analysis of different solutions in order to improve the plan; · use computers and computer systems to process large amounts of information. Used literature and sources

1. Aleksinskaya T.V. Tutorial on solving problems in the course "Economic and mathematical methods and models". Taganrog: TRTU Publishing House, 2002, 153 p.

2. Ventzel E.S. Operations research. M, Soviet radio, 1972.

3. Zabolotsky V.P., Ovodenko A.A., Stepanov A.G. Mathematical models in management: Proc. allowance/SPbGUAP. St. Petersburg, 2001, 196 pp.: ill.

4. Ivasenko A.G. Project management: textbook/A.G. Ivasenko, Ya.I. Nikonova, M.V. Karkavin - Rostov n/Don: Phoenix, 2009. - 330 p. - Higher education.

5. Kudryavtsev E.M. Microsoft Project. Methods of network planning and project management. - M.: DMK Press, 2005. - 240 p., ill.

6. Mazur I.I., Shapiro V.D., Olderogge N.G. Project management: Academic manual/ Ed. ed. I.I. Mazura. - 3rd ed. - M.: Omega-L, 2004. - p. 664.

7. Tynkevich M.A. Economic and mathematical methods (operations research). Ed. 2, rev. and additional - Kemerovo, 2000. -177 p. ISBN 5-89070-043-X

8. Project management. Fundamentals of project management: student/col. author: ed. prof. M.L.Razu. - M.: KNORUS, 2006. - 768 p.

9. Budgeting. http://www.informicus.ru/default.aspx?SECTION=6&id=89&subdivisionid=25

10. INTRODUCTION to project management. http://www.hr-portal.ru/article/vvedenie-v-proektnyi-menedzhment

11. Probabilistic planning of construction of facilities. http://prosvet.su/articles/menegment/article1/

12. Network planning. http://www.inventech.ru/lib/glossary/netplan/

13. Critical path method. http://ru.wikipedia.org/wiki/Critical_path method

14. Network planning. http://ru.wikipedia.org/wiki/Network_planning

15. Rebrin Yu.I.. Fundamentals of economics and production management. Network planning and management. http://polbu.ru/rebrin_management/ch24_all.html

Applications

Rice. 1. Network fragment" top-work"

Rice. 2. Network fragment" vertex-event"

Rice. 3. Legend in network diagram

Rice. 4. Gantt chart.

Rice. 5. Cyclogram a)equalsrhythmic and b) non-rhythmic flow.

Rice. 6. Calculation using the critical path method

Rice. 7. Histogram of the Monte Carlo method

Rice. 8. Tabular form for the methoddiagonal table

Figure 9. Sector method

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discipline

Network diagram (network, network graph, PERT diagram) - a graphical display of project activities and dependencies between them. In project planning and management, the term “network” refers to the full range of activities and milestones of a project with the dependencies established between them.

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

Rice. 3. Fragment of the “vertex-job” network

There is another type of network diagram, the vertex-event network, which is used less frequently in practice. With this approach, work is represented as a line between two events (graph nodes), 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 the tool is used to model business processes. The fundamental difference from a flowchart is that a network diagram displays only logical dependencies between activities, and not inputs, processes and outputs, and also does not allow repeating cycles or so-called loops (in graph terminology - an edge of the graph starting from a vertex and returning to the same vertex, Fig. 5).

Fig.5. Example of a loop in a network model

Network planning methods - methods whose main goal 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 of evaluating and revising plans, developed almost simultaneously and independently.

Critical path - the maximum duration of a complete path in the network is called critical; work along this path is also called critical. It is the duration of the critical path that determines the shortest 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 activities lying on the critical path. Accordingly, any delay in the completion of work on the critical path will increase the duration of the project.

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

Full time reserve, or time reserve , is the difference between the dates of late and early completion (start) of work. The managerial meaning of the time reserve is that, if necessary, to resolve 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. Activities on the critical path have a slack of zero.

Gantt chart- a horizontal line chart in which project tasks are represented as long segments 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. To calculate and analyze a network diagram, a set of network procedures known as “critical path method procedures” are used.

The network model development process includes:

defining a list of project works;

assessment of work parameters;

identifying dependencies between jobs.

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

Work packages define the activities that must be completed to achieve project results, which can be identified as milestones.

Before starting to develop a network model, it is necessary to make sure that at the lower level of the development work system, all the work that ensures the achievement of all specific goals of the project is identified. The network model is formed by defining the dependencies between these activities and adding connecting activities and events. In general, this approach is based on the assumption that each work is aimed at achieving a particular result. Connecting work may not require any material final result, for example, the work of “organizing execution.”

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

The value of schedules, cost and resource plans obtained as a result of network model analysis depends entirely on the accuracy of work duration estimates, as well as estimates of the work's resource and financial requirements.

Estimates must be made for each detailed activity and can then be aggregated and summarized for each of the WBS levels in the project plan.

Figure 6 Ganga Diagram