Methodology and technology of network management planning. Network planning and management method. Problems solved by the network method

Managing the planning process and the progress of work is not an easy task. Obviously, the most correct thing in this case would be to use network planning and management methods (NPM).

SPU methods are developed as mathematical methods for constructing operations research models. The development of the method has been brought to working computer programs and we just have to learn how to use them in relation to our work of searching for ideas. You will master the use of SPM methods in practical classes. SPC methods are based on modeling processes using network diagrams and represent a set of calculation methods, organizational and control measures for planning and managing a set of works. The SPU system allows:

formulate a calendar plan for the implementation of a certain set of works;

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

carry out management of a complex of works according to the “leading link” principle with forecasting and prevention of possible disruptions in the course of work;

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

A network model is a plan for the implementation of a certain set of interrelated works (operations), specified in a specific form of a network, the graphical representation of which is called a network diagram. The elements of the network model are events and activities.

A network diagram is a model for achieving a set goal, and the goal is a model dynamically adapted for analyzing options for achieving the goal, for optimizing planned tasks, for making changes, etc.

The method of working with network graphs - network planning - is based on graph theory. Translated from Greek, a graph (grafpho - I write) represents a system of points, some of them are connected by lines - arcs (or edges). This is a topological (mathematical) model of interacting systems. Using graphs, you can solve not only network planning problems, but also other problems. The network planning method is used when planning a set of interrelated works. It allows you to visualize the organizational and technological sequence of work and establish the relationship between them. In addition, it allows for coordination of operations of varying degrees of complexity and identification of operations on which the duration of the entire work (i.e., organizational event) depends, as well as focusing on the timely completion of each operation.

The network method is a system of techniques and methods that, based on the use of a network diagram (network model), make it possible to rationally carry out the entire management process, plan, organize, coordinate and control any set of works, ensuring the effective use of monetary and material resources. Using this method allows you to improve:

planning, ensuring its complexity, continuity, creating conditions for improving the identification of required resources and the distribution of existing resources;

financing of work, because there are ways to more accurately calculate the cost of work, their labor intensity and the formation of a regulatory and reference base;

the structure of the management system by clearly defining and distributing tasks, rights, and responsibilities;

organizing procedures for coordinating and monitoring the progress of work on the basis of prompt and accurate information, as well as assessing the implementation of the plan.

A network diagram is an information model that displays the process of performing a set of works aimed at achieving a single goal. The purpose of network planning is to influence management, and management is designed to maintain a rational mode of operation, restore the disturbed state of moving equilibrium of dynamic systems, ensuring the coordinated operation of all its links. At the same time, the system is managed according to a number of parameters: time, cost, resources, technical and economic indicators. However, the most common are systems with the “time” parameter.

The management process when representing the managed system in the form of a model is significantly simplified. The basis of network planning and management is a network diagram, reflecting the technological and logical relationship of all operations of the upcoming work. It consists of three components (main concepts), such as “work”, “event” and “path”.

“Work” is any process that requires time and resources, or just time. If no resources are required to complete the work, but only time is spent, then they are called “waiting”. The work on the network diagram is indicated by a solid arrow (graph arc), above which a number indicates the duration of the work. There is fictitious work (waiting, simple dependence) - work that does not require time, labor and money. It is shown as a dotted arrow on the graph.

Works in the form of an arrow (then the graph is called oriented, or digraph) on the graph are not vectors, therefore they are drawn without scale. Each work begins and ends with an “event”, which is indicated by a circle in which the number indicates the name (name) of this event. An event is the result of the execution of one or more activities, which is necessary for the start of subsequent activities. The antecedent event is the starting point for the work (the cause), and the subsequent event is its result.

Events, unlike jobs, take place at certain points in time, without using any resources. The beginning of a set of works is the initial event. The moment of completion of all work is the final event.

Any network diagram has one initial (initial) and one final (final) event. Any work - an arrow - connects only two events.

The event from which the arrow comes out is called prior to this work, and the event into which the arrow enters is called subsequent. The same event, in addition to the initial and final one, is antecedent in relation to one work, and subsequent to another. Such an event is called an intermediate event. Events can be simple or complex. Simple events have only one input and one output operation.

Complex events have multiple inputs or multiple outputs. Dividing events into simple and complex is of great importance when calculating network graphs. The event is considered completed when the longest duration of all the works included in it is completed.

A continuous technological sequence of work (chain) from the first event to the last is called a path. This path is the complete path. There can be several complete paths. The length of the path is determined by the sum of the duration of the work lying on it. Using the graphing method, each of the paths can be determined. This is achieved by sequentially identifying the elements of each path.

As a result of comparing various paths, the path on which the duration of all contained activities is the longest is selected. This path is called the “critical path”. It determines the time required to complete the entire plan for which the schedule is drawn up. The final deadline for completing the plan depends on the activities located on the critical path and their duration.

The critical path is the basis for plan optimization. In order to reduce the duration of the entire plan, it is necessary to reduce the duration of those activities that are on the critical path.

All complete paths whose duration is less than the critical one are called non-critical. They have time reserves. Time reserves are understood as permissible shifts in the timing of events and completion of work that do not change the timing of the final event.

Time reserves can be full or free. Full time slack is the period by which the start of work can be postponed or its duration can be increased while the length of the critical path remains unchanged. Total slack is defined as the difference between the late and early start of work or between the late and early finish of work.

Activities on the critical path do not have a full time reserve, because their early parameters are equal to their late ones. Using the full slack time on other non-critical paths causes the path to which the slack belonged to to become critical.

Free time reserve is the period by which the start of work can be postponed or its duration can be increased, provided that the early starts of subsequent work do not change. This time reserve is used when one event includes two or more jobs. Free time reserve is defined as the difference between the early start of the subsequent work and the early finish of the work in question.

The time reserve allows you to increase the duration of work or start it a little later, and also makes it possible to maneuver internal financial, material and labor resources (money, amount of equipment, number of employees, start time of work).

Analyzing network graphs, you can see that they differ not only in the number of events, but also in the number of relationships between them. The complexity of the network diagram is assessed by the complexity coefficient. The complexity coefficient is the ratio of the number of works on the network schedule to the number of events and is determined by the formula:

K = R / C, (3)

where K is the complexity coefficient of the network diagram;

P and C - number of works and events, units.

Network diagrams with a complexity coefficient from 1.0 to 1.5 are simple, from 1.51 to 2.0 are of medium complexity, and more than 2.1 are complex.

When starting to build a network diagram, you should establish:

What work must be completed before this work begins;

What work can be started after completion of this work;

3. What work can be performed simultaneously with this work. In addition, you must adhere to the general provisions and rules:

the network is drawn from left to right (the work arrows also have the same direction);

each event with a large serial number is depicted to the right of the previous one;

the schedule should be simple, without unnecessary intersections;

all events except the final one must have subsequent work (there should be no event in the network, except the initial one, which would not include any work);

the same event number cannot be used twice;

in the network diagram, no path should pass through the same event twice (if such paths are detected, this indicates an error);

if the beginning of any work depends on the end of two previous works coming from one event, then a fictitious work (dependency) is introduced between the events - the endings of these two works.

The use of network models can provide significant assistance in planning and implementing activities within the framework of innovation management, so they cannot be neglected.

2.2 The concept of network planning, construction of network models

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 creating complex production systems and other long-term use objects.

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, etc. Network planning is usually understood as a graphical representation of a certain set of work 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. Network models or graphs are intended for the design of complex production facilities, economic systems and all kinds of work consisting of a large number of different elements. For simple work, linear or cycle graphs are usually used.

The use of network planning in modern production helps achieve 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, timely make the necessary planning and management decisions and adjust deadlines;

6) make the necessary adjustments to work schedules taking into account changes in the external environment, internal environment and other market conditions.

Thus, the use of a network planning system contributes to the development of an optimal version of the enterprise’s strategic development plan, which serves as the basis for the operational management of a set 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.

The network model operates with such concepts as: work, event, path.

Works are any production processes or other actions leading to the achievement of certain results of events. The work is indicated by an arrow (vector) without a scale, indicating the direction from left to right from the smaller event number to the larger one and is encoded by the numbers of these events. Works can be of three types:

real, i.e. a production process that requires labor, time and resources;

waiting - work that does not require labor and resources, but takes the time necessary for the actual work to be considered completed, i.e., subsequent work can begin;

dependency or fictitious work, meaning a logical (technological) connection between two or more events and indicating that the possibility of starting one work depends on the completion of another. Fictitious work requires no labor, no time, no resources; it is indicated in the network diagram by dotted arrows.

An event means the completion of one or more activities that are necessary and sufficient for the start of subsequent ones. Events can be initial and initial, final or final, simple or complex, as well as intermediate, antecedent or subsequent.

There are three main ways to represent events and activities on network graphs: activity vertices, event vertices, and mixed networks. In networks of the vertex-work type, all processes or actions are represented in the form of rectangles following one another, connected by logical dependencies (Fig. 3, 4).

A B C D E Fig. 3 - Network of the "vertex-work" type

Rice. 4 - Network of the “vertex-event” type

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; the path preceding a given event from the initial one;

the path following this event to the final one;

path between several events;

the critical path from the initial to the final event is equal to the maximum duration of the work.

Network models can be very diverse both in the organizational structure of the production system and in the purpose of network diagrams, as well as the information processing tools used for regulatory data. According to the organizational structure, intra-company or industry models of network planning are distinguished, and according to purpose - single and permanent action.

Network models can be deterministic, probabilistic and mixed. In deterministic network schedules, all activities of a strategic project, their duration and relationships, 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 or multi-purpose.

Network models can be widely used at all domestic enterprises when developing both long-term and current plans. Network planning allows you not only to determine the need for various production resources in the future, but also to coordinate their rational consumption in the present. With the help of network graphs, it is possible to connect into a single system all material, labor, financial and many other resources and means of production in both ideal (planned) and real (existing) economic conditions.

The creation of network planning and economic activity management systems at our enterprises involves, first of all, determining the structure and functions of planning bodies, justifying the goal and choosing a planning object, building a network model of the project, establishing the order of functioning of the model at the stages of initial planning and operational management of the project.

The most important stages of network planning for a wide variety of production systems or other economic objects are the following:

1) dividing the complex of works into separate parts and assigning them to responsible performers;

2) identification and description by each performer of all events and work necessary to achieve the goal;

3) construction of primary network diagrams and clarification of the content of planned work;

4) linking private networks and building a consolidated network schedule for completing a set of works;

5) justification or clarification of the execution time of each work in the network schedule.

The breakdown of the complex of planned works is carried out by the project manager. During network planning, two methods of distributing work performed are used: horizontal division of functions between performers and vertical construction of a diagram of project management levels. In the first case, a simple system or object is divided into individual processes, parts or elements, for which an enlarged network diagram can be built. Each process is then divided into operations, techniques and other calculation activities. For each component of the work package, its own network diagram is created. In the second case, a complex projected object is divided into separate parts by constructing a known hierarchical structure of the corresponding levels of project management.

Primary network diagrams, constructed at the level of responsible executors, must be detailed to such a degree of dissection that they can reflect both the entire set of work performed and all existing relationships between individual works and events. First, it is necessary to identify what events will characterize this set of works entrusted to the responsible executor. It is recommended to list all events and work included in a given complex in the order in which they were performed.

The network diagram is stitched together by the responsible person based on the list of work performed. The construction of a network can begin both from the initial event, gradually approaching the final one, and vice versa - from the final event to the initial one.

When constructing network graphs of the “vertex-event” type, the following rules must be observed:

No work should have the same code as another.

There should be no dead ends in the network diagram, i.e. events from which no work comes out, if these events are not final for a given network diagram and tails, i.e. events that do not include any work, if these events are not the source for this network diagram

The network diagram also should not have more than one initial event, as this indicates the impossibility of its implementation;

There should be no closed contours (cycles) in the network diagram, i.e. a chain of works returning to the event from which it came. The presence of such a cycle in the network indicates an error in the source data or an incorrect representation of the relationship of work.

In the network model, it is not allowed to depict the connection between adjacent events and two or more activities.

After compiling and checking the primary network diagrams developed by each performer for his/her set of works, the private networks are stitched together and combined into a consolidated model. A consolidated network schedule constructed using the above rules will ensure the achievement of the planned goals set for the performers.

The final stage of network planning is to determine the duration of individual work or cumulative processes. In deterministic models, the duration of work is considered constant. In real conditions, the time it takes to complete various jobs depends on a large number of both internal and external factors and is therefore considered a random variable. To establish the duration of any work, it is necessary first of all to use the appropriate standards or labor cost standards. And in the absence of initial regulatory data, the duration of all processes and work can be established by various methods, including the use of expert estimates.

The following methods can be used to determine the duration of activities contained in network models.

According to current standards, with the help of which the duration of a wide variety of labor, technological and production processes can be most accurately justified at each enterprise.

According to the achieved labor productivity, on the basis of which it is possible to establish the duration of previously performed work on various types of technological equipment.

According to expert estimates, which are usually used to determine the duration of newly designed original works.

In the process of network planning, expert estimates of the duration of upcoming work are usually established by responsible executors. For each job, as a rule, several time estimates are given: minimum, maximum and most probable. If you determine the duration of work by only one time estimate, then it may turn out to be far from reality and lead to disruption of the entire progress of work according to the network schedule. Estimated duration of work is expressed in man-hours, man-days or other units of time. The most probable time estimate obtained cannot be accepted as a standard indicator of the expected time to complete each job, since in most cases this assessment is subjective and largely depends on the experience of the responsible performer of the work. Therefore, to determine the expected completion time for each job, expert estimates are subjected to statistical processing. Assuming that the probability of the duration of any job corresponds to the law of normal distribution, the expected time of its completion can be calculated using the following formula:

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International University of Nature, Society and Man
"Dubna"

Department of System Analysis and Management

Abstract on the discipline

"Development of 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, scientific research, design and technological preparation of production, new types of products, construction and reconstruction, overhaul of fixed assets through the use of network models.

Target work - to describe and understand what, in general, is network planning and management (NPM).

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

Ø highlight the history of SPU,

Ø show what the essence and purpose of SPU is,

Ø define the main elements of the SPU,

Ø indicate the rules for constructing and organizing network diagrams,

Ø describe the time indicators of the SPU,

Ø give rules for optimizing the network diagram,

Ø show the construction of a network diagram on a time scale.

History of network planning and management

Network planning techniques were developed in the late 50s in the USA. In 1956, M. Walker of DuPont, exploring possibilities for more efficient use of the company's Univac computer, joined forces with D. Kelly of Remington Rand's capital planning group. 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 path method- 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 involves about 3,800 prime contractors and consists 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. Program management was so successful that the project was completed two years ahead of schedule. Because of this successful start, this management method was soon used for project planning throughout the US military. The technique has proven itself to be excellent in coordinating work carried out by various contractors as part of large projects to develop new types of weapons.

Large industrial corporations began to use such management techniques almost simultaneously with the military to develop new types of products and modernize production. The project-based work planning technique has become widely used in construction. For example, to manage a project for the construction of a hydroelectric power station on the Churchill River in Newfoundland (Labrador Peninsula). The cost of the project was $950 million. The hydroelectric power plant was built from 1967 to 1976. The project included more than 100 construction contracts, some of which cost as much as $76 million. In 1974, the project was 18 months ahead of schedule and within cost estimates. The client for the project was Churchill Falls Labrador Corp., which hired Acress Canadian Betchel to design the project and manage construction.

Essentially, a significant gain in time resulted from the use of precise mathematical methods in managing complex sets of work, which became possible thanks to the development of computer technology. 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.

Initially, large companies developed software to support their 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.

The main indicators of systems of this class were their high power and, at the same time, the ability to describe projects in sufficient detail using complex network planning methods. These systems were aimed at highly professional managers managing the development of large projects, well acquainted with network planning algorithms and specific terminology. As a rule, project development and project management consultations were carried out by special consulting firms.

The most rapid development of project management systems began with the advent of personal computers, when the computer became a working tool for a wide range of managers. A significant expansion of the range of users of management systems has given rise to the need to create systems for managing projects of a new type; one of the most important indicators of such systems is ease of use. New generation management systems were developed as a project management tool that is understandable to any manager, does not require special training and ensures easy and quick implementation. Time Line belongs precisely to this class of systems. The developers of new versions of systems of this class, trying to maintain the external simplicity of the systems, invariably expanded their functionality and power, and at the same time maintained 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. Moreover, the bulk of the planned projects are small-sized projects. For example, research conducted by InfoWorld showed that fifty percent of users in the United States require systems that can support schedules consisting of 500-1,000 activities, and only 28 percent of users develop schedules containing more than 1,000 activities. In terms of resources, 38 percent of users have to manage 50-100 types of resources within a project, and only 28 percent of users need to manage more than 100 types of resources. As a result of the research, the average sizes of project schedules were also determined: for small projects - 81 activities and 14 types of resources, for medium ones - 417 activities and 47 types of resources, for large projects - 1,198 activities and 165 types of resources. These figures can serve as a starting point for a manager considering the usefulness of switching to a project-based form of managing the activities of his own organization. As we can see, the use of a 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, there is an 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.

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

The essence and purpose of network planning and management

The more complex and larger the planned work or project, the more complex the tasks of operational planning, control and management. Under these conditions, the use of a calendar schedule may not always be quite satisfactory, especially for a large and complex facility, since it does not allow for reasonable and prompt planning, choosing the optimal option for the duration of work, using reserves and adjusting the schedule during activities.

The listed 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 use of network models ensures thoughtful, detailed organization of work and creates conditions for effective management.

The entire process is reflected in a graphical model called a network diagram. The network schedule takes into account all work from design to commissioning, identifying the most important, critical work, the completion 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, 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.

Drawing1 . 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 final event has no subsequent activities or 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.

1. 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.

2. 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.

3. 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.

4. 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 schedule that has several final events is called multi-objective and the calculation is carried out with respect 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.

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.

Temporary parameters of network diagrams

Early (or expected) date of occurrence of an event determined by the duration of the maximum path preceding this event.

A delay in the completion of an event in relation to its earlier date will not affect the time period for the completion of the final event (and therefore the time period for completing the set of works) as long as the sum of the time period for the completion of this event and the duration (length) of the maximum path following it does not exceed length of the critical path.

That's why late (or deadline) date for the event to occur is equal to the difference between the maximum time of occurrence of the event following the work and the time of work before this (future) event.

Event time reserve is defined as the difference between the late and early dates of its completion.

The reserve time of an event shows by what acceptable period of time the occurrence of this event can be delayed without causing an increase in the period of completion of the work package.

I have no time reserves for critical events, since any delay in the completion of an event lying on the critical path will cause the same delay in the completion of the final event.

It follows from this that in order to determine the length and topology of the critical path, it is not at all necessary to go through all the complete paths of the network diagram and determine their lengths. By determining the early date of the final event of the network, we thereby determine the length of the critical path, and by identifying events with zero time reserves, we determine its topology.

If a network diagram has a single critical path, then this path passes through all critical events, that is, events with zero slack. If there are several critical paths, then identifying them using critical events can be difficult, since some critical events can pass through both critical and non-critical paths. In this case, it is recommended to use critical works.

An individual job can start (and finish) at early, late, or other times in between. In the future, when optimizing the schedule, any placement of work in a given interval, called duration of work.

It's obvious that early start date coincides with the early date of the preceding event.

Early completion date coincides with the earliest date of the subsequent event.

Late start date coincides with the late date of the preceding event.

Late work completion date coincides with the late date of the subsequent event.

Thus, within the framework of the network model, the moments of the beginning and end of work are closely related to neighboring events by corresponding restrictions.

If the path is not critical, then it has reserve time, defined as the difference between the length of the critical path and the path under consideration. It shows how much the duration of all jobs belonging to this path can be increased in total. From this we can conclude that any of the work of the path on its section that does not coincide with the critical path (closed between two events of the critical path) has a reserve of time.

There are four types of work time reserves.

Full time reserve work shows how much the time for completing a given work can be increased, provided that the deadline for completing the set of works does not change.

The total slack of work time is equal to the slack of the maximum of the paths passing through this work. This reserve can be used when performing this work if its initial event occurs at the earliest possible date, and the final event can be allowed to occur at its latest date.

An important property of a complete work time reserve is that it belongs not only to this work, but also to all complete paths passing through it. If the full time reserve is used for only one job, the time reserves of the remaining jobs lying on the maximum path passing through it will be completely exhausted. The time reserves for jobs lying on other (non-maximum in duration) paths passing through this job will be reduced accordingly by the amount of the reserve used.

The remaining operating time reserves are parts of its total reserve.

Private reserve time of the first type there is a part of the total slack by which the duration of the work can be increased without changing the late date of its initial event. This reserve can be used when performing this work on the assumption that its initial and final events occur at their latest dates.

Private reserve time of the second type, or free time reserve work represents a part of the total reserve of time by which the duration of the work can be increased without changing the early date of its final event. This reserve can be used when performing this work on the assumption that its initial and final events will occur at their earliest possible date.

Free time reserve can be used to prevent accidents that may arise during the execution of work. If you plan the execution of work according to early start and finish dates, then you will always have the opportunity, if necessary, to switch to later start and finish dates.

Independent time reserve work - part of the total time reserve obtained for the case when all previous work finishes at a late date, and all subsequent work begins at an early date.

The use of an independent time reserve does not affect the amount of time reserves for other activities. They tend to use independent reserves when the completion of the previous work occurred at a late acceptable date, and they want to complete subsequent work at an early date. If the value of the independent reserve is zero or positive, then there is such a possibility. If this value is negative, then this possibility does not exist, since the previous work has not yet finished, and the next one must already begin. That is, a negative value of this value has no real meaning. In fact, only those jobs that do not lie on the maximal paths passing through their initial and final events have an independent reserve.

Thus, if the private time reserve of the first type can be used to increase the duration of this and subsequent work without spending the time reserve of previous work, and the free time reserve can be used to increase the duration of this and previous work without violating the time reserve of subsequent work without violating the time reserve of subsequent work , then the independent time reserve can be used to increase the duration of only this job.

Activities lying on the critical path, as well as critical events, do not have time reserves.

Figure 3. Key to calculation by sector method

It should be noted that in the case of fairly simple network graphs, in addition to the tabular method for calculating the parameters of network graphs, one can apply sector representation time parameters, that is, the parameters can be calculated on the chart itself. For this purpose, each event is divided into four sectors. In the left sector of the event, the early start of work is recorded, in the right - the late finish, in the upper - the number of this event, in the lower - the number of the previous event, from which the path of maximum duration goes to this event. Occurs when the event number is placed in the lower sector and the upper sector is not filled in. Certain time reserves are written under the arrow in the form of a fraction: the numerator is the general reserve, and the denominator is the private reserve.

Network diagram 5. Sector representation of time parameters

In reality, in practice, the duration of work and its actual condition may vary. At the same time, the expected time of occurrence of an event, completion of work, and the critical path may also change. Knowing the critical path, management can focus on those activities that are critical in terms of completion dates for all activities.

Network diagram analysis and optimization

After finding the critical path and work time reserves and assessing the probability of completing the project within a given time frame, a comprehensive analysis of the network schedule should be carried out and measures taken to optimize it. This very important stage in the development of network graphs reveals the main idea of SPU. It consists in bringing the network schedule into compliance with the given deadlines and capabilities of the organization developing the project.

Optimization of the network diagram, depending on the completeness of the problems being solved, can be divided into partial and complex. Species private optimization network diagram are: minimizing the time it takes to complete a set of works at a given cost; minimizing the cost of a set of works for a given project completion time. Comprehensive optimization represents finding the optimal ratio of the cost and timing of the project, depending on the specific goals set during its implementation.

First, we will consider the analysis and optimization of calendar networks in which only estimates of the duration of work are given.

The analysis of the network diagram begins with an analysis of the network topology, which includes control over the construction of the network diagram, establishing the appropriateness of the selection of works and the degree of their division.

Then the work is classified and grouped according to the amount of reserves. It should be noted that the amount of total time slack cannot always sufficiently accurately characterize how stressful it is to perform a particular job on a non-critical path. It all depends on which sequence of work the calculated reserve applies to and what the duration of this sequence is.

The degree of difficulty of completing each group of work on a non-critical path on time can be determined using the work intensity coefficient.

Work intensity coefficient is called the ratio of the durations of path segments that do not coincide, but are concluded between the same events, one of which is the path of maximum duration passing through a given work, and the other is the critical path.

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

Let us pay attention to the fact that a greater full reserve of one job (compared to another) does not necessarily indicate a lesser degree of intensity in its implementation. This is explained by the different proportion of total work reserves in the duration of segments of maximum paths that do not coincide with the critical path.

The calculated stress coefficients make it possible to further classify the work by zone:

Ø critical K > 0.8,

Ø subcritical 0.6< К < 0,8,

Ø reserve K< 0,6.

Network schedule optimization represents the process of improving the organization of the execution of a set of works, taking into account the deadline for its completion. Optimization is carried out with the aim of reducing the length of the critical path, equalizing work intensity coefficients, and rational use of resources.

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

Ø redistribution of all types of resources, both temporary (using time reserves of non-critical paths), and labor, material, energy, while the redistribution of resources should proceed, as a rule, from zones that are less stressful to zones that combine the most intense work.

For example, it is possible to increase work shifts in “narrow” construction areas. This measure is the most effective because it allows you to achieve the desired result with the same driving machines (excavator, machine tool, etc.), only by increasing the number of workers.

Ø reducing the labor intensity of critical work by transferring part of the work to other routes that have time reserves;

Ø revision of the network topology, changes in the scope of work and network structure.

Ø ensure parallel (combined) work;

Ø divide a wide scope of work into smaller sections or sections;

Ø The duration of the program can be reduced by changing the technology used, for example, in construction, replacing monolithic reinforced concrete structures with prefabricated ones and other prefabricated elements manufactured at the factory.

When adjusting the schedule, it must be borne in mind that workers are saturated with resources up to a certain limit (so that each worker is provided with a sufficient scope of work and has the opportunity to comply with safety rules).

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 work on the new critical path and will continue until a satisfactory result is obtained. Ideally, the length of any of the complete paths can become equal to the length of the critical path or at least the path of the critical zone. Then all work will be carried out with equal stress, and the project completion time will be significantly reduced.

The most obvious option for private optimization of a network schedule, taking into account cost, involves the use of work time reserves. The duration of each job that has a slack time is increased until the slack is exhausted or until the upper duration value is reached. It is advisable to increase the duration of each job by the amount of such a reserve so as not to change the early timing of all network events, that is, by the amount of free time reserve.

In practice, when trying to effectively improve the drawn up plan, it is inevitable to introduce, in addition to the time estimates, the cost factor of the work. The project may require acceleration of its implementation, which, naturally, will affect the cost: it will increase. Therefore, it is necessary to determine the optimal relationship between the cost of the project and the duration of its implementation.

When using the time-cost method, it is assumed that the decrease in the duration of the work is proportional to the increase in its cost. An increase in cost with a decrease in time is called expenses for acceleration.

It is very effective to use a statistical modeling method based on multiple sequential changes in the duration of work (within specified limits) and “playing” on a computer various network schedule options with calculations of all its time parameters and work intensity coefficients.

For example, you can take as the initial plan that has the minimum duration of work and, accordingly, the maximum cost of the project. And then consistently increase the duration of a set of works by increasing the duration of work located on the non-critical, and then on the critical (critical) path to a satisfactory value of the project cost. Accordingly, you can take as the initial plan, which has the maximum duration of work, and then successively reduce their duration to such an acceptable value for the duration of the project.

The process of “playing” continues until an acceptable version of the plan is obtained or until it is determined that all available possibilities for improving the plan have been exhausted and the conditions set before the project developer are impossible to fulfill.

Currently, in practice, the network is first adjusted in time, i.e., it is brought to a given construction completion date. Then they begin to adjust the schedule according to the criterion of resource distribution, starting with labor resources.

It should be noted that with a linear dependence of the cost of work on its duration, the problem of constructing an optimal network schedule can be formulated as the problem linear programming, in which it is necessary to minimize the cost of project implementation while limiting, firstly, the duration of each work within established limits, and, secondly, the duration of any complete path of the network schedule to no more than the established deadline for the project.

Construction of a network diagram on a time scale

In practice, network graphs drawn up on a time scale linked to calendar dates have become widespread. When monitoring the progress of work, such a schedule will allow you to quickly find work performed in a certain period of time, determine whether they are ahead or behind, and, if necessary, redistribute resources.

A network diagram drawn up on a time scale makes it possible to construct graphs of resource requirements and thereby establish correspondence with their actual availability. The construction of a network diagram on a time scale is carried out according to early starts or late finishes of work and proceeds sequentially from the initial event to the final one.

It is convenient to link the network schedule to the calendar using a calendar ruler in which years, months and dates are recorded (excluding weekends and holidays). Using the table, you can easily find the calendar start or end date of work.

Network diagram 6. Network diagram in time scale

In cases of changes in the initial data and the actual progress of work, the network diagram drawn up in relation to the 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 network planning and management methods provide managers and performers in all areas of work with the reasonable information they need to make decisions on planning, organization and management. And when using computer technology, SPC is no longer just one of the planning methods, but an automated method of managing the production process.

Sources used

1. webforum.land.ru– forum on project management in Russia.

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7.1.NETWORK PLANNING

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

organizational, etc.).

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

Network work plans of an enterprise 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, schedules for the execution of production processes were used in American companies by G. Gant. On linear (tape) graphs, the duration of work at all stages of production is plotted along the horizontal axis on a selected scale. The content of work cycles (with the necessary degree of their division into individual parts or elements) is depicted along the vertical axis. Line graphs are usually used in domestic enterprises in the process of short-term or operational planning of production activities.The main disadvantage of such schedules is the impossibility of close interconnection of individual works into a single production system or the overall process of achieving the planned final goals of the enterprise.

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. Network planning provides not only images, but also modeling, analysis and optimization of projects for the implementation of complex technical specifications, design developments, etc.

Network planning is usually understood as a graphical representation of a certain set of work being performed, which not only reflects their logical sequence, existing relationships and planned duration, but also ensures subsequent optimization of the developed schedule in order to use it for ongoing management of the progress of work.

Network planning is based on graph theory. Under count is understood as a set of points (nodes) connected by lines. The direction of the lines is shown by arrows. The segments connecting the vertices are called edges (arcs) of graphs. A graph is called directed if arrows indicate the directions of all its edges, or arcs. Graphs are called maps, labyrinths, networks, and diagrams.

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

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

Events the final results of previous work are considered. An event records the fact of work completion, specifies the planning process, and eliminates the possibility of different interpretations 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 (initial) or final (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: activity vertices, event vertices, and mixed networks.

In networks of the “vertex-work” type, all processes or actions are represented as rectangles following one another, connected by logical dependencies.

As can be seen from the network graph (Fig. 1), it depicts a simple model, or network, consisting of five interconnected activities: A, B, C, D and E. The initial activity is A, followed by intermediate activities B, C and D and further the final work of D.

In networks of the “vertex-event” type, all jobs or actions are represented by arrows, and events are represented by circles (Fig. 2). This network graph shows a simple production process involving six interconnected events: 0, 1, 2, 3, 4 and 5. The initial event in this case is event zero, the final event is event five, and all others are intermediate.

Network schedules serve not only for planning a variety of work, but also for their coordination between project managers and executors, as well as for the rational use of production resources.

Network planning is successfully used in various areas of business and production activity, such as:

Marketing research;

Research works;

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 of technological equipment;

Development of business plans for the production of new goods;

Restructuring of existing production in market conditions;

Preparation and placement of various categories of personnel;

Innovation management, etc.

The use of network planning in modern production helps to solve strategic and operational problems. Network planning allows you to:

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 planned period;

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

4) distribute and rationally use enterprise resources more efficiently;

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

6) conduct a multivariate economic analysis of various technological methods and the sequence of work paths, as well as resource allocation.

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

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

The most important stages of network planning for production facilities

Breakdown of a set of works into individual components and their

assignment to responsible executors;

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

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

Linking private networks and building a consolidated network schedule for completing a set of works;

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

The breakdown (division) of the complex of planned works is carried out by the project manager. During network planning, two methods of distributing work performed are used: division of functions between performers (horizontal distribution); constructing a diagram of project management levels (vertical distribution). In the first case, a simple system or object is divided into individual processes, parts or elements, for which an enlarged network diagram can be built. Each process is then divided into operations, techniques and other calculation activities. For each component of the work package, its own network diagram is created. In the second case, the complex projected object is divided into separate parts by constructing a known hierarchical structure of the corresponding levels of project management.

The drawing up of network diagrams at each level is carried out by their managers or responsible executives. Each of them in the network planning process:

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

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

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

o ensures implementation of decisions made.

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

The network diagram is stitched together by the responsible person based on the established list of works.

The final stage of network planning is determining the duration of individual work or cumulative processes. In deterministic models, the duration of work is considered constant. In real conditions, the time it takes to complete various jobs depends on a large number of factors (both internal and external) and is therefore considered a random variable. To establish the duration of any work, it is necessary first of all to use the appropriate standards or labor cost standards. In the absence of initial regulatory data, the duration of all processes and work can be established by various methods, including the use of expert estimates.

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

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

Minimum time - This is the shortest possible working time for executing the designed processes. The likelihood of getting the job done in that amount of time is low. Maximum time- this is the longest time to complete the work, taking into account the risk and extremely unfortunate combination of circumstances. Most likely time- this is the time it takes to complete the work, or one that is close to actual conditions.

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

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

Practical structuring of the project begins with drawing up a list of works, in which all types of work are given with the corresponding symbols. It is quite difficult to define and thereby differentiate between types of work. It is important to maintain a level of detail appropriate to the problem. The list of works contains the characteristics of the materials and capacities required for their implementation by type (personnel, machines, tools), timing and volume.

In conclusion, cause-and-effect relationships between the works are consistently established. This is done either by setting the parameters of some jobs that immediately precede other jobs, or by indicating the immediate next jobs. After this, an appropriate network plan is drawn up.

Annotation: Structural planning. Scheduling. Operational management. Practical classes on structural and calendar planning. Test assignments.

2.1. Theoretical course

2.1.1. Structural planning

Structural planning includes several stages:

dividing the project into a set of individual works, the implementation of which is necessary for the implementation of the project;
constructing a network diagram describing the sequence of work;
assessment of the time characteristics of work and analysis of the network diagram.

The main role at the stage of structural planning is played by the network diagram.

Network diagram is a directed graph in which the vertices indicate the work of the project, and the arcs indicate the temporary relationships of the work.

The network diagram must satisfy the following properties.

Each job corresponds to one and only one vertex. No work can be represented on the network diagram twice. However, any job can be divided into several separate jobs, each of which will correspond to a separate vertex of the graph.
No job can begin before all the jobs immediately preceding it have been completed. That is, if arcs enter a certain vertex, then work can begin only after the completion of all the works from which these arcs emerge.
No job that immediately follows a job can begin before it ends. In other words, if several arcs exit from a job, then none of the jobs that those arcs are part of can begin until that job ends.
The beginning and end of the project are indicated by activities with zero duration. Such work is called milestones and mark the beginning or end of the most important stages of the project.

Example. As an example, consider the project “Development of a software package”. Let's assume that the project consists of work, the characteristics of which are given in Table 2.1.

Table 2.1.

Work number	Job title	Duration
1	Start of the project	0
2	Formulation of the problem	10
3	Interface development	5
4	Development of data processing modules	7
5	Database structure development	6
6	Populating the Database	8
7	Debugging the software package	5
8	Testing and bug fixing	10
9	Preparation of program documentation	5
10	Completion of the project	0

The network diagram for this project is shown in Fig. 2.1. On it, the vertices corresponding to normal work are outlined with a thin line, and the project milestones are outlined with a thick line.

Rice. 2.1.

The network diagram allows you to find the critical activities of the project and its critical path using given values of work durations.

Critical is a job for which a delay in its start will delay the completion of the project as a whole. Such work does not have a reserve of time. Non-critical activities have a certain margin of time, and within this margin their start may be delayed.

Critical path– this is the path from the initial to the final vertex of the network diagram, passing only through critical activities. The total duration of the critical path activities determines the minimum project implementation time.

Finding the critical path comes down to finding critical jobs and is performed in two stages.

Calculation early start time each work of the project. This value shows the time before which work cannot start.
Calculation late start time each work of the project. This value indicates the time after which work cannot begin without increasing the duration of the entire project.

Critical jobs have equal early and late start times.

Let us denote – the work execution time , – the early work start time , – the late work start time . Then

where is the set of jobs immediately preceding job . The early start time of the project is assumed to be zero.

Since the last activity of the project is a milestone of zero duration, its earliest start time coincides with the duration of the entire project. Let's denote this quantity. Now it is taken as the late start time of the last job, and for the remaining jobs the later start time is calculated using the formula:

Here are many works directly following the work.

Schematic calculations of early and late start times are shown, respectively, in Fig. 2.2 and Fig. 2.3.

Rice. 2.2.

Rice. 2.3.

Example. Let's find the critical work and the critical path for the project "Development of a software package", the network diagram of which is shown in Fig. 2.1, and the duration of the work is calculated in days and is given in Table 2.1.

First, we calculate the earliest start time of each job. Calculations start from the initial work and end with the final work of the project. The process and results of the calculations are shown in Fig. 2.4.

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

At the next stage, we calculate the later start time of work. Calculations begin in the last and end in the first work of the project. The process and results of the calculations are depicted in Figure 2.5.

Rice. 2.4.

Rice. 2.5.

The summary results of the calculations are given in Table 2.2. Critical work is highlighted in it. The critical path is obtained by connecting the critical activities on the network diagram. It is shown by dotted arrows in Fig. 2.6.

Table 2.2.

Job	1	2	3	4	5	6	7	8	9	10
Early start time	0	0	10	16	10	16	24	29	29	39
Late start time	0	0	12	17	10	16	24	29	34	39
Time reserve	0	0	2	1	0	0	0	0	5	0

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