How to build a network graph. An example of building a network graph. Network plan preliminary analysis

Section VI.

NETWORK MODELING OF CONSTRUCTION PRODUCTION

147. What are the disadvantages of line charts?
Line charts are easy to use and clearly show progress construction works. However, they cannot reflect the complexity of the simulated construction process and therefore have the following disadvantages:
- the calendar schedule is static: it does not reflect the entire dynamics of the construction process and needs to be constantly adjusted. But while it is being adjusted, agreed and approved, new changes occur, as a result of which the revised schedule again does not reflect the actual state of affairs;
- according to the linear schedule, it is difficult to determine how the construction is going on at the moment - ahead or behind, and for how long;
- according to the linear schedule, it is difficult to determine how the non-fulfillment of one or several works affects the performance of other works, and for how long;
- on the calendar schedule, the works that determine the construction time are not highlighted; the role of secondary works is not visible, as a result of which the construction management is forced to disperse its attention to all works, not concentrating it on the decisive sections of the construction site;
- the line graph does not make it possible to predict the course of events at the construction site, which makes it difficult for the construction manager to choose the right decision for the implementation of subsequent work.

148. What is a network diagram?
A network diagram is a graphic representation of the technological sequence of work at an object or several objects, indicating their duration and all time parameters, as well as the total construction period.
Construction management should be based on a pre-developed model of the construction and production process. installation work, beginning with preparatory work and ending with the commissioning of the facility.

149. What are distinctive features network graph in comparison with linear and cyclogram?
The main features of a network diagram are:
- the presence of a relationship between the work and the technological sequence of their implementation;
- the possibility of identifying works, the completion of which primarily determines the duration of the construction of the facility;
- the ability to select options for the sequence and duration of work in order to improve the network schedule;
- facilitating the control of work over the progress of construction;
- the possibility of using a computer to calculate the parameters of the schedule in planning and managing construction.

150. What elements does the network diagram consist of?
A network diagram consists of four elements: activities, events, expectations, and dependencies.

151. What does the term "work" mean?
Work is technological process, requiring time, labor and material resources and leading to the achievement of a certain planned result. Work on the graph is indicated by a solid arrow, the length of which may not be related to the duration of the work (if the graph is not made on a time scale).

152. What does the term "event" mean?
The fact of completion of one or more works, necessary and sufficient for the beginning of subsequent works, is called an event. This means that the event takes place instantly, so it does not require time, material or labor costs. The event is depicted as a circle, inside which a certain number is indicated - the event code.

153. What types of events can there be?
Events can be initial, final, initial and final.
The initiating event starts the construction of the facility and has no previous activities. This event begins the development of the network diagram.
The end event has no follow-on work and ends the work in the network.
Events limit the work under consideration and in relation to this work they can be initial and final.
The start event for the activity in question determines the start of the activity and is the end event for previous activities.
The end event determines the fact of the end of this work and is the initial for subsequent work.

154. What does the concept of "waiting" mean?
In construction, there may be a need for breaks between work performed. Such breaks can be technological and organizational.
Technological breaks may be associated with the need for curing concrete, hardening the screed for rolled roofing, drying plaster before painting, etc.
Organizational breaks may occur when teams are busy the right professions at another facility, waiting for the warm season to perform landscaping work, and so on.
Such technological breaks are called waiting. Waiting is a process that takes time and does not consume material and labor resources. The wait is depicted, like the work, with a solid arrow indicating the duration and the name of the wait.

155. What does the concept of “dependence” mean?
There may be technological dependencies between certain types of construction and installation works (for example, it is impossible to carry out finishing work, installation technological equipment in the absence of a roof, landscaping work without laying underground utilities etc.).
Dependency (sometimes also called fictitious work) reflects the technological or organizational relationship of work. Addiction requires neither time nor resources; it determines the technological sequence of events.
Dependence is depicted on the network diagram by a dotted arrow.
Dependence can be technological (shows the necessary sequence of work) and resource or organizational, associated with the transition of teams or haul construction machines from object to object.

156. What is the concept of "path" in a network diagram?
Each activity in the network schedule has its own duration, calculated on the basis of the amount of work to be performed. Coming from initiating event to the final, sequentially, along the chain of work and dependencies, you can calculate the total duration of work in each chain.
A path is a continuous sequence of activities in a network diagram. The length of the desired path in time is determined by the sum of the duration of the works that make up this path.
In a network diagram, there can be several paths between the initiating and ending event, which vary in duration.

157. What is the full path of a network diagram?
The path from the initial to the final network event is called complete. The section of the path from the initial event to this event is called the previous one, and the path from the given event to any subsequent one is called the subsequent path.

158. What is a critical path in a network diagram?
The critical path of a network diagram is the complete path from the initial to the final event, which has greatest length(duration) of all full paths. Its time length determines the time for completion of all activities in the network.
There can be multiple critical paths in a network diagram.
Increasing the duration of activities on the critical path increases the total duration of activities; accordingly, the reduction of these works leads to a general reduction in the construction period of the facility.
The critical path on the network diagram is highlighted with a thick line or in some other way.

159. What is a critical zone in a network diagram?
A path whose length is slightly less than the critical path is called subcritical. By reducing the duration of activities on the critical path, the subcritical path can become critical.
The combination of critical and subcritical paths forms a critical zone in the network diagram. Identification of the critical zone in the network schedule allows you to identify the work that needs to be paid attention to if it is necessary to reduce the construction time, either when designing the network schedule, or when monitoring the progress of construction.

160. What is a job code?
In a network diagram, each job is between two events (the initial one, from which it exits, and the final one, into which it enters). Each event has its own number, so each work gets its own code, consisting of the numbers of its initial and final events.

161. What are the basic rules for building a network graph?
There are certain rules for constructing a network graph:
- for the convenience of building a network graph, the direction of the arrows should be taken from left to right, avoiding, if possible, crossing lines;
- each work must have its own code. In the case of performing parallel jobs that have a common beginning and end, additional events must be introduced, otherwise various works will receive a single name;

- in the network diagram there should not be "dead ends" (events from which no work comes out) and "tails" (events that do not include any work);

– numbering (coding) of events must correspond to the sequence of work in time, i.e. previous events are assigned lower numbers;
- the numbering of events should be done only after the complete construction of the network and the conviction that the network is technologically built correctly;
- the initial version of the network diagram is built without taking into account the duration of its constituent works, providing only a technological sequence (in this case, the length of the arrows does not matter).

162. What does the concept of "time reserve" mean?
Comparing the length of the critical path with the length of any non-critical path, we establish that it is possible to increase the length of non-critical works for a certain amount of time without increasing the overall construction time of the facility. These days constitute a reserve of time, which can be private or general.

163. What is a private time reserve?
The private reserve of work time is the amount of working time by which the duration of this work can be increased or its start can be postponed so that the early start of subsequent work does not change.

164. What is the general reserve of time?
Under the total (full) reserve time is understood the amount of working time by which the duration of this work can be increased, provided that the duration of the longest of the paths passing through this work does not exceed the length of the critical path.

165. What is the calendar ruler used for when developing a network diagram?
When developing a network diagram, it is a non-scale model, but it becomes necessary to present it in a familiar form on a time scale that is available for use at any level of management. To link the chart to calendar time, a calendar ruler is used. By linking network events to a calendar, you can clearly see when what work is being done and when it should be completed.
A large-scale chart is usually built according to the early dates of events.

166. How to determine the earliest possible date for the completion of an event?
An event that includes one work can be started when the event of the previous work has occurred and the work of the event in question has been completed.
If the event under consideration includes several activities, then it is possible to proceed to the subsequent activity only when the longest activity included in this event is completed. Having data on the duration of each work included in this event, it is possible to determine for this event the earliest possible date for its completion.
The earliest possible date for the completion of an event is equal to the early start of the previous event and the duration of the longest path preceding this event.

167. How to determine the latest of the admissible dates for the completion of an event?
If the work in question has one successor, then its late finish is equal to the late finish of the successor minus the duration of the work in question.
If the job under consideration has two or more subsequent jobs, then its late completion will be the minimum of the difference between the late finishes of subsequent jobs and their duration.

168. What is the purpose of developing a "card-determinant" network diagram?
The card-determinant of the network diagram is the source document for the calculation of the network diagram. With the help of the identification card, the duration of each work is assigned based on the accepted methods of work production, the composition of the team and shifts are assigned.

169. What data is needed to draw up a map-determinant of the network diagram?
The initial data for the development of a map-determinant of the network diagram (Fig. 4) are:
- the exact name and composition of each work;
- data on the teams available in the construction organization and their composition;
- information on the productivity of labor achieved by these brigades;
- supply data building materials and structures, equipment;
- information about current normative documents(SNiP, ENiR, instructions and guidelines for the production of work);
- data on the mechanisms that construction and installation organizations have.

Rice. 4. Card-determinant of works and resources of the network diagram

170. How to determine the duration of work?
Having determined the complexity of the work, you can determine the duration of the work in two ways:
- having appointed the strength of the brigade, divide the labor intensity of the work by the number of workers in the brigade;
- having assigned the duration of the work in days, divide the labor intensity of the work by its duration; in this case, we will find out the required strength of the brigade.
But these provisions do not apply to the performance of mechanized work. In this case, it is necessary to determine the required number of machine shifts of work and, dividing by the number of mechanisms and their shifts, obtain the duration of work in days; in accordance with ENiR, we appoint the composition of the installation team.

171. How are network graphs stitched together?
For certain types of construction and installation works, local schedules can be developed, which must be combined into a single network schedule for the construction of buildings and structures.
In connection with this, it is necessary to link related works (this is the so-called "stitching" of the schedule). This linking must be done with the help of boundary events, i.e. events that are common to different local schedules and occur as a result of the completion of the work included in these schedules.

172. How to construct diagrams of labor and material resources?
As a result of calculating the network parameters and the possibility of linking it to the calendar, it is possible to identify the need for labor and material resources at each moment of the construction of the facility. To do this, a resource demand diagram is built, the horizontal vector of which is tied to the calendar, and the vertical vector indicates the amount of resources consumed. The construction of the diagram is based on the constancy of the expenditure of resources during the performance of each work. Adding the needs of work vertically within a certain calendar period provides the necessary information.
In order to correctly link the network to the calendar, the start dates of a particular work must correspond to the early start of work, located in the left sector of events.
Works that have a spare time should be highlighted on the network diagram (on the graph they may have a broken line in that part of the work where there is a private time slack), and only that part of the work where there are resources is projected onto the diagram (Fig. 5 and 6). ).

Fig.5. An example of calculating a network diagram directly on the diagram

Fig.6. Building a network graph on a time scale and a diagram of the movement of labor (the number above the arrow is the number of people employed in this work)

173. For what purpose is the network schedule adjusted?
The first stage of developing a network schedule ends with the calculation of its parameters, determining the duration of the critical path and its trajectory. However, the initial (rather, initial) version of the schedule rarely turns out to be immediately optimal. Most often, the network has to be adjusted, bringing it into line with the normative or directive term for the construction of the facility, with the resources available to the performers (labor, material, necessary mechanisms).
After receiving the first version of the network schedule with the definition of the critical path, the calculation of time parameters for each work and the definition of time reserves, the network schedule needs to be analyzed.
Under the adjustment (optimization) of the network schedule, we mean the introduction of possible changes into its original version in order to achieve beneficial results and bring the schedule parameters to the indicators for which the network is planned.
To make these amendments, it is necessary to find the most profitable and possible technological solutions, and sometimes design solutions associated with a reduction in the period of construction and installation work or with a change in the technological sequence of their execution.
Adjustment of the network schedule can be made according to the given construction time, according to labor and material resources and other necessary indicators.

174. How is the network schedule adjusted in time?
If the initial version of the network schedule has a critical path that does not exceed the established construction deadline, then such a schedule can be considered optimal and recommended for execution.
In cases where the critical path in the original version of the network schedule exceeds the established construction time, it is necessary to adjust the schedule in terms of "time" in order to reduce the critical path period.
You can shorten the critical path in the following ways:
- redistribute labor resources from non-critical work to critical work, as a result of which the duration of non-critical work may increase within the available time reserves, and critical work will be reduced;
- to attract additional labor and material resources to perform critical work;
- review the network topology (change the technological sequence of work); increase the number of captures; perform separate construction and installation operations, where technology and safety of work allow in parallel);
- change, if possible, design solutions in order to reduce the duration of construction (increase the factory readiness of structures, conveyor-block assembly of coating structures, use prefabricated structures instead of monolithic ones, etc.).

→ Construction production

Methodology for compiling network graphs

Network graphs are based on certain rules and in the appropriate order based on some source documents and data. The order of building the network may be different, but in all cases it is recommended to follow a series of general provisions and rules and practices developed by practice. First of all, the network is drawn from left to right, while the arrow-works can have an arbitrary length and slope, but their general direction should be precisely from left to right. First, a network is built in a draft version without event numbering (Fig. 20.3), after which this network is streamlined; in the process of streamlining, all missed and unaccounted for work and relationships are added to it. An example of an ordered graph network is shown in fig. 20.4. The arrows should not intersect each other, it is better to slightly shift the event or depict it as a broken line, as shown in Fig. 20.5, a, b.

In practice construction industry there are many cases where two or more jobs have start and end events but different durations, such as plumbing and electrical work in a civil building. They are usually carried out in combination, but not always simultaneously, after the frame or walls are ready, but end by the time the painting work begins.

Rice. 20.3. Primary Model Schematic

Rice. 20.4. Scheme of working network

Rice. 20.5. Construction examples network model

Rice. 20.6. Model scheme for parallel operations

If we take two parallel works A and £, then they should be depicted as shown in Fig. 20.5, c, d, and in fig. 20.5, e shows an incorrect image of parallel work.

Rks. 20.7. Linking the supply of materials and structures to the network model

When performing parallel work, it is necessary to introduce an additional (intermediate) event 6 and a dependence in the form of an idle connection 6-7 (Fig. 20.b). As can be seen from fig. 20.6, XX.b, one event serves as the beginning of two or more works, and the other as the end.

In addition to individual work and technological breaks, the network diagram depicts all kinds of supplies of material and technical resources, equipment and technical documentation. Deliveries are external works to the production process. External deliveries are represented by a solid arrow with the index P, going from the event in the form of a double circle with a zero designation to the event 8, 5 or 12, from which the consumption of materials, semi-finished products, prefabricated structures or equipment begins (Fig. XX.7, c). If more than one, two jobs 12-13 and 12-14 start from this event 12 (Fig. XX.7, a), and the corresponding delivery O is intended only for job 12-13, it is impossible to connect event O with event 12 with an arrow, you need introduce an intermediate event 13' and a fictitious connection 12-13' (Fig. XX.7,b). The duration of delivery is determined from the moment of the application until the arrival of materials, structures or equipment at the facility.

In network diagrams, it is necessary to reflect organizational activities related to the organization of the flow and the breakdown of the general front of work into captures. Dependence of an organizational nature is expressed in the successive transition of teams of workers and the movement of equipment from grip to grip.

Example. Suppose there are three works interconnected by a technological sequence: excavation of trenches, installation of foundations and laying the walls of a building. Each work in the schedule is considered independent, having its own previous and subsequent events (Fig. 20.8, a).

Rice. 20.8. Schemes of a network model for a grip-by-grip system for the production of work

When performing these works, we use the principle of flow, for which we organize two grips. At work sites, workers of a certain profession consistently perform the corresponding work. Graphically, the relationship between individual types of work is depicted using fictitious relationships. With the help of these relationships (dependencies), the transition of one profession of teams of workers from grip to grip is shown when performing earthworks for digging trenches, laying foundations and laying walls. And in fact, after excavating the trench on the grip, diggers or electric welders move on to the second grip. At this time, foundations are being laid on the grip in the trench by means of concrete masonry or installation of prefabricated foundation elements, etc.

Suppose that we have another job - laying pipes for the purpose of arranging an external water supply. Pipe laying is directly related to excavation. To complete the work, we divide the work on this front into three sections. Graphically, the network model for these works will have the form shown in (Fig. 20.8, b). Here dummy links are 2-5, 3-6 and 4-7; earthworks are divided into three parts corresponding to the three parts of pipe-laying work.

A trench excerpt and pipe laying can be graphically depicted in another version (Fig. 20.8, c).

When constructing network graphs, one-way and two-way links are used. One-way links between jobs are depicted by using a fictitious job. If, after the completion of two jobs a and b, you can start work c, and the start of work d depends only on the completion of work b, then a fictitious connection and an additional event 3' are introduced (Fig. 20.9, a). If there are five jobs: a, b, c, d, e, there are the following relationships: job c starts after the end of jobs a and b, and job e - after the end of jobs bud. Graphically, this dependence should be depicted as shown in Fig. XX.9, b, but not according to fig. XX.9, c (here the job c depends not only on the jobs a and b, but also on the job d, which contradicts the condition).

If, after the completion of two jobs a and b, you can start work c, and the start of work d depends only on the end of work a and the start of work e- on the end of work b, then on the network these dependencies are displayed in the following form (Fig. XX.9, G).

Two-way communication occurs under the condition that subsequent work begins before the completion of the previous work; this dependence is shown in fig. XX.10, a. Here, each process A, L, C is presented as the sum of sequentially performed works of the same name: the first two processes A and B develop independently and independently of each other, and the third C is performed as the first two are completed.

Rice. 20.9. Schemes of a network model with one-way communication between jobs

Obviously, each process is performed on three captures (sections) and the dependence of process C on processes A and B has a two-way idle connection.

Two-way communication also occurs with a large number of processes and their streaming execution in several areas.

An example of showing two-way communication during in-line construction is shown in fig. 20.10, b, which shows the execution of four processes in three areas.

Rice. 20.10. Diagrams of a network model with two-way communication between jobs

Rice. 20.11. Idler circuits and critical path definitions

Here the network has an incorrect construction. In order to correctly reflect the technological and organizational ties, intermediate events and dummy links are introduced (Wig variant). The network diagram is more complicated than the d scheme; it is simplified by reducing the number of events and dummy links (variant d).

The number and direction of intermediate (dummy) bonds affect the length of the critical path.

Example. There is a network of 4 jobs, 4 events and one idle connection from event 2 to event 3 (Fig. XX.11, a). The critical path passes through events 1, 3, 4 and is equal to 9+7=16 days. An idle link in this case has no effect, since the path through this link will be less than the critical one 5+0+7 16 days.

Rice. 20.12. Schemes of the network model before the enlargement, after the enlargement

When building a network, one should pay attention to the inadmissibility of closed loops, dead-end and tail events in network diagrams. A network deadlock is an event from which no work comes out. The presence of closed loops, dead ends and tail events, free hanging events indicates an error in the initial data or an incorrect network construction.

If the network schedule covers a large complex of works, then it becomes necessary to enlarge (simplify) it by replacing the set of homogeneous works with one composite work. Such a replacement is possible when any group of activities has one start and one end event.

Example. For clarification, let's take the network diagram shown in Fig. 20.12, a. In this schedule, the group of works between events 3 and 6, 6 and 13 can be enlarged. When enlarging the network model, it should be borne in mind that the temporal estimation of the schedule is carried out along the longest path.

For example, between events 3 and 6 there are five jobs: 3-4, 3-5, 4-5, 4-6 and 5-6. Taking the longest path 6+8+ +9=14 days. and jobs 7-10, 10-12, 12-13 in the enlarged network are presented as one job 7-13 with a duration of 8+3+7=16 days. Thus, boundary events are preserved

When zooming in on network diagrams, you cannot enter into it events that are not in detailed network diagrams (the network in Fig. XX. 12, a is detailed).

Usually, such works that are assigned to one responsible executor or department are subject to consolidation. Each performer or subdivision constitutes a primary or partial network for a certain set of works assigned to him. It must be assumed that events (boundary) appear in the network of one performer that other performers need, and vice versa. In order to coordinate the actions of individual performers or departments, it is necessary to combine private network graphs into one common one. The process of combining many private networks into one shared network is called network stitching. When stitching, all cases of inconsistency between individual sections of the network are identified and eliminated.

The general contractor and subcontracting specialized construction organizations take part in the construction of a large building and structure. Each specialized organization develops its own private network schedule, and the general contractor draws up a network schedule for its work package and a consolidated network schedule. Sometimes it is useful to have a master network schedule for the production of all construction, installation and special works with the allocation of subcontractors.

8 Each particular schedule has its own numbering of events. However, each organization is allocated a predetermined number of numbers for numbering network events: the first from 0 to 100, the second - from 101 to 150, for the third - from 151 to 200, etc. Each specialized organization can also accept its own conventions for events. Instead of circles, rectangles, squares, trapezoids, ovals, etc. can be taken. Introduction symbols affairs
It makes the summary network diagram more visible and allows each organization to quickly find their jobs and their connections on a common network.

Rice. 20.13. Scheme of the unified network model

Rice. 20.14. Scheme of a free network model with the highlighting of the work of subcontractors

Rice. 20.15. Network model with calculated parameters

When stitching a network diagram, you must adhere to next rule: two numbers are put inside the event - the old one is on top ( private network), and below the new serial number (of the summary network). On fig. 20.13 shows the numbering of the combined networks in one graph. Manual stitching of networks is laborious work, and therefore, for large construction projects with more than 200 events, the construction and correction of network graphs is performed by a computer using a specially developed program. Boundary events of individual primary networks are entered into the memory of the machine, which stitches them together and renumbers the events.

The scheme of the summary network diagram with the allocation of subcontractors is shown in fig. XX. 14. This graph shows that four organizations are involved in the construction of the facility: the general contractor and three subcontractors: EM-3 (electrical installation department), SMU-9 (construction and installation department) and MU-8 (installation department).

On fig. 20.15 is a network diagram with a critical path plotted. In this network diagram, there are several full paths between the initial and final events, placed in Table. XX.2. This table also contains the duration of work; on the graph they are placed under the arrows. The critical path is equal to the largest sum of activity durations: 1-2, 2-3, 3-7, 7-8, 8-9. All work on the network schedule will end on the 36th day. If we take the path 1_4-6-8-9, then its total duration is 22 days. This path has a margin of time 36-22=14 days. This margin of time can be used to increase the duration of non-critical work and free up inventory for critical work.

Initial data for drawing up a network diagram. The source document for compiling a network schedule is a list of works and material and technical resources, which is compiled on the basis of: - norms for the duration of the construction of the facility and the deadline; - design and estimate documentation (design assignment and working drawings) for the construction of an object or a complex of buildings and structures; - a construction organization project (POS) and a project for the production of works (PPR) „ technological maps;
valid issues of ENiR for construction and installation and special works; - data on the duration of the performance of certain types of work during the construction of similar facilities; - information about the current structure and availability of resources of construction and installation organizations, the material and technical base of construction (capacity of concrete plants, prefabricated reinforced concrete plants, fleet of machines, mechanisms, etc.);
- data on technology and organization of construction of similar facilities; - date of commencement of construction.

When drawing up a network schedule for the production of works, the following issues are resolved: - the nomenclature and technological sequence of construction and installation and special works are established; – the need for human and material and technical resources is determined for certain types works: – the initial and final events are set; – critical path and time margins are determined; - the actually established construction period is compared with the normative one according to SNiP.

The beginning of design is taken as the initial event when compiling a POS, when drawing up a PPR - the beginning of design or the beginning of work, and when compiling an educational (course or diploma) project - the start of work.

When developing a network diagram, it is necessary first of all to outline an enlarged scheme of the original network diagram with a limited number of events. Such a scheme is mandatory for issuing tasks to responsible executors for compiling individual sections of the network schedule. This scheme allows responsible performers to establish a relationship with other sections of the schedule, determine the inputs and outputs of individual sections of the schedule, determine the work package of other performers, etc. This scheme, finally, serves as the basis for merging a single schedule from private networks.

If the scheme of the original network schedule does not comply with the construction deadlines, then it is optimized by repeated or multiple planning and calculation until the schedule satisfies: the deadlines.

For possible reduction critical path (construction period), it is necessary to determine the reduced duration of work by introducing two-shift work and increasing the number of workers in critical work, dividing work into sections and introducing several works in parallel, installing additional machines, and revising the work production technology. The increase in resources for activities on the critical path is carried out by reallocating resources from activities on non-critical paths and sometimes by attracting additional resources from outside.

Methodology for calculating network models. next step when drawing up a network diagram is its calculation. The calculation of the network schedule consists in determining its following parameters: the duration of the critical path and the work lying on it: the earliest of the possible and the latest of the admissible dates for the start and end of work; all types of time reserves for activities not on the critical path; calendar dates.

The parameters of the network diagram are calculated manually and on electronic computers.

Calculation of network diagrams manually is performed by an analytical, tabular or graphical method.

The analytical method for calculating the network diagram is based on the use of formulas and is directly related to the definition of the concepts of the calculated parameters of the network and to the design scheme.

The tabular method for calculating the network model is based on the use of various forms of tables and methods for filling them out; characterized by great clarity and completeness. Unlike the tabular form of calculating all the operating parameters of the network, the graphical method is performed directly on the graph itself. There are several ways to graphically calculate network graphs: multi-sector, four-sector, square and oval, numerator and denominator methods, using a scaled network graph.

In order to better follow the calculation methodology, let's take a ready-made simple network graph shown in Fig. 20.17. This network diagram consists of six events and nine impersonal works, of which one is fictitious; the duration of work in days is indicated under the arrows.

Example. We will show the methodology for calculating this network diagram in the technological sequence.

One of the firms decided to implement a computer information system. The appointed project manager compiled a list of actions (works) to be performed for this, and indicated the sequence of their implementation and the duration given in the table. Build a network diagram.
Note:
a) there must be one initiating and one terminating event in the network;
b) looking closely at the list of works, you will find that works A, B and C do not have
previous jobs (they only have subsequent jobs), which means they can be performed
in parallel, starting from the initial event;
c) avoid crossing paths;
d) direct work from left to right;
e) there should be as few fictitious jobs on the chart as possible.

Work	Duration of work t, days	Subsequent work
A	4	D, E
D	3	O, N
O	6	End
E	2	K
K	8	P
N	1	P
P	9	End
B	6	F, G, H
F	7	K
G	4	L, M
L	2	End
C	5	I
H	7	I
I	3	M
M	1	End

Video instruction

Scale network diagram

Calculate the parameters of the network schedule of measures to improve the management system. The network model is given tabularly (Table). The duration of the work is given in the form of minimum and maximum estimates. Required:

1. Calculate by tabular method all the main characteristics of work and events, find the critical path and its duration.
2. Build a scaled network diagram.
3. Estimate the probability of completing the entire complex of works in 30 days.
4. Estimate the maximum possible time for the completion of the entire complex of works with a probability of 95%.

Table - Network model.

Job code (i,j)	Duration
	tmin(i,j)	tmax(i,j)
1,2	5	10
1,4	2	7
1,5	1	6
2,3	2	4,5
2,8	9	19
3,4	1	3,5
3,6	9	19
4,7	4	6,5
5,7	2	7
6,8	7	12
7,8	5	7,5

Solution we find using the service Network model. In our assignment, the duration of the work is given by two estimates - the minimum and maximum. The minimum estimate characterizes the duration of the work under the most favorable circumstances, and the maximum t max (i, j) - under the most adverse conditions. The duration of work in this case is considered as a random variable, which, as a result of implementation, can take any value in a given interval. Such estimates are called probabilistic (random), and their expected value t exp (i, j) is estimated by the formula
t exp (i,j)=(3 t min (i,j)+2 t max (i,j))/5
To characterize the degree of spread of possible values ​​around the expected level, the dispersion index is used:
S 2 (i, j)=0.04(t max (i, j)-t min (i, j)) 2
Calculate the expected value and the variance.
t cool (1,2)=(3*5+2*10)/5=7
t cool (1,4)=(3*2+2*7)/5=4
t cool (1.5)=(3*1+2*6)/5=3
t cool (2.3)=(3*2+2*4.5)/5=3
t cool (2.8)=(3*9+2*19)/5=13
t cool (3.4)=(3*1+2*3.5)/5=2
t cool (3,6)=(3*9+2*19)/5=13
t cool (4.7)=(3*4+2*6.5)/5=5
t cool (5,7)=(3*2+2*7)/5=4
t cool (6.8)=(3*7+2*12)/5=9
t cool (7.8)=(3*5+2*7.5)/5=6
S 2 (1.2) \u003d 0.04 * (10-5) 2 \u003d 1
S 2 (1.4) \u003d 0.04 * (7-2) 2 \u003d 1
S 2 (1.5) \u003d 0.04 * (6-1) 2 \u003d 1
S 2 (2.3) \u003d 0.04 * (4.5-1) 2 \u003d 0.25
S 2 (2.8) \u003d 0.04 * (19-9) 2 \u003d 4
S 2 (3.4) \u003d 0.04 * (3.5-1) 2 \u003d 6.25
S 2 (3.6) \u003d 0.04 * (19-9) 2 \u003d 4
S 2 (4.7) \u003d 0.04 * (6.5-4) 2 \u003d 0.25
S 2 (5.7) \u003d 0.04 * (7-2) 2 \u003d 1
S 2 (6.8) \u003d 0.04 * (12-7) 2 \u003d 1
S 2 (7.8) \u003d 0.04 * (7.5-5) 2 \u003d 0.25

The obtained data will be entered in the table.
Table - Network model.

Work (i,j)	Duration		Expected duration t exp (i,j)	Dispersion S 2 (i,j)
	tmin(i,j)	tmax(i,j)
1,2	5	10	7	1
1,4	2	7	4	1
1,5	1	6	3	1
2,3	2	4,5	3	0,25
2,8	9	19	13	4
3,4	1	3,5	2	6,25
3,6	9	19	13	4
4,7	4	6,5	5	0,25
5,7	2	7	4	1
6,8	7	12	9	1
7,8	5	7,5	6	0,25

Using the obtained data, we can find the main characteristics of the network model using a tabular method, the critical path and its duration.
Table - Tabular method for calculating the network diagram.

CRC	Job code (i,j)	Duration of work t(i, j)	Early dates		Late dates		Reserves of time
			t pH (i, j)	t ro (i,j)	t mon (i, j)	t by (i,j)	R p	Rc
1	2	3	4	5	6	7	8	9
0	1,2	7	0	7	0	7	0	0
0	1,4	4	0	4	17	21	17	8
0	1,5	3	0	3	19	22	19	0
1	2,3	3	7	10	7	10	0	0
1	2,8	13	7	20	19	32	12	12
1	3,4	2	10	12	19	21	9	0
1	3,6	13	10	23	10	23	0	0
2	4,7	5	12	17	21	26	9	0
1	5,7	4	3	7	22	26	19	10
1	6,8	9	23	32	23	32	0	0
2	7,8	6	17	23	26	32	9	9

Thus, the critical path jobs are (1,2),(2,3),(3,6),(6,8). The duration of the critical path T kr =32.

Figure - Scale graph of the network model
To estimate the probability of completing the entire complex of works in 30 days, we need the following formula: P(t cr Z is the standard deviation of a random variable, S cr is the standard deviation calculated as the square root of the variance of the duration of the critical path. Correspondence between Z and Ф (Z) presented in the table.
Table - Table of the standard normal distribution.

Z	F(Z)	Z	F(Z)	Z	F(Z)
0	0.0000	1.0	0.6827	2.0	0.9643
0.1	0.0797	1.1	0.7287	2.1	0.9722
0.2	0.1585	1.2	0.7699	2.2	0.9786
0.3	0.2358	1.3	0.8064	2.3	0.9836
0.4	0.3108	1.4	0.8385	2.4	0.9876
0.5	0.3829	1.5	0.8664	2.5	0.9907
0.6	0.4515	1.6	0.8904	2.6	0.9931
0.7	0.5161	1.7	0.9104	2.7	0.9949
0.8	0.5763	1.8	0.9281	2.8	0.9963
0.9	0.6319	1.9	0.9545	2.9	0.9973

The critical path passes through the jobs (1,2)(2,3)(3,6)(3,8).
Critical path variance:
S 2 (L cr) \u003d S 2 (1.2) + S 2 (2.3) + S 2 (3.6) + S 2 (6.8) \u003d 1 + 0.25 + 4 + 1 \u003d 6 .25
S(L cr)=2.5
p(t cr<30)=0,5+0,5Ф((30-32)/2,5)=0,5-0,5Ф(0,8) = 0,5-0,5*0,5763=0,5-0,28815=0,213
The probability that the entire complex of works will be completed in no more than 30 days is 21.3%.
To determine the maximum possible time for the completion of the entire complex of works with a reliability of 95%, we will use the following formula: T=T cr +Z*S cr

To solve the problem, we find the value of the argument Z, which corresponds to a given probability of 95% (the value of the column Ф(Z) 0.9545*100% in Table 5 corresponds to Z=1.9).
T=32+1.9*2.5=36.8
The maximum term for completing the entire complex of works at a given probability level of 95% is only 36.8 days.

Preliminary stage of building a network diagram

At the preliminary stage of network planning, it is necessary to determine the nature of the planned operations and the potential of the employees who will be responsible for their implementation.

As an example, let's take the work of the regional Agency for Youth Policy for a month and plan a list of operations for a month.

Let's say there are 10 employees.

Typical organizational structure of the Agency for Youth Policy

Building a network diagram represents an element of managerial activity and corresponds to the overall decision-making process. It is an integral part of the management process. During the construction of a network diagram, several options for performing planned operations are considered and, as a result, the best alternative is selected from the many available. The network schedule includes directly management actions and operations related to the technical side of the organization's activities.

Operations in the network schedule must be documented, for example, in administrative documents. The main purpose of such documentation is to regulate the activities of the control object, providing it with financial, labor, material and information resources. The main forms of documenting planned operations are:

1. Orders - including orders, instructions;
2. Acts - including acceptances and protocols;
3. Agreements - including agreements, contracts, offers;
4. Regulations - instructions, regulations, rules, plans, models.

Development of a identification card

All operations that are scheduled for execution for the coming period are entered into the key card, based on the data of the key card, a network schedule will be drawn up. Let's make a table in which we will present the operations of the Youth Policy Agency, given that there are only 10 employees, of which there are 2 people in the accounting department, 5 people in the special programs department (including the head), and 3 people in the health campaign organization department.

The determinant is compiled with the most detailed indication of the planned operations.

Key card for network diagram

	the name of the operation	Number of performers, pers.	duration,	Performers
	Prepare a report for June 2018 on the work done and report to the management			Experts from all departments
	Prepare a summary of earmarked spending indicators			Accounting department specialists
	Preparation of reporting data on the implementation of the DKTsP "Organization of recreation, rehabilitation and employment of children and youth"
	Prepare information and analytical materials related to youth policy issues
	Holding a meeting of the Round Table of children's and youth organizations on the implementation of youth policy			Special Program Specialists
	Preparation for the organization of meetings with the heads of health institutions			Specialists of the department for organizing a wellness campaign
	Preparation for organizing meetings with deputy heads of educational institutions for educational work			Special Program Specialists
				Experts from all departments
	meeting			Experts from all departments
	Organization and holding of meetings with the heads of health-improving institutions and deputy heads of educational institutions for educational work			Special Program Specialists
				Special Program Specialists
	Updating the register of children's recreation and recreation organizations			Accounting department specialists
	Preparation and organization of a student scientific and practical conference in the field of prevention of alcohol consumption			Specialists of the department for organizing a wellness campaign
	Preparation of statistical and information-analytical materials on the prevention of alcoholism			Accounting department specialists
	Conducting a student scientific and practical conference in the field of prevention of alcoholism			Specialists of the department for organizing a wellness campaign
	Preparation of a report on the work performed by the department for the week			Experts from all departments
	meeting			Experts from all departments
	Preparation for holding a student interuniversity event on historical topics			Special Program Specialists
	Conducting a brain-ring among student teams "Battle of Borodino"			Special Program Specialists
	Preparation of statistical and reporting data on the implementation of the DKTsP "Organization of Recreation, Rehabilitation and Employment of Children and Youth" for the 1st quarter. 2018			Accounting and economic analysis specialists
				Specialists of the department for organizing a wellness campaign
				Specialists of the department for organizing a wellness campaign
	Preparation of reporting information to the Ministry of Regional Development of the Russian Federation on the implementation of the subprogram "Provision of housing for young families" for 1 quarter. 2018			Accounting department specialists
	Preparation of a report on the work performed by the department for the week			Experts from all departments
	meeting			Experts from all departments
	Preparation of a report for the meeting of the regional commission on state awards and scholarships			Special Program Specialists
	Organization and holding of the School of Youth Entrepreneurship			Special Program Specialists
	Organization and holding of seminars on the protection of the rights and interests of young people, the prevention of alcoholism for counselors of children's health camps			Specialists of the department for organizing a wellness campaign
	Instructive seminar for counselors of children's health camps			Specialists of the department for organizing a wellness campaign
	Preparation of statistical and reporting data on the implementation of the DCCP for 1 quarter. 2018			Accounting department specialists
	Preparation of a report on the work performed by the department for the week			Experts from all departments
	meeting			Experts from all departments
	Preparation of terms of reference for the production of anti-drug banners and posters			Specialists of the Department of Special Programs and the Department of Organization of a Health Campaign
	Selection of municipalities for the provision of subsidies within the framework of the subprogram "Providing housing for young families" for 1 sq. 2018			Accounting department specialists
	Prepare a program for the implementation of activities on the ongoing DKTsP in the field of youth policy for the second half of the year			Experts from all departments

Network plan preliminary analysis

According to the plan, all operations scheduled for July 2018 must be completed in four full working weeks and two days in the fifth week.

Each working week includes 5 working days. There are no holidays during this period.

Thus, in July 2018, the planned operations should be carried out in 22 working days with a 5-day working week:

1. from 07/02/2018 to 07/06/2018 - 5 days
2. from 07/09/2018 to 07/13/2018 - 5 days
3. from 07/16/2018 to 07/20/2018 - 5 days
4. from 07/23/2018 to 07/27/2018 - 5 days
5. from 07/30/2018 to 07/31/2018 - 2 days

Total: 22 days.

To build a network diagram, it is necessary to distribute responsible persons and group parallel operations. The distribution of specialists performing planned operations within the formalized structure of operations presented in the identification card is carried out in accordance with the functional duties of employees and the allocation in the structure of operations that are regular and mandatory.

Joint types of work performed by several departments are identified in accordance with the formalized structure of planned operations.

At the same time, operations that are carried out by departments independently need to be grouped, they will be performed in parallel for the effective implementation of planned operations.

In the event of non-compliance with the plan for the implementation of planned operations, it will be possible to adjust the network model. At the same time, it is impossible to involve employees from different departments to perform operations that do not correspond to their functional duties.

The grouping of parallel operations is presented in the table.

Parallel Operation Groups

	Parallel Operations of the Week
		Department of Special Programs
	10 (11), and operations 10 and 11 are also parallel	Department of Special Programs
		Health Campaign Organization Department
		Department of Accounting and Economic Analysis
		Department of Accounting and Economic Analysis
		Health Campaign Organization Department
		Department of Special Programs
		Health Campaign Organization Department
		Department of Accounting and Economic Analysis
		Department of Special Programs
		Department of Special Programs and Department of Health Campaign Organization
		department of accounting and economic analysis

Building a network diagram

In our example, to build a network diagram, it is necessary to draw up a form of operations, it can be used as a model in practice.

We summarize the following data for each operation in a table:

• operation number;
• previous operations;
• the number of performers;
• duration of the operation in days.

In the table of operations, their numbers correspond to the numbering in the identification card in accordance with the grouping of parallel operations.

Table of operations for building a network diagram

Operation number	Previous operations	Number of performers, pers.	Duration, days

Based on the table of operations and the identification card, taking into account the grouping of parallel operations, building a network diagram.

Network diagram, example

Let's define the critical path. The critical path on this network diagram is the operations: 1, 4, 5, 7, 8, 9, 13, 15, 16, 17, 18, 19, 24, 25, 28, 29, 31, 32, 33 (34), 35.

As a result of building a network work schedule, it can be concluded that the organization's activities do not fit into a given period equal to 22 working days, amounting to 26 days instead. At the same time, the operations of the first, second and third weeks do not fit into the period set for them, equal to 5 business days. According to the network model, operations of 1 week last 7 days, 2 weeks - 6 days, 3 weeks - 6 days. Operations of the fourth and fifth weeks fit into the deadlines set for them.

To meet the planned deadlines, we will adjust the network schedule.

In our example network diagram based on the distribution card data, we can conclude that for some operations within the planned activities there is a reserve of specialists in the department. Given that the total number of employees is relatively small, you can use the method of adjusting the network model with the involvement of additional resources, which are the specialists of this department who are free at the time of the operation. Due to this, the time for performing critical path operations will be reduced, and, accordingly, the time of the entire network model. Operations of 1, 2 and 3 weeks are subject to adjustment, since operations of 4 and 5 weeks of the network schedule fit into the specified time.

After the adjustment, we will build an alternative network graph.

It is necessary to attract additional specialists to perform operations 4 (Special Programs Department), 13 (Health Campaign Organization Department) and 18 (Special Programs Department). The calculation of the complexity of operations (Q) is determined based on the product of the number of specialists (N) performing the operation by the number of days (t) allocated for its implementation:

Q4 = 2*4 = 8 h/day

Q13 = 2*3 = 6 h/day

Q18 = 2*2 = 4 h/day

There are 5 people in the Special Programs department, but only 2 people are involved in Operation 4. As a result of attracting two specialists, the new term for the operation will be: 8 / 4 = 2 days. Therefore, operation 4 will take 2 days instead of 4 days.

There are 3 specialists in the department for organizing a health campaign, but only two people are involved in the implementation of operation 13. In this case, the involvement of one additional specialist will reduce the duration of the operation: 6 / 3 = 2 days. Therefore, operation 13 will take 2 days instead of 3 days.

Operation 18 involved 2 specialists from the Special Programs Department. Involvement of two additional specialists will reduce the period of its implementation: 4 / 4 = 1 day. Therefore, operation 18 will take 1 day instead of 2 days.

As a result, we obtain the time period for performing operations after adjusting the network schedule with the involvement of additional resources:

26 - 2 - 1 - 1 = 22 days.

Thus, due to the correction of the network schedule, the time for performing operations corresponds to the originally set period of 22 business days.

The alternative schedule will be similar to the previous one in terms of its structure, the timing of the implementation of operations will be adjusted according to the constructed network model.

Alternative network diagram

Evaluation of the effectiveness of the network diagram

Let us calculate the total labor intensity of the planned operations in the primary (Q1) and alternative (Q2) construction of the network diagram.

Q1 = 10 * 26 = 260 h/day

Q2 = 10 * 22 = 220 h/day

To evaluate the effectiveness of the network schedule, we will use the method of comparing the results of the implementation of a management decision.

E \u003d K * * 100%

K is a proportionality coefficient that takes into account the share of efficiency attributable to SD (usually K = 0.4-0.5).

K is taken equal to 0.4.

E \u003d 0.4 * * 100% \u003d 16%.

According to this method, the efficiency of the solution is 16%, which is a good result. Thus, in the considered example, the expediency of the network diagram is confirmed.

conclusions

Building a network schedule in managing the work of an organization can significantly increase its effectiveness. If, based on the results of the initial construction of the network schedule, it turns out that the planned operations cannot be completed within the allotted time, it is necessary to correct the work of the organization and form a new schedule. In the considered example, the network schedule was adjusted by attracting additional labor resources.

Antipyretics for children are prescribed by a pediatrician. But there are emergency situations for fever when the child needs to be given medicine immediately. Then the parents take responsibility and use antipyretic drugs. What is allowed to give to infants? How can you bring down the temperature in older children? What medicines are the safest?

In addition to the tabular method, there are the following calculation methods: graphical method, potential method.

Example. Determine the time parameters of the network graph in the figure, using the tabular method.
Solution we carry out through the calculator: we will enter all calculations in table 3.
The list of works and their duration will be transferred to the second and third columns. In this case, the work should be recorded in column 2 sequentially: first, starting from number 1, then from number 2, etc.
In the first column, we put a number that characterizes the number of immediately preceding works (KPR) to the event from which the work in question begins. So, for the work (5,10) in column 1 we put the number 2, because 2 jobs end at number 5: (1.5) and (3.5).
Table 3 - Tabular method for calculating the network diagram

Stay on top of your daily and weekly tasks with this checklist template. You get the ease of simple organization and the satisfaction of labeling items off the list as you complete them. Scheduling your doses for the week can help keep you from taking on too many tasks in one day while still keeping up with your agenda.

Laboratory work. Calendar charts in Excel (Gantt chart)

Objective: Get basic Gantt charting skills.

Gantt chart (eng. Gantt chart, also a strip chart, Gantt chart) is a popular type of bar charts (histograms), which is used to illustrate a plan, schedule for a project. It is one of the methods of project planning. Used in project management applications.

Method 1

Using conditional formatting, we can force Excel to fill a cell with any selected color if it falls between the start and end of the stage by date. The easiest way to do this is to use the logical function And, which in this case checks the obligatory fulfillment of both conditions (January 5 is later than January 4 and earlier than January 8):

Let's fill in the table with the initial data.

In column D, calculate the end date of the stage using the formula = B3 + C3-1. Copy the received values.

Next, we will create a template for the calendar plan, while the data for the columns (Jan 1, Jan 2, etc.) must be in the Date format. Note that the year must be set to 2005, otherwise the year will automatically be set to 2015.

Apply conditional formatting. To do this, select cell E3, open the Home tab and select the Conditional Formatting / Create Rule command. Select the most recent command from the list, enter the formula, and select a color. Then copy the resulting formula.

Method 2

So, we have a table listing the stages of the project, the start and end dates and the duration of each stage:

The task is to build a chart-calendar chart using standard tools, as in the figure:

Description step by step:

Select the source data for the chart - range A1:C13 and choose from the menu Insert - Diagram , type of - Ruled with accumulation (note that cell A1 must be made empty - remove the text from there):

The second necessary step is to hide the first row. To do this, make it invisible. Click on the blue data, right click Data Series Format/Fill/No Fill. Then Go to section border color and switch from " Autoselect" on the " no lines". The window can be closed.

Select the horizontal axis, right-click and select the menu item Axis Format. The horizontal axis should be understood as a list of dates.

Then select the vertical axis and select the "Format Axis" command. In the axis options, select Reverse category order, and in the "Horizontal axis intersects" section, check the box for the maximum category.

Let's add a grid line on the Layout tab.

Note that the chart does not start on the first date. To do this, select column B and set the cell format to General. Look at the first and last values.

Method 3

The task is to visually show the entire chronology of work on the project by placing the key points of the project (milestones, milestones) on the time axis.

In project management theory, such a schedule is usually called a calendar or project timeline, a timeline.

Step 1. Initial data

To build, you will need to arrange the initial information on the milestones of the project in the form of the following table:

Pay attention to two additional service columns:

Line- a column with the same constant near zero for all cells. It will give a horizontal line on the graph, parallel to the X axis, on which nodes - points of the project will be visible.

Callouts- invisible columns for raising signatures to milestones by a given (different) value, so that signatures do not overlap. Values ​​1,2,3 etc. set the level of elevation of signatures above the time axis and are chosen arbitrarily.

Step 2: Building the Foundation

Now we select everything in the table except the first column (i.e. the range B1:D13 in our example) and build a regular flat chart with markers on the tab Insert - Graph - Graph with markers(Insert - Chart - Line with markers):

We remove the grid lines, vertical and horizontal scales and the legend. You can do this manually (selection with the mouse and the key Delete) or by disabling unnecessary items on the tab Layout / grid (horizontal and vertical lines put no). The result should be the following:

Now select a row Callouts(i.e. broken orange line) and on the tab Layout select a team Lines - Projection lines(Layout - Lines - Projection Lines):

From each point of the upper graph, a perpendicular will be lowered to the lower one. In the new Excel 2013, this option is on the tab Constructor - Add Chart Element(Design - Add Chart Element).

Step 3. Adding Step Names

In Excel 2013, you need to select the data row (orange) and on the tab Constructor choose Add Chart Element - Labels - Advanced Options(Design - Add Chart Element - Data Labels), and then in the panel that appears on the right, check the box Values ​​from cells(Values ​​from cells) and select the range A2:A13:

In versions of Excel 2007-2010:

Let's make the final edits to bring our already almost finished diagram to a complete and final masterpiece:

Select a row Callouts(orange line), right-click on it and select Data series format(Format Data Series). In the window that opens, remove the fill and color of the lines. The orange graph, in fact, disappears from the diagram - only the captions remain. Which is what is required.

Adding date labels to the blue time axis on the tab Layout - Data Labels - Additional Data Label Options - Category Names(Layout - Data Labels - More options - Category names). In the same dialog box, labels can be positioned below the graph and rotated 90 degrees, if desired.

Assignment for independent work

Build a Gantt chart that illustrates the stages of work on your project.

According to method three, build a timeline of 7 events on the topic of your project, add the necessary drawings, captions.

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