Downtime example of using a network diagram. Creating a Network Diagram in Microsoft Excel

Optimizing the work of a company, especially a manufacturing enterprise, is one of the most important conditions for the existence of a company. It is not only competition that requires the uninterrupted flow of the production process. Modern trends in minimizing the cost of manufactured products involve, first of all, the elimination of downtime and the consistency of operations.

To solve these problems, a methodology is used to optimize activities and calculate deadlines for completing work. The developed network schedule allows you to determine the logical sequence of individual operations, the possibility of combining them in time, as well as the timing of the entire production cycle of work.

What is this?

One of the methods for effectively planning the activities of a manufacturing enterprise is the construction of a network diagram. Initially, it was used in construction and determined not so much the sequence of work as the timing of teams of workers of different specialties entering the construction site. It is called a “scheduled work schedule.”

In modern conditions, when large enterprises mass produce products, to facilitate and increase productivity, the entire process is divided into simple operations. Therefore, the network diagram “migrated” from construction to almost all industries.

So what does this document show? Firstly, all operations necessary for the production of goods (production of services) are listed in detail. Secondly, the logical interdependence between them is determined. And finally, thirdly, not only the deadlines for completing each specific job are calculated, but also the time required to completely complete the production process.

By revealing the internal dependencies of project operations, the network schedule becomes the basis for scheduling the workload of equipment and labor.

The concept of “operation” in network planning

In the network diagram, you can estimate the start (completion) periods of work, forced downtime and, accordingly, the maximum delay time for certain operations. In addition, critical operations are identified - those that cannot be performed behind schedule.

When understanding planning terminology, you need to clearly understand what an operation is. Most often, this is understood as an indivisible part of the work that requires time to complete. Further, we understand that there are costs associated with performing an operation: time and resources (both labor and material).

In some cases, performing some actions does not require resources, only time is required, which takes into account the network schedule. An example of this is waiting for concrete to harden (in construction), cooling time for rolled parts (metallurgy), or simply approving (signing) a contract or permitting documentation.

Most often, operations in planning are given names in the imperative mood (develop a specification); sometimes verbal nouns are used for names (specification development).

Types of operations

When drawing up a network schedule, there are several types of work:

merge - this operation is immediately preceded by more than one job;
parallel operations are performed independently of each other and, at the request of the design engineer, can be performed simultaneously;
A splitting operation assumes that after its completion, several unrelated jobs can be performed at once.

In addition, there are several other concepts necessary for planning. The path is the execution time and the sequence of interdependent operations. And the critical path is the longest path of the entire system of work. If any operation along this path is not completed in a timely manner, the deadlines for the implementation of the entire project will be missed.

And lastly: the event. This term usually denotes the beginning or end of an operation. The event does not require resources.

What does the graph look like?

Any graph familiar to us is represented by a curve located on a plane (less often in space). But the type of network plan is significantly different.

The network diagram of a project can look two ways: one technique involves designating operations in the nodes of the block diagram (DC), the second uses connecting arrows (OS) for this. It is much more convenient to use the first method.

The operation is indicated by a round or rectangular block. The arrows connecting them determine the relationships between actions. Since the titles of the work can be quite long and voluminous, operation numbers are entered in the blocks, and a specification is drawn up for the schedule.

Rules for developing a schedule

To plan correctly, you need to remember a few rules:

The graph unfolds from left to right.
Arrows indicate connections between operations; they may overlap.
Each simple job must have its own serial number; any subsequent operation cannot have a number lower than the previous one.
There can be no loops in the graph. That is, any looping of the production process is unacceptable and indicates an error.
You cannot use conditions when building a network diagram (an example of a conditional order: “if the operation is completed.., perform the work... if not, do not take any action”).
To indicate the beginning and end of work, it is more convenient to use one block that defines the initial (final) operations.

Graph construction and analysis

For each job you need to find out three things:

A list of operations that must be performed before this work. They are called preceding in relation to the given one.
A list of operations that are performed after a given action. Such works are called the following.
A list of tasks that can be carried out simultaneously with the given one. These are parallel operations.

All the information received provides analysts with the necessary basis for building logical relationships between the operations included in the network diagram. An example of constructing these relationships is given below.

A realistic schedule requires a serious and objective assessment of production schedules. Determining the time and entering it into the schedule makes it possible not only to calculate the duration of the entire project, but also to identify the most important nodes.

Graph calculation: direct analysis

The time spent on performing one operation is estimated on the basis of standard labor costs. Thanks to the direct or reverse calculation method, you can quickly navigate the order of work and identify critical steps.

Direct analysis allows us to determine the early start dates of all operations. Reverse - gives an idea of later dates. In addition, using both analysis techniques, it is possible not only to establish the critical path, but also to identify time intervals by which the completion of individual works can be delayed without disrupting the overall project deadlines.

Direct analysis examines the project from beginning to end (if we talk about the compiled schedule, then movement along it occurs from left to right). While moving through all chains of operations, the time required to complete the entire complex of work increases. Direct calculation of the network schedule assumes that each subsequent operation begins at the moment when all its predecessors end. It is necessary to remember that the next job starts at the moment when the longest of the immediately preceding ones ends. At each step of direct analysis, the execution time of the calculation operation is added. This is how we get the early start (ES) and early finish (EF) values.

But you need to be careful: the early end of the previous operation becomes the early start of the subsequent one only if it is not a merge. In this case, the start will be the early completion of the longest previous work.

Reverse analysis

In reverse analysis, the following parameters of the network schedule are taken into account: late completion and late start of work. The name itself suggests that the calculation is carried out from the last operation of the entire project towards the first (from right to left). Moving towards the start of work, you should subtract the duration of each action. In this way, the latest start (LS) and finish (LF) dates for the work are determined. If the project time frame is not initially specified, then the calculation begins from the late end of the last operation.

Calculation of slack

Having calculated the network schedule of work in both directions, it is easy to determine temporary downtime (sometimes the term “fluctuation” is used). The total time of possible delay in the execution of an operation is equal to the difference between the early and late start of a particular action (LS - ES). This is the time reserve that will not disrupt the overall project deadlines.

After calculating all the fluctuations, they begin to determine the critical path. It will go through all operations for which there is no downtime (LF = EF; and accordingly LF - EF = 0 or LS - ES = 0).

Of course, in theory everything looks simple and straightforward. The developed network diagram (an example of its construction is shown in the figure) is transferred to production and implemented. But what is behind the numbers and calculations? How to use possible technological downtime or, conversely, avoid force majeure situations.

Management experts suggest assigning the most experienced employees to perform critical operations. In addition, when assessing project risks, you need to pay special attention not only to these steps, but also to those that directly affect the critical path. If it is not possible to control the progress of work as a whole, then it is necessary to find time to obtain primary information specifically from critical path operations. The point is to talk directly with the performers of such work.

Network diagram - a tool for optimizing the company’s activities

When it comes to the use of resources (including labor), it is much easier for a manager to manage them if there is a network work schedule. It shows all the downtime and busyness of each specific employee (team). Using an idle employee at one facility to implement another allows you to optimize the company’s activities as a whole.

One more practical piece of advice should not be neglected. In reality, project managers are faced with the “desires of higher management” to see work completed “yesterday.” In order to avoid panic and the release of defects, it is necessary to strengthen resources not so much on the operations of the critical path, but on those directly affecting it. Why? Yes, because there is already no downtime on the critical path, and it is often impossible to reduce the production time.

Purpose of the service. The online calculator is designed to find network model parameters:

early date of the event, late date of the event, early start date of the work, early end date of the work, late start date of the work, late end date of the work;
time reserve for the event, full time reserve, free time reserve;
duration of the critical path;

and also allows you to estimate the probability of completing the entire complex of work in d days.
Instructions. The online solution is carried out analytically and graphically. Formatted in Word format (see example). Below is a video instruction.

Example. A description of the project in the form of a list of operations performed, indicating their relationship, is given in the table. Build a network diagram, determine the critical path, build a schedule.

Work (i,j)	Number of previous works	Duration t ij	Early dates: beginning t ij R.N.	Early dates: end t ij R.O.	Late dates: beginning t ij P.N.	Late dates: end t ij P.O.	Time reserves: full t ij P	Time reserves: free t ij S.V.	Time reserves: events R j
(0,1)	0	8	0	8	0	8	0	0	0
(0,2)	0	3	0	3	1	4	1	0	1
(1,3)	1	1	8	9	8	9	0	0	0
(2,3)	1	5	3	8	4	9	1	1	0
(2,4)	1	2	3	5	13	15	10	10	0
(3,4)	2	6	9	15	9	15	0	0	0

Critical path: (0.1)(1.3)(3.4) . Critical path duration: 15.

Independent operating time reserve R ij N is part of the total time reserve if 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 if the completion of the previous work occurred at a late acceptable date, and they want to complete subsequent work at an early date. If R ij Н ≥0, then such a possibility exists. If R ij Н<0 (величина отрицательна), то такая возможность отсутствует, так как предыдущая работа ещё не оканчивается, а последующая уже должна начаться (показывает время, которого не хватит у данной работы для выполнения ее к самому раннему сроку совершения ее (работы) конечного события при условии, что эта работа будет начата в самый поздний срок ее начального события). Фактически независимый резерв имеют лишь те работы, которые не лежат на максимальных путях, проходящих через их начальные и конечные события.

BUILDING A NETWORK SCHEDULE

A network diagram or arrow diagram is a directed graph without contours. A graph is called directed because the arrows show the directions of its edges (arcs). The absence of contours creates conditions under which, moving in the direction of the arrows, each edge can be passed through only once. A network diagram allows you to clearly show the sequence and interconnection of the work included in a program or any action plan. Works on such a diagram are depicted as arcs. Thus, each arc of the network diagram, which looks like an arrow, indicates the beginning and end of the work, which is an event. We will depict these events with circles. The circle at the beginning of the arrow will be the start event for the work shown by that arrow. The circle at the end of the arrow is the final event of this work and the starting event for subsequent work.

The graph used to construct a network diagram has one more property - it does not have hanging vertices. In this case, all events on the chart, except for the initial one and the final one of the program or action plan, have both previous and subsequent work. Arrows within the circle representing an event will display previous work. Arrows coming out of the circle characterizing the event will show subsequent work. The initial event is represented by a circle with arrows just coming out of it. A final event is characterized by the fact that it only has incoming arrows (predecessors).

Constructing a network diagram requires compliance with a number of rules.

Rule 1. The sequence of jobs following each other is depicted as a chain of arrows connected to each other by circles. For example: work b must follow the work A (A ® b ), Job V must be executed after completion of work b (b ® V ) and finally work V G (V ® G ). This sequence of work on the network diagram will look like this (Fig. 3.3.2):

Rule 2. Several jobs that simultaneously immediately precede any one subsequent job are called convergent. For example: work G immediately preceded by work A , b And V (A , b, c ® G ). This situation on the network diagram should be depicted as shown in Fig. 3.3.3.

Rule 4. The network diagram should not show non-existent connections between subsequent and immediately preceding activities. For example: works A , b , V precede work G (a B C ® G ), at the same time, work A immediately precedes the work d (A ® d ). On the network diagram this situation should be displayed in the manner shown in Fig. 3.3.5 ( A) and cannot be depicted in the manner shown in Fig. 3.3.5 ( b), since in the latter case there will be non-existent connections between the works b , V And d .

In Fig. 3.3.5 ( A) the dashed arrow depicts a fictitious work (4–5), indicating that the work G cannot start until job is completed A . Such work does not require time or any other resources to complete it. It serves only to reflect the existing connection between the works A And G .

Rule 5. Any two adjacent events on a network diagram can be connected by a single arrow. This means that when work is performed in parallel, to display the specified situation, it becomes necessary to introduce an additional event and fictitious work. For example: works A , b , coming out of the event 6 , are immediately preceding for the work V (a, b ® V ). This situation should be depicted in the manner shown in Fig. 3.3.6 ( A) and cannot be depicted in the manner shown in Fig. 3.3.6 ( b).

When constructing a network diagram, it is convenient to use the technology shown in Fig. 3.3.7. In this case, we are considering the construction of a network schedule for the implementation of a project that includes 11 works, indicated by letters. The project work has the following technological connections:

® a, d, f, g

A ® b, c

V ® G

and ® h

f, h ® k, l

g, d, k, ® n

f, l ® O

https://pandia.ru/text/78/182/images/image008_101.gif" alt="Oval: I" width="28" height="28 src=">В перечне связей знаком обозначено исходное событие комплекса работ, а знаком – завершающее событие.!}

Building a network diagram is not enough to monitor and manage the progress of the project. It is necessary to calculate a number of network diagram parameters and determine the critical path. Any sequence of work on a network diagram that begins at the initial event and ends at the final event is called the full way. The complete path that requires the maximum amount of time is called critically. Any other sequence of work is simply path.

To monitor and manage the progress of work on the network schedule, it is necessary to calculate the following parameters:

1. The time required to complete each individual job. This is called the expected time (). Since the actual time required may depend on many factors, it is determined as a probabilistic value based on expert assessments of the proposed performers. Determining the expected time to complete the work can be done using either two or three expert estimates. Based on the two estimates, the calculation is carried out using the following formula:

where https://pandia.ru/text/78/182/images/image013_71.gif" width="39 height=21" height="21"> is the expert’s optimistic assessment, assuming the absence of unexpected delays.

Based on three expert estimates, the calculation is carried out using the following formula:

where, in addition to the estimates discussed above, the estimate of the most probable time is used https://pandia.ru/text/78/182/images/image017_53.gif" width="24" height="25">). It represents the minimum period, necessary to complete all work preceding a given event and equal to the maximum duration of the path from the initial event to the event under consideration.It can be calculated using the following formula:

Where i– number of the initial event for this operation;

j– number of the final event.

For example:

Calculation of the late time of events begins with the final one, which has .

4. Event time reserve, that is, the time by which the occurrence of the corresponding event can be delayed. It is equal to the difference between the late and early dates of the event.

5. The total operating time slack shows the time by which the operating duration can be increased without changing the duration of the critical path. If, when performing any work, its entire full time reserve is used up, then all other jobs on this path following it will not have time reserves..gif" width="147" height="25"> .

6. Free time reserve shows the time by which the duration of work can be increased without changing the time reserves of subsequent work lying on this path. Calculation of free work time (https://pandia.ru/text/78/182/images/image029_32.gif" width="147" height="25">.

Free time reserve, as well as full time reserve, allow managers to make adjustments to the managed process based on current control data. The difference is that the free time reserve can be allowed to be used by the performers, since this will not affect other work of the program, and the use of the full reserve requires taking into account the capabilities of the performers of subsequent work.

7. Work intensity coefficient () characterizes the degree of freedom in the start and finish times of work that is not on the critical path. Activities on the critical path do not have time reserves, and their intensity coefficient is equal to 1. For activities not on the critical path, this coefficient is > 1. This indicator is calculated only for activities not on the critical path, using the following formula:

where is the duration of the maximum path passing through this work;

– the duration of the critical path segments lying on the path under consideration;

– duration of the critical path.

Provided that the resources used in the labor process are interchangeable, their redistribution should be carried out taking into account the value of the indicator Development of decisions" href="/text/category/virabotka_reshenij/" rel="bookmark">development of a decision on the time of stopping individual pieces of equipment for preventive repairs is shown in Fig. 3.3.8. For example, milling machine 3 is loaded only on September 24 and September 25. Therefore, the first three days of the week it can be loaded with unscheduled work or its preventive maintenance can be carried out, as provided for in the schedule for drilling machine 1 on September 21 and 22. Strip schedule Gantt can be used as a plan for the implementation of the technological process of production of products. In Fig. 3.3.8 you can see an example of a fragment of such a plan. A batch of parts A on 09/21 and a quarter of the working day on 09/22 should be processed on lathe 1. Then three quarters of the working time on 09/22, full working day 23.09 and quarter 24.09 these parts must be processed on milling machine 1. After completing the above operations, batch of parts A on 24.09 is transferred to drilling machine 1.

The Gantt chart shows the time required to complete the work and the sequence. The graph does not show the interconnections of the work being performed, and therefore it is difficult to make decisions about changing their sequence.

The strip chart does not show the interrelationships of work, but it is more visual when used to control the start and end times of individual work. This feature makes it preferable to use the network and strip Gantt charts together.

Let's assume that you need to prepare production and manufacture a device. This must be done as soon as possible, which must be agreed upon with the customer. The manager plans to control and manage this project using a network and Gantt chart.

First, a list of necessary works and their relationships is developed. Then a network diagram is constructed (Fig. 3.3.9) and, using expert assessments of the proposed performers, calculations are made for each job (Table 3.3.3).

Table 3.3.3

	Name of works	Duration work in days
	Development of working drawings of parts (PD)
	Development of technological processes for manufacturing parts (TD)
	Development of drawings of assembly units (AS)
	Design and ordering of equipment for the production of parts (ZOD)
	Standardization of technological process operations for the manufacture of parts (NTD)
	Development of assembly technological processes (TA)
	Manufacturing of equipment for performing operations of technological processes for the production of parts (IOD)
	Design and ordering of equipment for product assembly (PA)
	Standardization of technological process operations for product assembly (NTS)
	Manufacturing of product parts (ID)
	Manufacturing of equipment for assembly work (IOS)
	Product assembly and testing (IP)

Based on the information received, the parameters of the network diagram are calculated. We will perform the calculation directly on the chart. To do this, we introduce the following form of data notation:

Rebuilding the network diagram in Fig. 3.3.9, taking into account the reflection of the above information on it, we will calculate the parameters according to the rules formulated above. As a result, we obtain an image of this network diagram in the form shown in Fig. 3.3.10.

To visually analyze the complex of works and the intensity of their timely completion, we will “link” the network diagram to the time scale (Fig. 3.3.11).

As can be seen from the diagram (Fig. 3.3.11), the work of the network diagram formed four complete paths. The first path: BH - TD - NTD - ID - IS, in which the work of NTD has a full reserve of time - 20 days. The second path: BH - TD - ZOD - IOD - ID - IS, where not a single job has a slack time, and therefore it is called the critical path. The third way: BH - ChS - TS - NTS - IS, in which the work of the NTS has a full reserve time of 32 days. The fourth way: ChD - ChS - PM - ZOS - IOS - IS, where the work of ChS, PM, ZOS and IOS have a full time reserve of 27 days. This time reserve can be used when performing one of the named jobs or divided between the listed jobs.

Table 3.3.4

Summary table of network diagram parameters

Start Event	End Event

For the convenience of practical work on monitoring and maneuvering resources, we summarize the calculated parameters in Table 3.3.4, and depict the sequence of work in the form of a Gantt strip chart (Fig. 3.3.12). The table shows that work 3–7 (NTD) has a free time reserve of 20 days, work 6–9 (NTS) – 32 days, and work 8–9 (IOS) – 27 days. This shows the possibility of presenting freedom in planning the start of this work, but it is possible to postpone these works only within the free reserve of time.

The Gantt bar chart shows the calendar dates for the start and end of each job. At the top of the graph is the critical path. The manager must constantly monitor the work of this path and take management actions to prevent violation of the deadlines for completing these works.

→ Construction production

Methodology for drawing up network diagrams

Network diagrams are built according to certain rules and in the appropriate order based on some source documents and data. The procedure for constructing a network may be different, but in all cases it is recommended to adhere to a number of general provisions and rules and techniques developed by practice. First of all, the network is drawn from left to right; arrow works can have an arbitrary length and slope, but their general direction should be from left to right. First, a network is built in a draft version without numbering events (Fig. 20.3), after which this network is subject to ordering; in the process of ordering, all missed and unaccounted works 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 shift the event slightly or depict it as a broken line, as shown in Fig. 20.5, a, b.

In the practice of construction production, there are many cases where two or more works have initial and final events, but different durations, such as plumbing and electrical installation work in a civil building. They are usually carried out simultaneously, but not always simultaneously, after the frame or walls are ready, but are completed by the time painting work begins.

Rice. 20.3. Primary model diagram

Rice. 20.4. Working network diagram

Rice. 20.5. Examples of building a network model

Rice. 20.6. Model diagram for parallel work

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

Rx. 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 dependency 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 serves as the end.

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

Network diagrams have to reflect organizational activities related to the organization of flow and the breakdown of the overall scope of work into tasks. Dependence of an organizational nature is expressed in the sequential transition of teams of workers and the movement of equipment from grip to grip.

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

Rice. 20.8. Schemes of a network model for a grabby system of work production

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

Let's assume that we have another job - laying pipes for the purpose of installing an external water supply system. Pipe laying is directly related to soil development. 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. 20.8b). Here fictitious connections include 2-5, 3-6 and 4-7; The excavation work is divided into three parts corresponding to the three parts of the pipe laying work.

The excavation of the trench and the laying of pipes can be graphically depicted in another version (Fig. 20.8, c).

When constructing network graphs, one-way and two-way connections are used. One-way connections between jobs are depicted by using fictitious work. If, after finishing 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. 20.9a). If there are five jobs: a, b, c, d, e, the following relationships exist: job c begins after the completion of jobs a and b, and job e - after the completion 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 work c depends not only on work a and b, but also on work d, which contradicts the condition).

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

Two-way communication occurs provided that subsequent work begins before the previous work is completed; this dependence is shown in Fig. XX.10, a. Here, each process A, £, C is presented as the sum of sequentially completed works of the same name: the first two processes A and B develop independently and independently of each other, and the third C is executed 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 when there are a large number of processes and their continuous execution in several areas.

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

Rice. 20.10. Network model diagrams for two-way communication between jobs

Rice. 20.11. Idle communication circuits and critical path determinations

Here the network is incorrectly constructed. In order to correctly reflect technological and organizational connections, intermediate events and idle connections are introduced (variant vig). Network diagram c is more complex than diagram d; it is simplified by reducing the number of events and idle connections (option d).

The number and direction of intermediate (idle) connections influence 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 connection in this case does not have any effect, since the path through this connection will be less than the critical 5+0+7 16 days.

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

When building a network, you should pay attention to the inadmissibility of closed loops, dead-end and tail events in network graphs. 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 source data or an incorrect construction of the network.

If the network schedule covers a large set of works, then there is a need to enlarge (simplify) it by replacing a set of homogeneous works with one composite work. Such a replacement is possible when any group of works has one initial and one final 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 kept in mind that the time schedule is estimated 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 works 7-10, 10-12, 12-13 in the enlarged network are presented in the form of one work 7-13 with a duration of 8+3+7=16 days. Thus, boundary events are preserved

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

Typically, work that is assigned to one responsible person or department is subject to consolidation. Each performer or division makes up a primary or partial network for a specific set of works assigned to it. It must be assumed that in the network of one performer events (boundary) appear 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 diagrams into one common one. The process of combining many private network diagrams into one common one is called network stitching. When stitching, all cases of inconsistency between individual sections of the network are identified and eliminated.

A 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 set of works and a consolidated network schedule. Sometimes it is useful to have a consolidated network schedule for the production of all construction, installation and special work, identifying subcontractors.

8 Each particular chart 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, the third from 151 to 200, etc. Each specialized organization can also adopt its own symbols for events. Instead of circles, rectangles, squares, trapezoids, ovals, etc. can be accepted. Introduction of business symbols
Makes the summary network diagram more visual and allows each organization to quickly find its activities and their connections on the common network.

Rice. 20.13. Scheme of the interconnected network model

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

Rice. 20.15. Network model with design parameters

When stitching a network diagram, you must adhere to the following rule: two numbers are placed inside the event - the old one at the top (private network), and the new serial number at the bottom (the consolidated network). In Fig. 20. 13 shows the numbering of the combined networks in one graph. Stitching networks manually is labor-intensive work, and therefore for large construction projects with a number of events of more than 200, the construction and adjustment 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.

A diagram of the consolidated network diagram highlighting subcontractors is shown in Fig. XX. 14. From this graph it is clear that four organizations take part in the construction of the facility: the general contractor and three subcontracting organizations: EM-3 (electrical installation department), SMU-9 (construction and installation department) and MU-8 (installation department).

In Fig. 20. 15 shows a network diagram with the critical path. In this network diagram, there are several complete paths between the start and end events, listed in the table. XX.2. This table also contains the duration of the work; on the chart they are located under the arrows. The critical path is equal to the largest sum of work 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 time reserve of 36-22=14 days. This time reserve can be used to increase the duration of non-critical work and free up material and technical resources for performing critical work.

Initial data for drawing up a network diagram. The initial document for drawing up 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 construction of the facility and the target date; – design and estimate documentation (design specifications and working drawings) for the construction of an object or complex of buildings and structures; – construction organization project (COP) and work performance project (WPR)„ technological maps;
current issues of ENiR for construction, installation and special works; – data on the duration of certain types of work during the construction of similar facilities; – information about the existing structure and availability of resources of construction and installation organizations, the material and technical base of construction (capacity of concrete plants, precast concrete plants, fleet of machines, mechanisms, etc.);
- data on the technology and organization of construction of similar facilities; – construction start date.

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

When drawing up a project plan, the beginning of design is taken as the initial event; when drawing up a project plan, the beginning of design or the beginning of work; when drawing up an educational (course or diploma) project, the beginning of work.

When developing a network diagram, it is necessary first of all to outline a large-scale diagram of the original network diagram with a limited number of events. Such a scheme is mandatory for issuing tasks to responsible executors for drawing up individual sections of the network schedule. This scheme allows responsible executors to establish relationships with other sections of the schedule, determine the inputs and outputs of individual sections of the schedule, determine the complex of work of other performers, etc. This scheme, finally, serves as the basis for stitching together a single schedule from private networks.

If the initial network schedule diagram does not comply with the construction deadlines, then it is optimized through repeated or multiple planning and calculations until the schedule meets the target deadlines.

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

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

Network diagram parameters are calculated manually and on electronic computers.

Network graphs are calculated manually using the analytical, tabular or graphical method.

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

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

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

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

Often during the development of various types of projects, a plan for completing tasks is drawn up. Microsoft Excel tools allow you to create a network diagram, which serves to solve the problem of planning project stages.

Let's create a simple schedule using a Gantt chart.
First you need to create the table itself with columns with appropriate headings.

After this, you can see a new window in which we select the “Alignment” tab. In the fields, set the alignment to “Center”, and in the display settings, check the box next to “Wrap by words”.

Go to the working window and set the table boundaries. Select the headers and the required number of cells for the table, open the “Home” section, and in it, using the corresponding icon in the list, select the “All borders” item.

As a result, you can see that a table frame with headers has been created.

The next step is to create a timeline. This is the basic part in network graphics. A certain set of columns corresponds to a particular period in the planning of project tasks. This example will create a 30 day timeline.

For now, we leave the main table and select thirty columns near its right border in the context of this example. It is worth noting that the number of rows = the number of rows in the previously created table.

Go to the “Home” section and select “All borders” in the borders icon, just like with the previously created table.

In this example, we define the plan for June 1-30. And we enter the corresponding dates into the timeline. To do this, the Progression tool will be used.

After clicking on the "Progression" item, a new window will appear. In it we mark the location by lines (in this example), and select dates as the type. Depending on what time period is used, select the “Day” item. The step value is 1. We set the date June 30 as the final value and confirm the action.

Next, the timeline will be filled with days from the 1st to the 30th. Next, you need to optimize the table for its convenience by selecting the entire time period and clicking the right mouse button. In the context menu, select "Format Cells".

A new window will appear in which you need to open the "Alignment" tab and set the value to 90 degrees. We confirm the action.

But the optimization is not complete. Go to the main section "Home" and click on the "Format" icon and select auto-selection in it according to line height.

And to complete the optimization, we do a similar action and select auto-selection based on column width.

As a result, the table has acquired a complete look.

The final step is to populate the first table with the relevant data. Also, if there is a large amount of data, then by holding down the “Ctrl” key on the keyboard, drag the cursor along the border of the numbering field down the table.

And as a result, the table is ordered. And you can also fill in the remaining fields of the table.

In the "Home" section, click on the "Styles" icon and in it click on the "Conditional Formatting" icon. And in the list that appears, select the “Create rule” item.

After this action, a new window will open in which you need to select a rule from the list of rules. Select "Use a formula to determine which cells to format." A suitable selection rule specifically for our example is shown in the box.

Let's look at the elements of the formula:

G$1>=$D2 is the first argument, which determines that the value in the timeline is equal to or greater than a certain date. The first part of the element points to the first cell, and the second part to the desired part of the column regarding the plan.
G$1И - check values for truth
$ - allows you to set values as absolute.

To set the color for the cells, click "Format".