Building a network diagram: an example. Manufacturing process model

Network graphs and rules for their construction

A network diagram is a graphical representation of the processes that must be completed to achieve a set goal.

Methods of network planning and management (SPU) are based on graph theory. A graph is a collection of two finite sets: a set of points, which are called vertices, and a set of pairs of vertices, which are called edges. Two types of graphs are commonly used in economics: tree and network. A tree is a connected graph without cycles, having an initial vertex (root) and extreme vertices. A network is a directed finite connected graph that has a start vertex (source) and an end vertex (sink). Thus, each network graph is a network consisting of nodes (vertices) and oriented arcs (edges) connecting them. Graph nodes are called events, and the oriented arcs connecting them are called jobs. On the network diagram, events are depicted by circles or other geometric shapes, and the works connecting them are dimensionless arrows (they are called dimensionless because the length of the arrow does not depend on the amount of work that it reflects).

Each network event is assigned a specific number ( i), and the work connecting the events is denoted by the index ( ij). Each work is characterized by its duration (duration) t(ij). Meaning t(ij) in hours or days put down as a number above the corresponding arrow of the network diagram.

In the practice of network planning, several types of work are used:

1) real work, a production process that requires labor, time, materials;

2) passive work (waiting), a natural process that does not require labor and material resources, but the implementation of which can only occur within a certain period of time;

3) fictitious work (dependence), which does not require any costs, but shows that some event cannot happen before another. When constructing a graph, such activities are usually indicated by a dotted line.

Each work, alone or in combination with other works, ends with events that express the results of the work performed. In network diagrams, the following events are distinguished: 1) initial, 2) intermediate, 3) final (final). If the event has an intermediate character, then it is a prerequisite for the start of the work following it. It is believed that the event has no duration and is carried out instantly after the completion of the work preceding it. The initiating event is not preceded by any work. It expresses the moment of the onset of conditions for the start of the implementation of the entire complex of works. The final event does not have any subsequent work and expresses the moment of completion of the entire complex of work and achievement of the intended goal.

Interconnected activities and network events form paths that connect the initial and final events, they are called complete. The full path on the network diagram is a sequence of work in the direction of the arrows from the initial to the final event. The full path of maximum duration is called the critical path. The duration of the critical path determines the deadline for completing the entire complex of works and achieving the intended goal.

Activities located on the critical path are called critical or stressful activities. All other works are considered non-critical (non-stressed) and have time reserves that allow you to move the deadlines for their implementation and the timing of events without affecting the overall duration of the entire complex of works.

Rules for constructing a network diagram.

1. The network is drawn from left to right, and each event with a higher sequence number is displayed to the right of the previous one. The general direction of the arrows depicting jobs should also generally be from left to right, with each job exiting a lower-numbered event and entering a higher-numbered event.

False Correct

3. There should be no “dead ends” in the network, that is, all events, except for the final one, must have subsequent work (intermediate events are called dead ends, from which no work exits). This situation may occur when the given work is not needed or some work is omitted.

4. There should be no events in the network, except for the initial one, which are not preceded by at least one job. Such events are called "tail events". This may be the case if previous work is missed.

For the correct numbering of events in the network diagram, use the following scheme of actions. The numbering starts from the initial event, which is assigned the number 0 or 1. From the initial event (1), all outgoing jobs (directed arcs) are deleted, and on the remaining network, an event is again found that does not include any job. This event is assigned a number (2). The specified sequence of actions is repeated until all events of the network diagram are numbered. If during the next deletion, two events simultaneously occur that do not have incoming jobs, then numbers are assigned to them arbitrarily. The number of the final event must be equal to the number of events in the network.

Example.

In the process of building a network diagram, it is important to determine the duration of each work, that is, it is necessary to give it a time estimate. The duration of the work is set either in accordance with applicable standards, or on the basis of expert assessments. In the first case, duration estimates are called deterministic, in the second - stochastic.

There are various options for calculating stochastic time estimates. Let's consider some of them. In the first case, three types of duration of a particular job are set:

1) the maximum period, which is based on the most unfavorable conditions for the performance of work ( tmax);

2) the minimum period, which is based on the most favorable conditions for the performance of work ( tmin);

3) the most probable period, based on the actual provision of work with resources and the presence of normal conditions for its implementation ( t in).

Based on these estimates, the expected time to complete the work (its time estimate) is calculated using the formula

. (5.1)

In the second case, two estimates are given - the minimum ( tmin) and maximum ( tmax). 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. The expected value of these estimates ( t cool) (with beta probability density distribution) is estimated by the formula

. (5.2)

To characterize the degree of spread of possible values ​​around the expected level, the dispersion index is used ( S2)

. (5.3)

The construction of any network diagram begins with the compilation of a complete list of works. Then the sequence of works is established, and for each specific work, immediately preceding and subsequent works are determined. To establish the boundaries of each type of work, questions are used: 1) what should precede this work and 2) what should follow this work. After compiling a complete list of works, establishing their order and time estimates, they proceed directly to the development and compilation of a network schedule.

Example.

Consider, as an example, a program to build a warehouse building. The list of operations, their sequence and time duration will be drawn up in a table.

Table 5.1

Network Schedule Work List

Operation	Operation description	Immediately preceding operation	Duration, days
A	Construction site clearing	-
B	Foundation pit excavation	A
IN	The way of foundation blocks	B
G	Laying of external engineering networks	B
D	Construction of the building frame	IN
E	Roofing	D
AND	Internal plumbing work	G, E
Z	Flooring	AND
AND	Installation of door and window frames	D
TO	Thermal insulation of floors	E
L	Laying the electrical network	Z
M	Plaster walls and ceilings	I, K, L
H	Interior decoration	M
ABOUT	Exterior finish	E
P	Landscaping	BUT

Built on the basis of the data in Table. 5.1 the preliminary network work schedule is as follows (Fig. 5.1).

Rice. 5.1. Preliminary network schedule

Below is the same timetable for the construction of a warehouse building, numbered and with time estimates for the work (Figure 5.2).

Rice. 5.2. Final Network Diagram

Example 8 Information about the construction of the complex is given by the list of works, their duration, sequence of execution and is given in the table. Build a network diagram of a set of works and find the correct numbering of its vertices.

	Name of works	List of subsequent works	Duration in months
	Road construction
	Preparation of quarries for operation
	Village construction
	Equipment order
	Plant construction
	Construction of a dam, dam
	Connection of plant and pipelines
	Preliminary tests

To build a draft network diagram, each job will be depicted as a solid oriented arc, and the connections between jobs as a dotted oriented arc. We will draw this connection arc from the end of the arc corresponding to the previous work to the beginning of the arc corresponding to the subsequent work. We get the network graph shown in the figure:

A large number of arcs complicates the solution, so let's simplify the resulting network. To do this, we will discard some connection arcs, the removal of which will not violate the order of work. The beginning and end of the ejected arc will be combined into one vertex. Vertices that do not include any arc can also be combined into one. We get the following network graph:

Let's find the correct numbering of vertices (events) of the network graph.

Number 1 is given to a vertex that does not include any arc. We delete (mentally or with a pencil) the arcs coming out of the vertex with number 1. In the resulting network graph, there is only one vertex that does not include any arc. Hence, it receives the next number 2 in order (if there are several of them, then all vertices that do not include any arc receive the next numbers in order). Then again (mentally) we delete the arcs, but already leaving the vertex with number 2. In the resulting network diagram, the network has only one vertex, which does not include any arc. So she gets the next number 3 in order, and so on.

6.4.6. Timing Example

Example 9 Let's say we have a graph:

Early completion of events:

Late deadline for events:

- duration of the critical path;

Time reserve:

Early start date:

Early completion date:

Late completion date:

Late start date:

Full working time reserve:

Private time reserve of the first type:

Private time reserve of the second type:

Independent time reserve:

We calculate the stress coefficient for several paths that do not coincide with the critical one ( ={0,3,5,6,8,9,10,11}=60).

Let's take job (4-7) and find the maximum critical path passing through this job: (0-3-7-10-11), t(L max)=49,

=10+8+5=23

K n (4.7) = (49-23) / (60-23) = 26/37;

Let's take job (1-2) and find the maximum critical path passing through this job: (0-1-2-7-10-11), t(L max)=48,

=8+9+3+5=25

Let's take job (2-7) and find the maximum critical path passing through this job: (0-1-2-7-10-11), t(L max)=48,

=8+9+3+5=25

K n (4.7) \u003d (48-25) / (60-25) \u003d 23/35;

All calculated parameters can be displayed on a network diagram. For this, a four-sector method of fixing parameters is used, which is as follows. The circle denoting the event is divided into four sectors. The event number (j) is written in the center; in the left sector - the latest date of the event j( ), on the right - the earliest date of the event j( ), in the upper one - the time reserve for the completion of the event j(R j), in the lower one - the numbers of previous events through which the path of maximum duration goes to the given one (
).

Display on the graph for our example:

Events must be correctly numbered, i.e. for each job ( i, j) i < j. If this requirement is not met, it is necessary to use the event renumbering algorithm, which is as follows:

a) the numbering of events begins with the initiating event, to which No. 1 is assigned;

b) all outgoing works (arrows) are deleted from the initial event, and on the remaining network an event is found that does not include any work, it is assigned No. 2;

c) then the jobs coming out of event #2 are crossed out, and again an event that does not include any job is found, and it is assigned #3, and so on until the final event, the number of which should be equal to the number of events in the network diagram;

d) if during the next deletion of works at the same time several events do not have works included in them, then they are numbered by successive numbers in random order;

There is only one final event.

There are no deadlock events (except for the final one), that is, those that are not followed by at least one job.

There is only one initiating event.

There are no events (except for the initial one) that are not preceded by at least one work.

Any two events must be directly connected by at most one arrow job. If two events are linked by more than one job, it is recommended to introduce an additional event and a dummy job:

The network should not have closed loops.

If for the execution of one of the activities it is necessary to obtain the results of all the activities included in the event preceding it, and for another activity it is enough to obtain the result of several of these activities, then an additional event must be introduced that reflects the results of only these last activities, and a dummy activity that links the new one. event with the former. The duration of the dummy job is zero.

For example, to start work D, it is enough to finish work A. To start work C, you need to finish work A and B.

Time parameters of networks. Time reserves.

The main temporal parameters of networks are the early and late dates of occurrence (commission) of events. Knowing them, you can calculate the rest of the network parameters - the start and end dates of work and the time reserves for events and work.

Denote
– duration of work with the initial event i and end event j.

early term
event j is determined by the value of the longest segment of the path from the initial to the event under consideration, and
, A
Where N - number of the final event. Calculation rule:

where the maximum is taken over all events i , immediately preceding the event j(connected by arrows).

late deadline
accomplishment of the event i characterizes the latest allowable time by which the event must occur, without causing the failure of the deadline for the completion of the final event. Calculation rule:

where the minimum is taken over all events j immediately following the event i.

Late dates of events are determined by "reverse motion", starting from the final event, taking into account the ratio
, i.e., the late and early terms of the completion of the final event are equal to each other.

Reserve
events i shows how long the event can be delayed i without violating the term of the end event:

.

Events lying on the critical path (critical events) do not have reserves.

There are various methods for calculating network parameters: tabular and graphical.

Consider the graphical method.

When calculating the network diagram, each circle depicting an event is divided by diameters into four sectors:

Example 55 Consider the project network represented by the following graph.

On the chart, events are represented by circles, and work by arrows. The robot can be designated as a letter inscribed on the graph next to the arrow corresponding to the work, or through the numbers of events from which the work begins and ends.

Find the critical path. How long will it take to complete the project? Is it possible to postpone the execution of the robot D without delaying the completion of the project as a whole? How many weeks can work be delayed C without delaying the completion of the project as a whole?

Stage 1. When calculating the early date of the event
we move from the initial event 1 to the final event 6.

.

Event 2 includes only one job: .

Likewise.

Event 4 includes two entries →

It follows that the critical time for the project completion = 22.

We will enter the relevant data into the network diagram.

Stage 2. When calculating late deadlinet P (i) event completionI we move from the final event 6 to the initial event 1 along the network diagram against the direction of the arrows.

.

Two jobs come out of event 4: (4, 5) and (4, 6). Therefore, we determine the late date of the event t P ( 4) for each of these jobs:

We will enter the obtained data into the network graph.

Stage 3. Calculate reserve
events i , that is, from the numbers obtained in step 2, subtract the numbers obtained in step 1.

Stage 4. For critical events, the time slack is equal to zero, since the early and late dates for their completion coincide. Critical events 1, 2, 4, 5, 6 and determine the critical path 1-2-4-5-6, which by definition should be the longest in time. On the network diagram, we will show it with two lines.

Now you can answer the questions of the problem.

It will take 22 weeks to complete the project. Job D located on the critical path. Therefore, it cannot be postponed without delaying the completion of the project as a whole. Job C not located on the critical path, it can be delayed by (weeks).

A network schedule is a table designed to draw up a project plan and monitor its implementation. For its professional construction, there are specialized applications, such as MS Project. But for small businesses, and even more so for personal business needs, it makes no sense to buy specialized software and spend a lot of time learning the intricacies of working in it. With the construction of a network graph, the spreadsheet Excel, which is installed by most users, quite successfully copes. Let's find out how to perform the above task in this program.

You can build a network graph in Excel using a Gantt chart. Having the necessary knowledge, it is possible to compile a table of any complexity, ranging from the duty schedule of the watchmen to complex multi-level projects. Let's take a look at the algorithm for performing this task by making a simple network graph.

Stage 1: building the table structure

First of all, you need to create a table structure. It will be the framework of the network diagram. Typical elements of a network diagram are columns that indicate the serial number of a specific task, its name, the person responsible for its implementation and deadlines. But besides these main elements, there may be additional ones in the form of notes, etc.

This completes the creation of the table blank.

Stage 2: creating the timeline

Now we need to create the main part of our network diagram - the timeline. It will be a set of columns, each of which corresponds to one period of the project. Most often, one period is equal to one day, but there are cases when the value of the period is calculated in weeks, months, quarters, and even years.

In our example, we use the option when one period is equal to one day. Let's make a time scale for 30 days.

1. We pass to the right border of the blank of our table. Starting from this border, we select a range with 30 columns, and the number of rows will be equal to the number of lines in the blank that we created earlier.



2. Then click on the icon "Border" in mode "All Borders".



3. After the boundaries are outlined, let's add the dates to the time scale. Let's say we control a project with a validity period of June 1-30, 2017. In this case, the name of the time scale columns must be set in accordance with the specified time interval. Of course, manually entering all the dates is quite tedious, so we will use an auto-complete tool called "Progression".

   Insert the date into the first object of the time jackal header "01.06.2017". Move to tab "Home" and click on the icon "Fill in". An additional menu opens, where you need to select an item "Progression…".



4. Window is activated "Progression". In Group "Location" value should be noted "By lines", since we will fill the header, represented as a string. In Group "Type" option must be checked "Dates". In the block "Units" put the switch near the position "Day". In area "Step" must be a numeric expression "1". In area "Limit value" indicate the date 30.06.2017 . Click on OK.



5. The header array will be populated with consecutive dates ranging from June 1 to June 30, 2017. But for the network diagram, we have cells that are too wide, which negatively affects the compactness of the table, and, therefore, its visibility. Therefore, we will carry out a series of manipulations to optimize the table.
   Highlight the head of the timeline. Click on the selected fragment. In the list, we stop at the item "Cell Format".



6. In the formatting window that opens, move to the section "Alignment". In area "Orientation" set value "90 degrees", or move the element with the cursor "Inscription" up. Click on the button OK.



7. After that, the names of the columns in the form of dates changed their orientation from horizontal to vertical. But due to the fact that the cells did not change their size, the names became unreadable, since they do not fit vertically into the designated elements of the sheet. To change this state of affairs, again select the contents of the header. Click on the icon "Format" located in the block "Cells". In the list, we stop at the option "Auto Fit Line Height".



8. After the described action, the names of the columns in height fit into the boundaries of the cells, but the width of the cells did not become more compact. Select the range of the timeline header again and click on the button "Format". This time, select the option from the list. "AutoFit Column Width".



9. Now the table has become compact, and the grid elements have taken on a square shape.

Stage 3: Filling in the data

Stage 4: Conditional Formatting

At the next stage of working with the network diagram, we have to fill in with color those cells of the grid that correspond to the interval of the period for the implementation of a particular event. You can do this with conditional formatting.

1. We mark the entire array of empty cells on the timeline, which is presented as a grid of square-shaped elements.



2. Click on the icon "Conditional Formatting". It is located in the block "Styles" This will open a list. It should select the option "Create a Rule".



3. A window is launched in which you want to create a rule. In the area for selecting the type of rule, we mark the item that implies the use of a formula to designate formatted elements. In field "Format Values" we need to set the selection rule, represented as a formula. For our particular case, it will look like this:

   AND(G$1>=$D2;G$1<=($D2+$E2-1))

   But in order for you to convert this formula for your network graph, which is quite possible to have other coordinates, we should decipher the written formula.

   "AND" is a built-in Excel function that checks if all values ​​entered as its arguments are true. The syntax is:

   AND(boolean1;boolean2;…)

   In total, up to 255 booleans are used as arguments, but we only need two.

   The first argument is written as an expression "G$1>=$D2". It checks that the value in the timeline is greater than or equal to the corresponding start date value for a specific event. Accordingly, the first reference in this expression refers to the first cell of the row on the timeline, and the second refers to the first element of the start date column of the event. dollar sign ( $ ) is set specifically so that the coordinates of the formula, which have this symbol, do not change, but remain absolute. And for your case, you must place the dollar signs in the appropriate places.

   The second argument is represented by the expression "G$1<=($D2+$E2-1)» . It checks that the indicator on the timeline ( G$1) was less than or equal to the project completion date ( $D2+$E2-1). The timeline figure is calculated as in the previous expression, and the project end date is calculated by adding the project start date ( $D2) and its duration in days ( $E2). In order for the first day of the project to be included in the number of days, one is subtracted from this amount. The dollar sign plays the same role as in the previous expression.

   If both arguments of the presented formula are true, then conditional formatting will be applied to the cells in the form of filling them with color.

   To select a specific fill color, click on the button "Format…".



4. In a new window, move to the section "Pouring". In Group "Background Colors" Various color options are available. We mark the color with which we want the cells of the days corresponding to the period of the specific task to be highlighted. For example, let's choose green. After the hue is reflected in the field "Sample", click on OK.



5. After returning to the rule creation window, also click on the button OK.



6. After the last activity, the network grid arrays corresponding to the period of the specific activity were colored green.

On this, the creation of a network diagram can be considered completed.

In the course of work, we created a network diagram. This is not the only version of such a table that can be created in Excel, but the basic principles for performing this task remain unchanged. Therefore, if desired, each user can improve the table presented in the example to suit their specific needs.

The following concepts and terminology are adopted in the network planning and construction management system.

Under the concept of a project, a range of organizational and technical tasks is generalized to be solved to achieve the final results of construction production. These include: the development of a feasibility study for the planned construction, the selection of a construction site, engineering and geological surveys, the design of a territory for development, the development and approval of the technical documentation necessary for construction, including schedules and schemes for the production of construction and installation works before the delivery of those under construction objects in operation.

The set of works performed to achieve a specific goal, which determines a certain part of the project, is called the function of the project. For example, work related to the preparation of construction production (development of working drawings of buildings and structures, a project for the production of work; placing orders for the manufacture of equipment, structures and their delivery to the construction site, etc.) or with the production of construction and installation works, with the construction foundations, (developing, laying out axes, digging pits, harvesting and installing formwork and reinforcement, preparing a concrete mixture, transporting and laying it into the formwork, stripping and capturing the sinuses of concreted foundations with soil) are functions in the construction project.

The most important indicators of project efficiency are the cost and duration of construction, which are directly dependent on similar indicators of individual project functions. If a list of all project functions is established and the execution sequence and time costs are determined for each of them, then by depicting these functions in the form of a graphical network, you can see which of them determine the timing of the remaining functions and the entire project as a whole.

It follows from this that the network schedule reflects the logical interconnection and interdependence of all organizational, technical and production operations for the implementation of the project, as well as a certain sequence of their implementation.

The main parameters of the network diagram are the work and the event, and the derivatives are the network, the critical path and the time reserves.

Work refers to any process that takes time. In network diagrams, this term determines not only certain production processes that require the expenditure of material resources, but also the expected processes associated with observing technological breaks, for example, for hardening laid concrete.

An event is an intermediate or final result of one or more activities, necessary for the start of other activities. An event is fired after all the jobs included in it have been completed. Moreover, the moment of the completion of the event is the moment of the end of the last (included in it work. Thus, the event is the final results of certain works and at the same time - the starting positions for the beginning of subsequent ones. An event that does not have previous works is called initial; an event that having no subsequent works is called finite.

Work on the network diagram is depicted with one solid arrow. The duration of work in units of time (days, weeks) is put down under the arrow, and the name of the work is above the arrow. Each event is depicted by a circle and numbered (Fig. 115).

Rice. 115. Designation of events and work m - n.

Rice. 116. Designation of the dependence of technological events.

Rice. 117. Designation of the dependence of events of an organizational nature.

The duration of a particular work, established depending on the accepted method of its implementation according to the UNIR or labor costing, is called a time estimate. The dependence between individual events, which does not require the expenditure of time and resources, is called fictitious work and is depicted on the network diagram by a dotted arrow.

These dependencies or fictitious works can be divided into three groups: technological, organizational, conditional.

Dependence of a technological nature means that the execution of one work depends on the completion of another, for example, the walls of the next floor cannot be laid before the floor panels of the lower floor are installed (Fig. 116).

Dependence of an organizational nature shows the transitions of teams of workers, the transfer of mechanisms from one section to another, etc. They arise mainly when work is performed by in-line methods (Fig. 117).

If there are several final events (for example, the commissioning of several objects included in the launch complex of the enterprise), they should be connected by conditional dependencies or fictitious work together - putting the enterprise into operation (Fig. 118, b).

The start event must be one. In cases where there are several initial events (for example, work on excavating the excavations of several objects begins independently of each other), they should be conditionally connected by the designation of fictitious works with a single initial event (Fig. 118, a).

If the timing of the actual initial events of individual objects of the complex is different, the concept of real-time dependencies converging at one initial node should be introduced.

The duration set taking into account single-shift, and for the leading machines two-shift work and the optimal saturation of the front of work, is called the normal duration of work. If the duration of work is due to the maximum load of the front of work for two or three shifts, then it is considered minimal.

Rice. 118. Notation of conditional dependencies.

The term of work differs in terms:

the earliest start date for work is the first day on which work can begin;

the earliest end date of the work - the day the work ends, if it is started at the earliest start date;

the latest start of work - the last day of the start of work without delaying the total construction period;

the latest completion date of the work is the day when the work must be completed without delaying construction, i.e. without disrupting the overall construction period.

The difference between the latest and earliest start dates determines the private slack, that is, the time that work can be postponed without increasing the duration of construction. The time for which work can be postponed without delaying the execution of any subsequent work determines the total (total) slack, which is the difference between the total slack of the considered and subsequent work. In the case of several subsequent jobs, the job that has the smallest amount of total slack is selected.

The continuous sequence of works and events from initial to final, requiring the greatest time for its implementation, determines the critical path, which determines the total duration of construction, since the critical activities lying on it do not have time reserves.

In network diagrams, the direction of the arrows depicting jobs can be chosen arbitrarily. Typically, such graphs are built from left to right. However, the arrows for individual jobs can go up, down, or right to left.

When drawing up a network diagram, each activity should be considered from the point of view of its relationship with other activities and the following questions should be answered:

what work should be completed before starting this work;

what other work can be completed simultaneously with the execution of this work;

which work cannot be started before the completion of this work. Let's consider some examples of graphic representation of connections and work sequences in network diagrams.

Rice. 119. Communication schemes between works (a, b, c, d, e, f, g - cases 1,2,3,4,5,6,7).

Case 1 (Fig. 119, a). Relationship between works A (1-2) and B (2-3). Job B cannot start until Job A has finished.

Case 2 (Fig. 119.6). Dependence of two jobs on one. Activities D (7-8) and F (7-9) cannot be started until activity D (6-7) is completed.

Case 3 (Fig. 119, c). The dependence of one job on the completion of two jobs. Job E (10-11) cannot start until jobs D (8-10) and E (9-10) are finished.

Case 4 (Fig. 119, d). The start of the two jobs depends on the completion of the two jobs as well. Works F (15-16) and D (15-17) can only start after the completion of works B (13-15) and C (14-15).

Case 5 (Fig. 119, 6). Dependence of two groups of works. Work B (15-16) depends only on the completion of work A (14-15), and work D (21-22) depends on the completion of works A (14-45) and C (19-21). Network linking is carried out by including fictitious work D (15-21).

Case 6 (Fig. 119, e). Job D (47-48) cannot be started until the end of job C (46-47). In turn, work B (50-51) cannot be started until the end of work C (46-47) and A (49-50). Job E (47-50) is fictitious, which determines the logical linking of the network by holding back the start of job B (50-51) until job C (46-47) is completed.

Case 7 (Fig. 119,g). Work D (8-14) cannot be started until the completion of works A (2-8) and B (4-6); work G (12-16) cannot be started until the completion of Fig. 120. Scheme of the network diagram, works D (10-12), B (4-6); the relationship between these works is indicated by the fictitious work E (6-12). Since work W (12-16) does not depend on the completion of work A (2-8), it is separated from the last fictitious work B (6-8).

Rice. 120. Diagram of a network diagram.

In order to clarify the methodology for constructing network graphs, consider the case when the following conditions arose during the construction of an object:

at the beginning of construction, work A and B must be carried out in parallel;

activities C, D and E can be started before the completion of activity A;

work B must be completed before the start of work F and G;

at the same time, work E also depends on the completion of work A;

activity 3 cannot be started before the completion of activities D and F;

work I depends on the completion of work D and 3;

work K follows the end of work G;

work L follows work K and depends on the completion of work D and 3;

the final work M depends on the completion of works B, I and L.

On fig. 120 shows one of several possible solutions to the problem defined by the given construction conditions. All decisions should be based on the same logical concept, regardless of the grid type. The grid must be considered from the point of view of the logical sequence of work. For this purpose, its review should begin with the last event on the object and go back from event to event, checking the following points: whether each work starting on the event depends on all the activities leading to the event; whether all activities on which the activity in question should depend are included in the event. If both questions can be answered in the affirmative, then the network schedule satisfies the requirements of the projected construction technology of the facility.

When constructing a network diagram, the concept of “work”, depending on the degree of desired accuracy, can mean certain types of work or complexes of production processes performed at a given facility by one of the organizations participating in the construction. For example, the chief engineer of a trust needs to know fewer details than a foreman. Therefore, to provide construction guidance at the trust level, the network schedule can be compiled on the basis of more aggregated indicators.