Representations of network models. Basic requirements for network models
Network schedules are drawn up at the initial stage of planning. First, the planned process is divided into individual works, a list of works and events is compiled, their logical connections and sequence of execution are thought out, the work is assigned to the responsible executors. With their help and with the help of standards, if any, the duration of each work is estimated. Then compiled (stitched) network diagram. After streamlining the network schedule, the parameters of events and work are calculated, the time reserves and the critical path are determined. Finally, the analysis and optimization of the network schedule is carried out, which, if necessary, is drawn anew with the recalculation of the parameters of events and work.
When constructing a network diagram, a number of rules must be observed.
In the network model, there should be no “dead end” events, that is, events from which no work exits, with the exception of the final event. Here, either work is not needed and must be canceled, or the need for a certain work following the event in order to accomplish any subsequent event is not noticed. In such cases, it is necessary to carefully study the interrelationships of events and activities in order to correct the misunderstanding that has arisen.
There should be no "tail" events in the network diagram (except for the initial one), which are not preceded by at least one work. Having found such events in the network, it is necessary to determine the performers of the previous works and include these works in the network.
The network should not be closed loops and loops, that is, paths connecting some events with themselves. When a loop occurs (and in complex networks, that is, in networks with a high complexity index, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the original data and, by revising the scope of work, achieve its elimination.
Any two events must be directly connected by at most one arrow job. Violation of this condition occurs when displaying parallel works. If these works are left as they are, then there will be confusion due to the fact that the two various works will have the same designation. However, the content of these works, the composition of the involved performers and the amount of resources spent on the work may differ significantly.
Figure 1.2 Examples of introducing dummy events
Dummy jobs and events need to be introduced in a number of other cases. One of them is a reflection of the dependence of events that are not related to real work. For example, jobs A and B (Figure 1, a) can be performed independently of each other, but according to the production conditions, job B cannot start before job A ends. This circumstance requires the introduction of fictitious job C.
Another case is the incomplete dependence of jobs. For example, work C requires the completion of work A and B for its beginning, work D is connected only with work B, and does not depend on work A. Then the introduction of fictitious work Ф and fictitious event 3" is required, as shown in Figure 1, b.
In addition, fictitious jobs may be introduced to reflect actual delays and expectations. In contrast to the previous cases, here the fictitious work is characterized by a length in time.
If the network has one end goal, then the program is called single-purpose. A network diagram that has several final events is called a multi-purpose one and the calculation is carried out with respect to each final goal. An example would be the construction of a residential community, where the commissioning of each house is the end result, and the schedule for the construction of each house is determined by its own critical path.
Suppose that when compiling a certain project, 12 events are selected: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 24 activities connecting them: (0, 1), (0, 2 ), (0, 3), (1, 2), (1, 4), (1, 5), (2, 3), (2, 5), (2, 7), (3, 6), (3, 7), (3, 10), (4, 8), (5, 8), (5, 7), (6, 10), (7, 6), (7, 8), (7 , 9), (7, 10), (8, 9), (9, 11), (10, 9), (10, 11). Compiled the original network schedule 2.1.
The ordering of the network diagram consists in such an arrangement of events and jobs, in which for any job the preceding event is located to the left and has a lower number compared to the event that completes this job. In other words, in an ordered network diagram, all the arrow jobs are directed from left to right: from events with lower numbers to events with higher numbers.
Let's divide the original network graph into several vertical layers (we circle them with dotted lines and denote them with Roman numerals).
Having placed the initial event 0 in the I layer, we mentally delete this event and all the arrow-works coming out of it from the graph. Then event 1, which forms layer II, will remain without incoming arrows. Having mentally crossed out event 1 and all the work coming out of it, we will see that events 4 and 2 remain without incoming arrows, which form layer III. Continuing this process, we get the network diagram 1.3.
Network diagram 1.3. Unordered Network Diagram
Network Diagram 1.4 Organizing a Network Diagram with Layers
Now we see that the initial numbering of events is not entirely correct: for example, event 6 lies in the VI layer and has a number less than event 7 from the previous layer. The same can be said about events 9 and 10.
Network Diagram 1.5 Ordered Network Diagram
Let's change the numbering of events in accordance with their location on the chart and get an ordered network chart 1.4. It should be noted that the numbering of events located in the same vertical layer is of no fundamental importance, so the numbering of the same network diagram may be ambiguous.
One of the most important concepts of a network diagram is the concept of a path. A path is any sequence of activities in which the end event of each activity coincides with the start event of the activity following it. Among the various paths of a network diagram, the most interesting is the complete way -- any path that starts with the initial network event and ends with the end event.
The longest complete path in a network is called the critical path. Works and events that are on this path are also called critical.
In network diagram 1.6, the critical path passes through jobs (1;2), (2;5), (5;6), (6;8) and is equal to 16. This means that all jobs will be completed in 16 units of time. The critical path is of particular importance in the SPM system, since the work of this path will determine the overall cycle for completing the entire set of works planned using the network schedule. Knowing the start date of work and the duration of the critical path, you can set the end date for the entire program. Any increase in the duration of activities on the critical path will delay program execution.
Network diagram 1.6. critical path
At the stage of management and control over the progress of the program, the main attention is paid to the activities that are on the critical path or, due to lagging behind, have fallen on the critical path. To reduce the duration of a project, you must first reduce the duration of activities on the critical path.
Network diagrams (network) models are a powerful and flexible organizational management tool. They allow scheduling work, optimizing the use of resources, reducing the duration of work depending on their cost or increasing the duration based on budget constraints, organizing operational management during the implementation of activities. Network diagrams occupy the most important place in modern project management.
network diagram is a directed graph ( geometric figure, consisting of vertices and directed arrows), depicting all the operations necessary to achieve the goal in their technological relationship.
The main concepts of the network model are:
- Job;
- event;
- way.
Work is a labor process that requires time and resources. In the model, work is depicted as a solid arrow (graph arc), above which there is a number indicating its duration. The job is identified by the start and end event numbers. Sometimes in more complex network models, it is allowed to apply (above or below the arrow) and other conditional images, such as the name of the work, its cost, volume, performer, duration, amount of resources. On the other hand, sometimes models are used without any numerical indicators and designations. Such a network is called structural network model, or topology.
Rice. 4.1.
The term "work" includes "waiting process", i.e. a process that does not require labor, but requires time. Usually, the wait is depicted as a dotted arrow, above which the duration of the wait is indicated (Fig. 4.1 a, b).
The concept of work takes into account "addiction" between two or more events, which does not require time or resources, but shows the logical connection of work, for example, that the start of one or more work depends on the results of another work. On the graph, the dependency (or how often it is incorrectly called "dummy work") is shown as a dotted arrow with no indication of time.
Dependence is used in network diagrams not only as a technological or organizational connection, but also as an element necessary to fulfill certain rules for constructing network diagrams.
Event is the result of completing one or more jobs, allowing another job to start. In network models, an event is usually depicted as a circle.
Events are not processes and have no duration, i.e. are done instantly. Therefore, each event included in the schedule must be fully, accurately and comprehensively defined (in terms of the logical connection of work), its formulation must include the result of all the work immediately preceding it.
An event at the beginning of a network diagram that does not include any work is called initiating event. The event at the end of the network diagram, from which no work comes out, is called final event.
Events are divided into simple and complex. simple events are those that include one job. Complex events are those in which two or more works are combined.
Rice. 4.2.
An event can be a particular result of a single activity, or the cumulative result of several activities. An event can take place only when all the work preceding it is completed. By following works can only start after this event occurs. Hence the dual nature of events (except for the initial and final ones): for all activities immediately preceding the event, it is final, and for all immediately following it, it is initial (Fig. 4.2).
Way is a continuous sequence of arrows, starting from the initial event of the network model and ending with the final one. Path length is determined by the duration of the work lying on this path.
When comparing the duration of the paths, the path is revealed, the length of which (the total duration of the work on this path) has the largest value compared to the length of any other path. This path is called the critical path. critical path determines the total duration of the work. An example of identifying the critical path is shown in fig. 4.3. The network diagram shown in the figure has five paths.
Rice. 4.3.
When monitoring the work performed according to the network schedule, the main attention is concentrated on the work of the critical path, since it is on them that the execution of all work on time depends. It is quite natural that in order to reduce the total duration of activities, it is necessary to look for ways to speed up activities that lie on the critical path.
Activities on the critical path are potential bottlenecks. Therefore, the attention of the leader should be focused on these works. And since the critical path has the longest duration compared to other paths, these latter have a margin of time, which makes it possible to quickly maneuver resources or reduce the cost of performing work by increasing their duration.
As practice shows, the more work includes a network diagram, the less specific gravity activities on the critical path. For example, in a model with 100 activities, 10-12% of the total number of activities will be on the critical path; with 1000 works - 7-8%; with 5000 works - 3-4%.
Rules for building network models
There is no single accepted sequence for compiling a network schedule. Therefore, you can build graphs in different ways - from the beginning to the end, and also vice versa - from the end to the beginning. A more logical and correct method should be recognized as the method of plotting graphs from the initial event to the final one, i.e. from left to right, since with such a construction, the technology for performing the simulated work is clearly understood. This method has received the most recognition.
Therefore, as the first job display sequence rules it should be indicated that network graphs should be built from beginning to end, i.e. from left to right.
Arrow rule. Arrows depicting jobs, expectations, or dependencies can have varying slopes and lengths, but should generally run from left to right. Arrows in a network diagram should not deviate to the left of the y-axis. And of course, it should be borne in mind that the arrows are always directed from previous events to subsequent ones, from events with lower numbers to events with higher numbers.
Arrow intersection rule. Arrow intersections are allowed, but the fewer intersections, the more thoughtful and visual the graph is.
These three rules can be regarded as preliminary. Now let's move on to the basic rules for building network graphs.
Job designation rule. In practice, there are often cases when two or more jobs come out of the same event, run in parallel, and end with the same event.
For example, the design of two design options starts at the same time new car. After their development, a comparison is made and the best option is selected.
But the correct representation of these jobs in a network diagram should not be to display two jobs from the same event and end them with the same event. With such an image, both jobs receive the same designation, and this is unacceptable, since when calculating the network it will be impossible to determine the parameters of these jobs, and indeed the entire network diagram (Fig. 4.4 a).
In a network diagram, only one arrow can pass between two adjacent events. Usually, an additional event is introduced to parallelize the work, as shown in Fig. 4.4 b.
Rice. 4.4.
The rule of division and parallelization of works. Many processes allow the next job to begin without waiting for the previous one to finish completely. In this case, the "dismemberment" of the previous work is performed.
Rice. 4.5.
An additional event is introduced on the graph at the place of the previous work, where a new one can begin. An example of this is shown in fig. 4.5. The work ahead assumes the need to correct the working drawings (work "a", duration 30 days) and make a test stand (work "b", duration 25 days). If these works are depicted sequentially, then the total duration will be 55 days, as shown in Fig. 4.5 a, between jobs. After drawing up a network diagram and analyzing the relationship, it is assumed that work "b" can be started after half of the work "a" is completed, i.e. after 15 days. You can finish work "b" only after the complete completion of work "a". Based on this, you can build a new network graph, shown in Fig. 4.5 b. It shows that the total duration of the work is now 42 days, i.e. we received a gain in time for 13 days.
No Closed Loops Rule(cycles or loops). When building a network, it is unacceptable to build closed loops, i.e. ways in which some events connect with themselves. A case cannot be allowed to arise in the network where the same path leads to the same event from which it originally exited. Various occasions closed contours are shown in fig. 4.6 a, b.
Rice. 4.6.
If such a closure has occurred, then this means that there are errors in the technology or in the scheduling.
Deadlock rule. There should be no dead ends in the network graph - events from which no work exits, with the exception of the final event (there are several final events in multi-purpose graphs, but this is a special case).
Rule of prohibition of "tail" events. There should be no tail events in the network diagram, i.e. events that do not include any work, if this event is not the initial one.
The rules for prohibiting "dead ends" and "tail" events are illustrated in fig. 4.7.
Rice. 4.7.
Rules for the representation of differentially dependent works. In the practice of building network diagrams, there are always cases when one group of works depends on another group, and one or more works have additional dependencies or restrictions. Usually, additional events are introduced to solve this problem, as shown in
Lecture 11
MODELS OF NETWORK PLANNING AND MANAGEMENT
Purpose and scope network planning and management
Searches for more effective ways planning complex processes led to the creation of fundamentally new methods of network planning and management (SPM).
The system of methods of SPU is a system of methods for planning and managing the development of large national economic complexes, scientific research, design and technological preparation of production, new types of products, construction and reconstruction, overhaul fixed assets by applying network diagrams.
The first systems using network graphics were applied in the USA in the late 50s and were called CPM(English abbreviation meaning critical path method) And PERT(method of program evaluation and review). System CPM was first used in the management construction work, system PERT - in the development of Polaris systems.
In Russia, network planning work began in the 1960s. Then the SPU methods found application in construction and scientific developments. Subsequently, network methods began to be widely used in other areas. National economy.
SPU is based on process modeling using a network diagram and is a set of calculation methods, organizational and control measures for planning and managing a set of works.
Network planning and management models
The SPU system allows:
Form a calendar plan for the implementation of a certain set of works;
Identify and mobilize time reserves, labor, material and financial resources;
Manage the complex of works according to the principle of "leading link" with forecasting and warning of possible disruptions in the course of work;
To increase the efficiency of management in general with a clear distribution of responsibility between managers different levels and performers.
The range of application of SPM is very wide: from tasks related to the activities of individuals, to projects involving hundreds of organizations and tens of thousands of people (for example, the development and creation of a large territorial-industrial complex).
Under a set of works (a set of operations, or project) we will understand any task for the accomplishment of which it is necessary to carry out a sufficiently large number of various works. This may be the construction of a building, a ship, an aircraft or any other complex object, and the development of a project for this structure, and even the process of drawing up plans for the implementation of the project.
In order to draw up a work plan for the implementation of large and complex projects, consisting of thousands of separate studies and operations, it is necessary to describe it using some mathematical model. Such a means of describing projects (complexes) is network model.
Network model and its main elements
network model represents a plan for the execution of a certain complex of interrelated works (operations) specified in a specific form of a network, graphic image which is called network chart. Distinctive feature network model is a clear definition of all temporal relationships of upcoming work.
The main elements of the network model are developments And work.
Term Job used in SPU in a broad sense. First, this actual work - a time-consuming process that requires resources (for example, assembling a product, testing a device, etc.). Each actual work must be specific, clearly described and have a responsible executor.
Secondly, this expectation - a time-consuming process that does not require labor costs (for example, the process of drying after painting, metal aging, concrete hardening, etc.).
Thirdly, this addiction, or fictitious job a logical connection between two or more works (events) that do not require labor, material resources or time. It indicates that the possibility of one job directly depends on the results of another. Naturally, the duration of the fictitious work is taken zero.
Event - this is the moment of completion of any process, reflecting a separate stage of the project. An event can be a particular result of a single activity or a summary result of several activities. An event can take place only when all the work preceding it is completed. Subsequent work can only begin when the event is complete. From here dual the nature of the event: for all works immediately preceding it, it is final, and for all immediately following it, it is initial. Wherein it is assumed that the event has no duration and is accomplished as if instantly. Therefore, each event included in the network model must be fully, accurately and comprehensively defined, its formulation must include the result of all the work immediately preceding it.
Among the events of the network model, there are initial And final developments. The initiating event has no previous activities and events related to the work package represented in the model. The final event has no follow-up activities and events.
Events on the network diagram (or, as they say, on graph) are depicted by circles (vertices of the graph), and the jobs are represented by arrows (oriented arcs), showing the connection between the jobs. An example of a fragment of a network diagram is shown in Fig.1.
On fig. 2. but a network diagram of the problem of modeling and constructing an optimal plan for some economic object is given. To solve this problem, it is necessary to carry out the following work: L - formulate a research problem; B - build a mathematical model of the object under study; IN - collect information; G - choose a method for solving the problem; D - build and debug a computer program; E - calculate the optimal plan; F - transfer the results of the calculation to the customer. The numbers on the graph indicate the numbers of events that result from the execution of the corresponding work.
From the graph, for example, it follows that the work IN And G you can start executing independently of one another only after the completion of the event 3, those. when the work is done BUT And B; work D - after the event 4, when the work is done A, B And G, but work E can only be executed after the event occurs 5, i.e. when performing all the previous work A B C D E.
In the network model shown in Fig. 2 but no numerical ratings. Such a network is called structural. However, in practice, networks are most often used in which estimates of the duration of work are given (indicated in hours, weeks, decades, months, etc. above the corresponding arrows), as well as estimates of other parameters, such as labor intensity, cost, etc. It is these networks that we will consider in what follows.
Let us first make the following remark. In the considered examples, network schedules consisted of jobs and events. However, there may be another principle of building networks - without events. In such a network, the vertices of the graph (for example, depicted by rectangles) mean certain jobs, and the arrows are the dependencies between these jobs, which determine the order in which they are performed. As an example, the "event - work" network diagram of the problem of modeling and constructing an optimal plan for some economic object, shown in fig. 2 but, is presented in the form of a network "work - communications" in fig. 2 b. And the network schedule "events - work" of the same task, but with an unsuccessfully compiled list of works, is shown in Fig. 2 in.
It should be noted that the "work-connection" network schedule, in contrast to the "event-work" schedule, has certain advantages: it does not contain fictitious jobs, it has a simpler construction and restructuring technique, it includes only the concept of work that is well known to performers without the less familiar concept of an event. At the same time, networks without events turn out to be much more cumbersome, since there are usually much fewer events than jobs. (indicator of network complexity, equal to the ratio of the number of jobs to the number of events, as a rule, significantly more than one). Therefore, these networks are less efficient in terms of complex management. This explains the fact that (in the absence of fundamental differences between the two forms of network representation in general) network schedules "event - work" are currently most widely used.
The procedure and rules for constructing network graphs
Network schedules are drawn up at the initial stage of planning. First, the planned process is divided into separate works, a list of works and events is compiled, their logical connections and sequence of execution are thought out, the works are assigned to the responsible executors. With their help, the duration of each work is estimated. Then compiled (stitched) network chart. After streamlining the network schedule, the parameters of events and work are calculated, time reserves are determined and critical path. Finally, the analysis and optimization of the network schedule is carried out, which, if necessary, is drawn anew with the recalculation of the parameters of events and work.
When constructing a network diagram, a number of rules must be observed.
1. There should be no "dead end" events in the network model, i.e. events from which no work exits, with the exception of the terminating event(Fig. 3a). Either work here (2, 3) not needed and must be canceled, or the need for certain work following the event is not noticed 3 for the completion of some subsequent event. In such cases, it is necessary to carefully study the interrelationships of events and activities in order to correct the misunderstanding that has arisen.
2. There should be no "Tail" events in the network diagram (except for the initial one), which are not preceded by at least one work(event 3 - in fig. 3 b). Here are the works leading up to the event 3, not provided. Therefore the event 3 cannot be done, and consequently, the work following it cannot be done (3, five). Having found such events in the network, it is necessary to determine the performers of the previous works and include these works in the network.
3. The network should not have closed circuits and loops, i.e. paths connecting some events with themselves(Fig. 3 c, d).
Imagine that in the network diagram shown in Fig. 2a, when formulating the initial list of works, we would combine works B and E into one work B 1 . Then we would get a network diagram presented in Fig. 2c. The event means that to work B", which cannot be performed before choosing a calculation method (work G), and the choice of the calculation method cannot be started until the end of the model building (event 3"). In other words, the simplest circuit was formed in the network: 2"->3"->2".
When a loop occurs (and in complex networks, i.e., in networks with a high complexity index, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the original data and, by revising the scope of work, achieve its elimination. So, in our example, we would need a division of work B" on the B And D.
4. Any two events must be directly connected by at most one arrow job.
Violation of this condition occurs when depicting parallel works (Fig. 3 e). If these papers are left as they are, there will be confusion due to the fact that two different papers will have the same designation (7, 2); usually taken under (i, y) understand the work that connects<-е событие с j-th event. However, the content of these works, the composition of the involved performers and the amount of resources spent on the work may differ significantly.
In this case, it is recommended to enter dummy event(event 2" in fig. 3 g) And fictitious job(Job 2", 2), in this case, one of the parallel jobs (7, 2) closes on this fictitious event. Dummy jobs are depicted on the graph by dotted lines.
5. In a network, it is recommended to have one start and one end event. If this is not the case in the composed network (cm rice. 3 g), then you can achieve what you want by introducing fictitious events and activities, as shown in Fig. 3 s.
Fictitious jobs and events must also be introduced in a number of other cases. One of them is a reflection of the dependence of events not related to real work. For example, work BUT And 1 (Fig. 3 And) can be performed independently of each other, but< условиям производства работа B can't start before the job is done BUT. This circumstance requires the introduction of a fictitious work by S.
Another case is the incomplete dependence of jobs. For example, job C requires completion of jobs to start. BUT And B, but work D only related to work B, but from work BUT does not depend. Then it is required to introduce a fictitious work Φ and a fictitious event 3", as shown in fig. 3 to.
In addition, fictitious jobs may be introduced to reflect actual delays and expectations. In contrast to the previous cases, here the fictitious work is characterized by a length in time.
When constructing a network diagram, a number of rules must be observed.
1. There should be no “dead end” events in the network model, that is, events from which no work exits, with the exception of the terminating event. Here, either work is not needed and must be canceled, or the need for a certain work following the event in order to accomplish any subsequent event is not noticed. In such cases, it is necessary to carefully study the interrelationships of events and activities in order to correct the misunderstanding that has arisen. (Fig. 2)
Figure 2 Deadlock exception
2. There should be no “tail” events in the network diagram(other than the original) that are not preceded by at least one work. Having found such events in the network, it is necessary to determine the performers of the previous works and include these works in the network. (Fig. 3).
Figure 3 Tail event inadmissibility
- 3. The network should not have closed circuits and loops, that is, paths connecting some events with themselves. When a loop occurs (and in complex networks, that is, in networks with a high complexity index, this occurs quite often and is detected only with the help of a computer), it is necessary to return to the original data and, by revising the scope of work, achieve its elimination.
- 4. Any two events must be directly connected by at most one arrow job. Violation of this condition occurs when displaying parallel works. If these works are left as they are, there will be confusion due to the fact that two different works will have the same designation. However, the content of these works, the composition of the involved performers and the amount of resources spent on the work may differ significantly.
- 5. In a network, it is recommended to have one start and one end event.
- 6. Closed loops of work are not allowed in the network diagram. The presence of closed contours indicates an error in the construction or in the source data. (Fig. 4).
Figure 4 Inadmissibility of closed loops of work
- 7. The numbering (coding) of events must correspond to the sequence of work in time, that is, the previous events are assigned lower numbers;
- 8. 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;
- 9. 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).
- 10. The length of the arrow does not depend on the time of the work;
- 11. Avoid crossing arrows;
- 12. There should be no arrows pointing from right to left;
- 13. the number of the start event must be less than the number of the end event;
- 14. There should be no cycles (see fig. 5).
A network schedule consists of two elements: activities and events. Works are any processes that lead to the achievement of certain results (events). In addition to real work that requires time, there are so-called fictitious work. This is a connection between two events that does not require time.
Work on the graph is depicted by an arrow, above which the time spent on it is indicated. The length of the arrow and its orientation on the chart do not matter. It is only desirable to maintain the direction of the arrows so that initial the event to work (denoted by i) was located on the left in the network diagram, and final(indicated by j) - on the right. To display fictitious works, dotted arrows are used, over which the time is not indicated or zero is put down.
Thus, an event is the result of the work done, therefore its formulation is always written in a perfect form that does not allow for different interpretations. For example, the wording of the work is "development of specifications for the furnace", the wording of its end event is "the specifications for the furnace are developed." Therefore, the event has no duration in time. It is depicted as a circle or a rectangle, inside which the serial number or code of the event is indicated.
Rules for building a network model
Rule 1. Each operation in the network is represented by one and only one arc (arrow). None of the operations should appear twice in the model. In this case, one should distinguish between the case when any operation is divided into parts; then each part is represented by a separate arc.Rule 2. No pair of operations should be defined by the same start and end events. The possibility of ambiguous definition of operations through events appears when two or more operations can be performed simultaneously.
Rule 3. When including each operation in a network model, the following questions need to be answered to ensure proper ordering:
a) What operations need to be completed immediately before the start of the operation in question?
b) What operations should immediately follow after the completion of this operation?
c) What operations can be performed simultaneously with the one under consideration?
When constructing a network diagram, the following rules should be observed:
- there should be no "dead ends" in the network, i.e., events from which no work starts, except for the final event of the chart;
- there should be no events in the network that do not have a previous event, except for the initial event of the chart;
- the network should not have closed loops (Fig. 1);
- there should not be jobs in the network that have the same start and end events. For two jobs running in parallel, you can introduce an additional event, such as i 3 and a dummy job (Figure 2).
Rules for constructing network graphs
When constructing a network diagram, a number of rules must be observed.- In the network model, there should be no “dead end” events, that is, events from which no work exits, with the exception of the final event.
- There should be no "tail" events in the network diagram, that is, events that are not preceded by at least one work, with the exception of the original one.
- The network should not have closed loops and loops, that is, paths connecting some events with themselves.
- Any two events must be directly related by no more than one work.
- In a network, it is recommended to have one start and one end event.
- The network diagram must be streamlined. That is, events and jobs should be arranged so that for any job, the preceding event is located to the left and has a lower number compared to the event that ends this job.
ends with a circle - an event in which the number of this event is affixed. The numbering of events is arbitrary. At the next stage of construction, we depict works that are preceded by already drawn works (that is, which rely on already built works), etc. At the next stage, we reflect the logical relationships between works and determine the end event of the network diagram, on which no works rely. The construction is completed, then it is necessary to streamline the network diagram.
A simple network ordering method is based on the concept of event rank:
- all network diagram events are divided into ranks,
- Several events can belong to the same rank,
- events are numbered in accordance with belonging to a particular rank,
- the higher the rank, the higher the number of the event,
- within one rank, the numbering of events is arbitrary.
