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Build a network diagram example. network model

Service assignment. The online calculator is designed to find network model parameters:

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

and also allows you to estimate the probability of completing the entire complex of works in d days.
Instruction. Solution in online mode carried out analytically and graphically. It is issued in Word format (see example). Below is a video instruction.

Example. Description of the project in the form of a list of operations performed with an indication of 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 tij	Early dates: beginning t ij R.N.	Early terms: end t ij P.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.	Reserves of time: 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 running time reserve R ij H - part of the total reserve of time, if all previous work ends late, and all subsequent work begins early.
The use of independent slack does not affect the amount of slack for other activities. Independent reserves tend to be used 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 H ≥0, then there is such a possibility. If R ij H<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.

Optimization of the work of the company, especially the manufacturing enterprise, is one of the most important conditions for the existence of the company. Not only competition requires the uninterrupted flow of the production process. Current 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 technique for optimizing activities and calculating the timing of work is used. 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 effective planning of 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 the arrival of teams of workers of different specialties on the construction site. It's called the "work schedule".

In modern conditions, when large enterprises mass-produce products, the whole process is broken down into simple operations to facilitate and increase productivity. Therefore, the network schedule "migrated" from construction to almost all industries.

So what is displayed in this document? First, all the operations necessary for the release of goods (production of services) are listed in detail. Secondly, the logical interdependence between them is determined. And, finally, thirdly, not only the timing of each specific work is calculated, but also the time required to complete the production process.

By exposing the internal dependencies of project activities, the network schedule becomes the basis for scheduling equipment and workforce utilization.

The concept of "operation" in network planning

In the network schedule, you can evaluate the periods of start (end) of work, forced downtime and, accordingly, the maximum delay in the production of certain operations. In addition, critical operations are identified - those that cannot be performed with a deviation from the schedule.

Understanding the terminology of planning, it is necessary 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 the operation is associated with costs: time and resources (both labor and material).

In some cases, no resources are needed to perform some actions, only time is required, which takes into account the network schedule. An example of this is the expectation of concrete hardening (in construction), the cooling time of rolled parts (metallurgy), or simply the approval (signing) of a contract or permits.

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

Operation types

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

merge - this operation is immediately preceded by more than one work;
parallel operations are performed independently of each other and, at the request of the design engineer, can be performed simultaneously;
a crushing operation implies that after its execution, several unrelated jobs can be performed at once.

In addition, there are a few more concepts necessary for planning. The path is the time to complete and the sequence of interdependent operations. A critical path is the longest path of the entire system of work. In the event that some operation on this path is not performed on time, the deadlines for the implementation of the entire project are disrupted.

And the last: event. This term usually refers to the beginning or end of some operation. The event does not require resources.

What does the chart 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 the project may look two ways: one technique involves the designation of operations in the nodes of the block diagram (OS), 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 define the relationships between the actions. Since the titles of works can be quite long and voluminous, the numbers of operations are put down in the blocks, and a specification is drawn up for the schedule.

Schedule Design Rules

For proper planning, you need to remember a few rules:

The graph unfolds from left to right.
Arrows indicate links between operations; they may intersect.
Each simple work must have its own serial number; any subsequent operation cannot have a number less than that of the previous one.
The graph cannot have loops. That is, any looping of the production process is unacceptable and indicates an error.
You cannot use conditions when a network graph is built (an example of a conditional order: “if an operation is performed .., perform 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.

Construction and analysis of the graph

For each job, three things need to be clarified:

A list of operations that must be completed prior to this job. 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.
The list of tasks that can be carried out simultaneously with the given one. These are parallel operations.

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

The real schedule requires a serious and objective assessment of the production time. 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

Estimation of time costs for the performance of one operation is made on the basis of standard labor costs. Thanks to the direct or inverse calculation method, you can quickly navigate the order of work and identify critical steps.

Direct analysis allows you to determine the early start dates for all operations. Reverse - gives an idea of late dates. In addition, using both analysis methods, you can not only establish the critical path, but also identify the time intervals for which you can delay the execution of individual works without disrupting the overall timing of the project.

Direct analysis looks at the project from start to finish (if we talk about the drawn up schedule, then the movement along it occurs from left to right). During the movement along all chains of operations, the time for completing the entire complex of works increases. Direct calculation of the network diagram assumes that each subsequent operation begins at the moment when all previous ones end. At the same time, it must be remembered 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 settlement operation is added. This gives us the values of early start (ES) and early finish (EF).

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

reverse analysis

The reverse analysis takes into account such parameters of the network schedule: 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 activity. Thus, the latest start (LS) and end (LF) dates for the production of work are determined. If the time frame of the project is not initially set, then the calculation starts from the late end of the last operation.

Calculation of temporary reserves

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 possible delay time for 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 derail the overall time frame for the project.

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

Of course, in theory, everything looks simple and uncomplicated. The developed network schedule (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 the risks of a project, it is necessary 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 from the operations of the critical path. It is about talking directly with the performers of such works.

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 schedule for the production of work. It shows all the downtime and employment of each individual employee (team). The use of an unemployed worker at one facility to implement another allows you to optimize the company's activities as a whole.

Do not neglect another practical advice. In reality, project managers are faced with the "desires of senior management" to see the work done "yesterday". In order to avoid panic and the release of marriage, it is necessary to strengthen resources not so much on the operations of the critical path, but on those that directly affect it. Why? Yes, because there is no downtime on the critical path, and it is often impossible to reduce the time of work.

Work planning always begins with determining the number of tasks, the persons responsible for their execution and the time required for complete completion. With such schemes are simply necessary. Firstly, in order to understand how much total time will be spent, and secondly, to know how to plan resources. This is what project managers do, they primarily carry out the construction of a network diagram. An example of a possible situation will be considered below.

Initial data

The management of the advertising agency decided to launch a new advertising product for its clients. The following tasks were set for the employees of the company: to consider the ideas of advertising brochures, to give arguments in favor of one or another option, to create a layout, to prepare a draft contract for clients and send all the information to the management for consideration. To inform clients, it is necessary to carry out a mailing list, put up posters and call all the companies in the database.

In addition, the chief manager made a detailed plan of all necessary actions, appointed responsible employees and set the time.

Let's start building a network graph. The example has the data shown in the following figure:

Matrix construction

Before forming it is necessary to create a matrix. Graphing starts from this stage. Imagine a coordinate system where the vertical values correspond to i (the start event) and the horizontal rows to j (the end event).

We begin to fill in the matrix, focusing on the data in Figure 1. The first work has no time, so it can be neglected. Let's consider the second one in more detail.

The initial event starts from the number 1 and ends at the second event. The duration of action is 30 days. This number is entered in a cell at the intersection of 1 row and 2 columns. In a similar way, we display all the data, which is shown in the figure below.

Basic elements used for a network diagram

The construction of graphs begins with the designation of theoretical foundations. Consider the main elements required to compile the model:

Any event is indicated by a circle, in the middle of which there is a number corresponding to the order of actions.
The work itself is an arrow leading from one event to another. Above the arrow write the time required to complete it, and under the arrow indicate the responsible person.

A job can run in three states:

- Current is an ordinary action that requires time and resources to complete.

- Expectation- a process during which nothing happens, but it takes time to move from one event to another.

- Dummy job is a logical connection between events. It does not require any time or resources, but in order not to interrupt the network schedule, it is designated. For example, preparing grain and preparing bags for it are two separate processes, they are not connected in series, but their connection is needed for the next event - packaging. Therefore, another circle is selected, which is connected by a dotted line.

Basic principles of construction

The rules for constructing network graphs are as follows:

Building a network graph. Example

Let's return to the original example and try to draw a network graph using all the data indicated earlier.

Let's start with the first event. Two come out of it - the second and the third, which unite in the fourth. Then everything goes sequentially until the seventh event. Three works come out of it: the eighth, ninth and tenth. Let's try to display everything:

Critical values

It's not all about building a network diagram. The example continues. Next, you need to calculate the critical moments.

The critical path is the longest time taken to complete a task. In order to calculate it, you need to add up all the largest values of successive actions. In our case, these are works 1-2, 2-4, 4-5, 5-6, 6-7, 7-8, 8-11. We summarize:

30+2+2+5+7+20+1 = 67 days

So the critical path is 67 days.

If such time for the project does not suit the management, it must be optimized according to the requirements.

Process Automation

Today, few project managers manually build network diagrams - this is an easy and convenient way to quickly calculate the cost of time, determine the order of work and assign performers.

Let's take a quick look at the most common programs:

Microsoft Project 2002- an office product in which it is very convenient to draw diagrams. But doing the calculations is a little inconvenient. In order to perform even the simplest action, you need a considerable amount of knowledge. When downloading the program, take care of purchasing the user manual for it.
SPU v2.2. Very common free software. Or rather, not even a program, but a file in an archive that does not require installation to use. It was originally designed for a student's graduation work, but it turned out to be so useful that the author posted it online.
netgraf- another development of a domestic specialist from Krasnodar. It is very easy, easy to use, does not require installation and a huge amount of knowledge on how to manage it. The advantage is that it supports importing information from other text editors.
Often you can find such an example - Borghiz. Little is known about the developer, how and how to use the program. But by the primitive method of "poke" it can be mastered. The main thing is that it works.

With the help of this program you can determine the parameters of the network graph online(calculate the timing of events, time reserves and the critical path), find the tension coefficients. Optimization of the network schedule is carried out according to the following criteria: the number of performers, reserves-costs, reduction of terms.
A network graph can be drawn, as well as set in the form of a matrix or table (Operations menu).

Select the desired vertex type and left-click on the graphics canvas

Graphics canvas dimensions

Width Height

● ■ ▲ ⊗ ↔ ✍ ⊗

network model parameters (critical path, time reserves, build a Gantt chart and much more).

For the generated graph, you can perform the following actions:

Service manual

To add a vertex to the graphics canvas, use the Add button corresponding to the shape. A new object can also be inserted by first selecting it with the left mouse button and then clicking on the workspace. Numbering of vertices can start from 0 , for this you need to uncheck the item Numbering of vertices from No. 1.

1 2 3 4 1 10 30 15

Vertex numbering starting from 0

0 1 2 3 1 10 30 15

To connect the vertices, you must first select them (one click on the object), and then click the Connect button.
The network model can be presented in tabular form and as a weight matrix (distance matrix). To use view data, select the Operations menu.

The constructed graph can be saved in docx or png format.
If a rectangle is used as the vertex shape, then when constructing a pie chart, the Microsoft Visio methodology is used with the display of parameters duration, ES, EF, LS, LF, and slack.

Basic definitions

Directed graph, in which there is only one vertex that has no incoming arcs, and only one vertex that has no outgoing arcs, called a network. The network that models the complex of works is called its network model or network diagram. The arcs connecting the vertices of the graph are oriented in the direction of achieving the result in the implementation of a set of works.
The most common way to represent the simulated complex of works in terms of works and events.
The concept of "work" has the following meanings:

"actual work" - a process that requires time and resources;
“dummy job” is a logical relationship between two or more jobs, indicating that the start of one job depends on the results of another. Dummy work does not require time and resources, its duration is zero.

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.

On the network model, events correspond to graph vertices.

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 "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 (Fig. 1);
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.

The construction of the network graph begins with the image of the initial event, which is indicated by the number 1 and circled. Arrows are fired from the start event corresponding to activities that are not preceded by any other activities. By definition, the moment of completion of work is an event. Therefore, each arrow
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.

Network Graph Optimization Methods

The logical-mathematical description, the formation of plans and control actions is carried out on the basis of the use of a special class of models called network models.
After constructing and calculating the network schedule (determining its parameters), performing an analysis of the schedule, which consists in assessing its feasibility and structure, assessing the workload of performers, assessing the probability of the final event occurring within a given period, you should start optimizing the network schedule. The optimization procedure consists in bringing the schedule in line with the given deadlines for the completion of work, the capabilities of contractors, etc. In general, optimization should be understood as the process of improving the organization of work.

To be able to optimize the network model, all initial data are entered in the form of a table (Operations / Add in the form of a table).

Optimization of the network model according to the "number of performers" criterion. The column Number of performers is being filled H
Optimization of the network model according to the criterion "time - cost" (time - costs). In the case of known cost factors for work acceleration, only this column h(i,j) is filled. Otherwise, the columns t opt (Normal mode), Minimum work time, t min (Fast mode), Normal cost, Cn and Urgent cost, Cc are filled.

Binding (a) and loading (b) plots before optimization

1,2 6 1,3 1 1,4 5 2,5 3 2,6 1 3,6 8 4,6 4 4,7 2 5,8 6 6,8 1 7,8 3 1 12 2 3 19 4 17 5 6 7 8 18 9 10 11 12 13 14 13 15 16 17 18 10 19 20 21 22 4 23 24 25 26 1 27

Binding (a) and loading (b) plots after optimization

1,2 6 1,3 1 1,4 5 2,5 3 2,6 1 3,6 8 4,6 4 4,7 2 5,8 6 6,8 1 7,8 3 1 12 2 3 11 4 14 5 6 7 15 8 9 10 11 18 12 13 14 15 10 16 17 18 4 19 20 21 22 10 23 24 25 26 7 27

Gantt Chart

1,2 4 1,3 3 1,4 5 2,5 11 2,6 14 3,6 4,6 17 4,7 5,8 19 6,8 27 7,8 25

Examples of network models

Consider options for network graphs from the culinary field using the example of cooking chicken borscht.
a) Cooking in a regular pot

1 2 3 4 5 1 10 30 15 7

Works:

1.3: boil chicken, 30 min.
2.3: put the cabbage and cook for 10 minutes.
3.4: put 1/2 beets, carrots and potatoes. Boil 15 min.
4.5: add the rest of the beets, onions, greens. Boil 7 min.
b) Cooking in a dish with the effect of a Russian stove (three-layer bottom, lid without holes)

1 2 3 4 5 10 10 20 30 60

Works:
1.2: cleaning vegetables (cabbage, carrots, potatoes, beets, onions), 10 min.
1.4: Boil the chicken in a normal pot, 30 minutes.
2.3: put vegetables in a special dish, add 3 tablespoons of water, heat to T=70 C and turn off, 10 min.
3.4: cooking vegetables in their own juice, 20 min.
4.5: Add the cooked vegetables to the chicken. Infused 60 min.

Bibliography

Mushik E., Muller P. Methods for making technical decisions. Per. with him. –M.: Mir, 1990.
Taha H. Introduction to Operations Research. In 2 books. Book. 2. Per. from English. –M.: Mir, 1985.
Management in RAV systems: Textbook. -L .: Military Publishing, 1980.

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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.