In we looked at how important a project management information system (PMIS) is for planning, accounting and analysis of project implementation, discussed the problems of operational updating of calendar and network schedules and the main advantages of MS Project and in communication scenarios between project participants. Now I propose to consider possible scenarios for using MS Project and PlanBridge in the management of investment and construction projects with the participation of managers of the Customer and the General Contractor.
Probably, any construction project manager, both on the part of the Client-investor and the General Contractor, who manage a variety of works and professional specialists, needs to know the answers to the following questions in order to make operational decisions:
- Are materials and equipment delivered on time?
- At what pace are construction, installation and commissioning works being carried out?
- How much work should be completed according to plan, and how much has been completed in fact?
- Which jobs are being completed behind schedule and which are on schedule?
- How do current delays and changes in work technology affect the timing and budget of the entire construction?
- How do the actual schedules of financing and disbursement of funds for the volume of work performed compare?
- Are work areas transferred between adjacent contractors in a timely manner?
To control the construction of the facility and obtain answers to the above questions, the General Contractor must conscientiously perform the following functions:
- Development and control of implementation of the construction calendar and network schedule;
- Development of an optimal plan for financing the construction of the facility;
- Coordination of work performed by subcontractors and transfer of work fronts;
- Monitoring compliance with the technological sequence of work at the facility;
- Organization of timely supply of construction sites with necessary materials, machinery and equipment.
It would be useful to find out who and how the General Contractor and the Customer perform the above functions. This can be quite a challenge if the General Contractor does not have a proper communication system between the planner and all those responsible for the work.
Planning
At the planning stage, the project manager needs to draw up a detailed schedule for construction work, taking into account the specifics of the detailed design, technology, number of labor and equipment at the site. But there is hardly a planner who knows the technology and the pace of execution better than the work producers themselves. Each contractor is professionally versed in the specifics of his work, the sequence and timing of completion, taking into account the productivity of available work crews and equipment.
In order to draw up a real construction plan based on the knowledge of all specialists performing the work, the planner needs to somehow magically collect information from all those responsible into a single model.
Accounting for completion
Further, the construction process must be accompanied by operational accounting of the actual completion of work. Current performance data is usually recorded by foremen and technical supervision in work production logs, defect reports, estimate forms, as-built diagrams, etc. On operational issues of construction, operational meetings are held, minutes are kept, and reports are prepared. But, unfortunately, it is almost impossible to collect all this information into a general operational plan. To obtain and systematize it, the project analyst or RP must call or gather all those responsible, write out a huge amount of data from logs and acts about the volumes completed, changes, delays. Then this data still needs to be manually entered into the MS Project operational plan to update and analyze the implementation of the project as a whole.
Obtaining operational information and manually making changes to the current MS Project plan usually requires a huge amount of time and labor.
Working scenarios for information exchange in the management of investment and construction projects
I propose to consider several simple working scenarios for exchanging operational data on projects using MS Project and PlanBridge, which can reduce the labor costs of a project manager or planner-analyst several times.
2. Detailing the enlarged tasks of the MS Project construction calendar and network schedule and filling it with data on the technological sequence, timing, physical volumes, material consumption, cost of work by loading data from exchange documents.
- As a result of the appropriate settings and launch of this function, special Excel tables are created and sent to responsible or assigned executors at the specified email addresses. Each document contains a specified selection of general work, which is supervised by a specific person in charge or executor.
- Those in charge fill out in Excel exchange documents a list of detailed work by groups, tasks, marks, determine deadlines for completion, assign physical volumes, materials, labor resources and mechanisms, and costs to these works. All data received using PlanBridge is correctly imported into the general MS Project plan, forming a holistic model of project implementation.
3. Accounting for the weekly (daily) fact about the volume of work completed (or % of completion), the actual start and completion of work, by group mailing, separately filling in by those responsible and loading data into the general operational plan for the construction of the facility.
To do this, it is necessary for those responsible to regularly fill out ODs about the physical volumes of work performed or % of completion, actual start and end dates. You can keep daily records of concreting structures, bricklaying walls, installing floor screeds, insulating and finishing facades, installing stained glass systems and windows, and other construction work. Having received OD by email or through common free document storage (OneDrive, Google Drive), the planner or RP uploads them to the MS Project plan. As a result, all relevant tasks and interactive reports in the plan are updated with real-time actual data.
After entering the accounting actual data and updating the operational plan, MS Project performs many calculations about deviations in progress rates, actual delays in work deadlines and predicted schedule changes. The manager uses the results of these calculations to make management decisions, which he can write directly in the Gantt chart table. As a result of creating and distributing exchange documents to those in charge, they receive all the estimated data on work delays, questions and instructions from management on certain work schedules and can quickly take appropriate measures to eliminate problems, make comments in exchange documents about the reasons for schedule deviations.
New PlanBridge functions for planning and updating construction projects
The latest version of PlanBridge has new tools that make the following functions possible in MS Project.
Importing estimate data into MS Project allows you to create a pool of resources and materials, form an appropriate structure of work, set connections in accordance with the execution technology, and calculate deadlines based on standard labor costs and the number of available resources.
Creation and configuration of special resource columns for recording and displaying planned and actual assignment data (planned and actual volumes, labor costs, costs) directly in the work table of the Gantt Chart view.
PlanBridge resource columns significantly complement the functions of MS Project and provide the following capabilities:
- When used in the Resource Sheet, Resource Usage, or Task Usage views, the created resource column is immediately associated with the allocated resource or assignment;
- the created columns allow recording and displaying the planned and actual quantities of physical volumes, materials, labor costs of workers and mechanisms assigned to work (separately and in groups) in the lines of the corresponding work;
- automatic calculation of subtotals of assigned volumes of work and materials in connection with the main structure of work and user groupings;
- use of standard coefficients for automatic calculation of assigned materials, labor costs of workers and mechanisms in relation to the value of physical volume;
- using formulas and indicators in task fields to monitor actual completion, planned balances and variances in work volumes, assigned materials and resource labor costs.
Using resource columns, the planner can enter both planned and actual data on volumes and materials assigned to work directly in the Gantt chart view and automate the calculation and display of subtotals of assignments.
For example: the amount of planned and actual concrete, reinforcement, brick, mortar by occupations, marks, teams (i.e. in relation to the selected work structure).
Updating the usual and physical % of completion of work, actual labor costs, % of completion by labor costs of all assignments in accordance with the actual labor costs of the main purpose - the scope of work.
The basic functions of MS Project do not allow you to automatically link the actual labor costs of one resource assigned to a task with other assignments of the same task. Synchronization of actual labor costs of all assignments is performed only through % completion of the task. Therefore, to update the actual completion of a certain physical volume of work (volume of concrete structures, brickwork, screed area, etc.), it is necessary to manually calculate and enter data into the “Actual labor costs” field for each associated material and labor resource.
- PlanBridge allows you to specify a group of main resources (Volumes) for which the update of the actual labor costs of all other assignments is linked.
- After you enter the actual amount of work completed, Update % Complete updates the % Complete and Actual Work of all other resources assigned to the task to match the % Complete work of the primary assigned resource (Volume).
- As a bonus, the physical % of task completion is additionally updated, which allows for a correct cost analysis of the mastered volumes for the project.
To summarize, we list the main processes for planning, accounting and analysis of the implementation of a construction project, which can be automated using MS Project and PlanBridge:
In subsequent training articles and video tutorials, I will try to describe in more detail the settings of MS Project and PlanBridge and working scenarios for planning, accounting and updating the work plan.
If you are interested in certain PlanBridge features, you can always ask questions to the developers on the page at
Network process planning is a general tool for project management. It helps to maximize the potential of company employees, carry out innovative developments and introduce new brands to the consumer market.
Peculiarities
Network planning and management allows you to determine the approximate completion date of a project by analyzing the deadlines for its implemented and unrealized parts. It is based on simple mathematical modeling of complex measures and targeted actions to solve one specific problem. In fact, planning is a set of calculation, organizational and graphical methods that allow not only high-quality development of a project, but also help to rebuild it in real time depending on changing external conditions.
It allows you to evenly distribute tasks taking into account:
- limited resources (material and intangible);
- regularly updated information;
- tracking deadlines.
This method minimizes risks and eliminates the possibility of a deadline. A systems approach is widely developed in network planning. Often, launching a project requires the work of employees from different departments of the enterprise (sometimes they even outsource specialists), so only their coordinated actions in a single organizational system will allow the work to be completed on time.
The key goal of network planning in management is to reduce the duration of the project, provided that the parameters of quality and volume of production are maintained.
Areas of application
Network methods for planning business processes and enterprise management are popular in various fields of activity. They have found the greatest application in those projects in which it is necessary to first invent and create a new product, and only then offer it to the consumer. These business areas include:
- R&D;
- innovation activity;
- technological design;
- pilot production;
- automation of business processes;
- testing of serial samples;
- equipment modernization;
- market research;
- personnel management and recruiting.
Problems to be solved
The introduction of network planning and management models at an enterprise allows you to solve a whole range of problems:
- project time analysis:
- calculation of work deadlines;
- determination of temporary reserves;
- finding problematic project areas;
- finding critical ways to solve problems;
- resource analysis, which allows you to draw up a calendar plan for spending available resources;
- project modeling:
- determination of the scope of required work;
- establishing a relationship between them;
- building a hierarchical business model of processes;
- determining the interests of all project participants;
- distribution of available resources:
- increasing revenues depending on existing needs;
- minimizing the timing and volume of supplied resources in one part of the project and increasing them in another.
But the exact formulation of planning and rational management tasks depends on the industry for which the business project is being developed. In some industries, human (intangible) resources are considered the main resource, and its expenditure depends not only on the funds invested by the enterprise in training and licensing, but also on the personal potential of employees, which is extremely difficult to measure.
Tools
The main tools for time and resource planning are graphs or diagrams. They allow you to visually determine the state of the work being performed and the relationship between them. The network schedule for planning and effective management shows the timing of operations, the required resources and monetary costs. There are two types of diagrams:
- modeling the project in the form of a set of vertices connected by lines that show the relationships between the works;
- displaying work as a line between events (“vertex-event”).
The first method is used more often, since when network planning it is more productive to start directly from the work being performed and the required resources, and not from the exact start and end dates of the project.
Step-by-step construction of a network diagram
Within the framework of the activities of any company, it is best to build a schedule using the critical path method. This construction method has several key points:
- formulation of the planning goal;
- establishing possible limitations (resources, finances);
- determining the set of actions that are needed to achieve the goal (all actions are formatted in separate files, loaded into a program like MS Visio or written on regular cards);
- for each action, the duration of execution, resources, tools and responsible persons are noted;
- drawing up a hierarchy of actions;
- displaying the relationship between operations (including the earliest and latest dates for the start and end of the process);
- calculating the slack time for each activity (the difference between the early and late start or finish of the project);
- defining a critical path in which there is no slack for each activity, i.e. all of them are carried out smoothly, quickly and without interruptions.
Benefits of use
The first network diagram was used in the 50s of the last century, but it still does not lose its relevance. This is due to its undoubted advantages. After all, with the help of diagrams you can:
- carry out coherent, reasonable and operational planning of critical business processes;
- choose the optimal duration of the process;
- identify and use available reserves;
- promptly adjust the work plan depending on changes in external factors;
- fully implement a systematic approach to production;
- apply computer technologies that increase the speed and quality of building network models.
Planning methods
Various network planning methods are used within project management. The use of certain technologies is associated with changeable or unchangeable parameters of the work performed.
Deterministic network models
Deterministic models are those projects in which the sequence and duration of work is recognized as unambiguous, regardless of environmental factors. They allow you to recreate the ideal process that you should strive for in real project activities. There are several methods for constructing deterministic models:
- a two-dimensional cyclogram, where one axis is responsible for time, and the second for the amount of work;
- Gantt chart, in which the project is presented in graphical and tabular form;
- a network diagram method that allows you to solve production problems through the rational use of resources or reducing design time.
Probabilistic models
These methods are used in cases where the exact duration and sequence of work performed is unknown. Most often this is due to a strong dependence on environmental factors:
- weather conditions;
- reliability of suppliers;
- public policy;
- results of experiments and experiments.
There are alternative and non-alternative probabilistic models. The following methods are used to construct them:
- PERT (for program evaluation and review);
- Monte Carlo (simulation modeling of project stages);
- GERT (Graphics Based Analysis and Evaluation).
Additional Methods
There are also additional graphic construction models:
- matrix method of diagonal table (with a focus on certain events);
- sector method, where the circle denoted by the action being performed is divided into several sectors that show the earliest and latest dates for the start and end of work;
- four-sector method.
The use of certain construction methods is associated with planning goals and objectives. Also, each company can develop its own network model and integrate it into the project.
Conclusion
The main task of network planning and management in an enterprise is to reduce the duration of the project, and not to increase it. Therefore, for effective work, you should use only those techniques and technologies that will be understandable to employees.
Network graphsA project manager at the planning stage is often faced with a situation where a structure, a milestone plan, and a responsibility matrix alone are not enough to develop a project schedule. This arises for very large project tasks, where the substantive part of the planned work needs to be carried out in the most efficient way, while reducing the consumption of time resources. Network planning can come to the aid of a project manager as an instrumental solution implemented using a standard optimization algorithm.
Network modeling method
Network planning and management have been actively developed since the 50s of the last century, first in the USA, then in other developed countries and in the USSR. Network planning methods such as CPM and PERT have made it possible to significantly raise the “bar” of project management in the direction of optimizing the time and content parameters of work schedules. This made it possible to develop schedules of project tasks based on a more effective network modeling methodology that incorporated all the best practices (a diagram of scheduling methods is given below). Network diagram has different names, among them:
- network diagram;
- network model;
- net;
- network graph;
- arrow diagram;
- PERT chart, etc.
Visually, the project network model is a graphical diagram of a sequential set of works and the connections between them. It is worth noting that the project planning and management system is holistically displayed in graphical form of the composition of operations, their time durations and interrelated events. The basis of the model construction method is a branch of mathematics called graph theory, which was formed in the early 50s - late 60s.
Scheduling and project management methods
In the network planning and management model, a graph is understood as a geometric figure that includes an infinite or finite set of points and lines connecting these lines. The boundary points of a graph are called its vertices, and the points connecting them oriented in directions are called edges or arcs. The network model includes directed graphs.
Type of directed graph
Let's look at other basic concepts of the project network model.
- Work is a part of a production or design process that has a beginning and an end in the form of a quantitatively described result, requiring time and other resources. The work is reflected on the diagram in the form of a unidirectional arrow line. We can consider operations, events and actions to be the form of work.
- An event is the fact of completion of work, the result of which is necessary and sufficient to begin the implementation of the following operations. The type of event on the model is reflected in the form of circles, diamonds (milestones) or other shapes, inside of which the identification number of the event is placed.
- A milestone represents work with zero duration and denotes an important, significant event in the project (for example, approval or signing of a document, the act of ending or beginning a project stage, etc.).
- Waiting is a procedure that does not consume any resources other than time. Appears as a line with an arrow at the end with a duration mark and the name of the wait.
- Fictitious work or dependence - a type of technological and organizational connection of work that does not require any effort or resources, including time. Shown as a dotted arrow on a network diagram.
Connection options and precedence relations
Network planning methods are based on models in which the project is presented as an integral set of interrelated works. These models are largely formed by the type and type of connections between project implementation operations. From the point of view of type, hard, soft and resource connections are distinguished. The specific difference in the interconnectedness of operations is based on the precedence relationship. Let's consider the main types of communication.
- Soft connections. They correspond to a special, “discretionary” logic, which provides a “soft” basis for the selection of operations to be placed on the diagram, dictated by technology. While technology has been developing over a long period of time over many cycles, business rules are being developed that do not require additional fixation and planning. This saves time, model space, cost and does not require additional monitoring by the PM. Therefore, the project manager himself decides whether he needs such a dedicated operation or not.
- Hard connections. This type of connection is based on technological logic. They prescribe the execution of specific actions strictly after others, which is in accordance with procedural logic. For example, equipment adjustment can be carried out only after its installation. It is permissible to test technology shortcomings if it has been put into trial operation, etc. In other words, the adopted technology (no matter in what area it is implemented) rigidly imposes the sequence of activities and events of the project, which determines the corresponding type of communication.
- Resource connections. When several tasks are assigned to one responsible resource, it becomes overloaded, which can lead to an increase in the cost of the project. By assigning an additional resource to a less critical task, this can be avoided, and such connections are called resource connections.
When creating a project schedule, hard connections are applied first, and then soft connections are applied. Further, if necessary, some soft connections are subject to reduction. Thanks to this, some reduction in the overall duration of the project can be achieved. In conditions of overload of some critical resources due to parallel work, it is permissible to resolve conflicts by introducing resource connections. However, care should be taken to ensure that new connections do not lead to significant changes in the overall plan.
Related work, as a certain sequence of a design task, is connected to each other. Let's call them operations A and B. Let's introduce the concept of a precedence relationship, which is considered as a certain limitation on timing and total duration, since operation B cannot begin until the end of operation A. This means that B and A are related by a simple precedence relationship, while It is not at all necessary that B begins at the same time as the end of A. For example, finishing work begins after the roof of the house is erected, but this does not mean that they should be carried out at the same moment when the specified event occurs.
Network model method number one
Network planning and management (NPC) involves two options for constructing a project network diagram: “edge - work” and “vertex - work”. In the first diagram display option, the critical path method and the PERT method are implemented. The method also has another name - “peak - event”, which essentially reflects the other side of the single content. In the English interpretation, this option for constructing a network model is abbreviated as AoA (Activity on Arrow Diagramming). The dominant place in the method is occupied by project events. There are three types of events:
- start event;
- intermediate event;
- final event.
The structure of the design task is such that in the process of its implementation there is only room for one initial and one final event. No work is performed before the start event and after the end event. At the end event, the project is considered complete. Before the intermediate event occurs, all incoming operations must be completed. It gives start to all operations emanating from it. Dummy jobs are used after jobs if it is not known which of them will be the last.
An example of a network diagram for the edge-to-work method
Network planning when constructing an AoA network diagram is guided by the following set of basic rules.
- Project events are subject to sequential numbering. Numbers are assigned to events without gaps.
- There should be only one start and end event each.
- Work cannot be planned and allocated towards a project event that has a lower number than the original event.
- A closed sequence of operations is unacceptable, and arrow lines are placed in the left-to-right direction.
- Double connections between events are not allowed.
The diagram formation algorithm is as follows.
- Place the initial event on the left side of the field.
- Find works in the list that do not have predecessors, and place their resulting events on the diagram to the right of the initial event without indicating numbers.
- Connect the initial and newly placed events with arrow lines of work.
- From the list of jobs that are not yet on the diagram, select a job for which a predecessor has already been posted.
- To the right of the previous event, insert a new event without a number and link them with the selected work.
- Taking into account the precedence relationship, connect with a fictitious work the initial event of the placed work and the event placed on the network diagram.
- Planning and control as one of the functions of project management.
- Basic methods of calendar and network planning in construction.
- The main processes of the "Planning" and "Control" groups.
- The main causes of errors in project planning and control.
- Construction project scope management.
- Gathering requirements, assumptions and limitations of the project.
- Decomposition. Development of ISR.
- Construction project time management. Development of a project schedule.
- Schedule and network schedule of the project and the purpose of its development.
- Logic of chart formation.
- Initial data for generating a graph. Definition of operations. Decomposition. Planning by the rolling wave method.
- Sequence of development of the project network schedule.
- Definition of dependencies, advances and delays.
- Estimating the duration of operations: tools and methods.
- The concept of resources, types of resources, main stages of resource planning, methods for eliminating resource conflicts.
- Critical path, critical chain.
- Characteristics of the critical path method (CPM).
- Project time reserve, buffer reserve.
- Monitoring the project schedule.
- The main types of reports on the progress of the project, forms for presenting data in reports, forms for presenting a network diagram.
Scheduling software
- Application tools MS Project 2013. Practical work.
Introduction to MS Project 2013.- Corporate project management system Microsoft Enterprise Project Managemant. Features of MS Project 2013 Professional. Interface. Initial parameters.
- Task scheduling modes.
- Entering project stages.
- Determination of target dates for project stages. Formation of an enlarged project budget. Maintain the project baseline.
- WBS Work Breakdown Structure. Detailing of project stages. Tasks. Changing the task hierarchy level. Summary and detailed tasks. Setting up WBS codes. Adding and removing fields in a spreadsheet.
- Dependencies between tasks. Estimating the duration of project tasks.
- How to create a project schedule in MS Project. Critical tasks, critical path.
- Resource assignment, resource calendars, resource sheet, resource leveling.
- Basic plan. Set up a workspace for tracking and control. Conclusion of the planned percentage of work completion. Select the status report date. Entering actual data on the progress of the project. Forecast of expected project completion dates.
- Reporting, baseline plan, task control. Generating a cash flow report.
- Interrupted and repetitive work. Insert hyperlinks, pictures, and text fields. Moving a project. Accounts. Global template and organizer. View project statistics. Program help system.
Having studied the material in the chapter, the student must:
know
- what role does network and scheduling play in project management;
- basic principles of network planning;
- basic network and scheduling tools;
be able to
- build project network graphs;
- determine the duration of the project and its critical operations based on network graphs;
- determine time reserves for each operation;
- determine the duration of operations based on the PERT method;
- distribute project resources taking into account their scarcity;
own
- generally accepted methods of network analysis;
- skills in drawing up network graphs and Gantt charts;
- skills in determining project duration;
- skills in creating a project schedule.
Key terms: network analysis, scheduling,
network graph, critical path, slack, Gantt chart.
Functions of network analysis in project planning
To successfully implement a project, it is necessary to draw up a realistic schedule, allowing you to allocate resources and monitor the progress of the project. For this purpose, network models of the project are compiled and analyzed, defining specific relationships between tasks (work packages). Based on network analysis, it is possible to determine the likely duration of the work, its cost, possible savings in time or money, as well as which operations can be postponed without affecting the project schedule as a whole, and which are critical, i.e. their delay means a delay in the implementation of the entire project. Network planning is also the basis for allocating project resources, including scarce ones.
Network analysis is carried out in the sequence shown in Fig. 8.1.
Rice. 8.1.
The first three stages constitute the essence of network analysis, and the last - scheduling. Typically, the process goes through several iterations.
The first stage was described by us in Chap. 7. At the second stage, the relationships between the project activities are established, which within the framework of network analysis are called operations.
The following types of dependencies can be distinguished.
- 1. Required dependencies – dependencies that are internally (physically) inherent in the work being performed (for example, when building a house, you cannot lay a roof before the walls are erected).
- 2. Dependencies at discretion – determined by the project team based on their preferences or common practice. Such dependencies should be strictly documented to avoid project deadlines.
- 3. External dependencies – determine the relationship between design and non-design work.
To establish logical relationships between operations, a precedence table is compiled, in which each operation is compared with the immediately preceding (preceding, if there are several) operation.
Example 8.1
Company ABC entered into a contract for the production of a batch of machines to be used to produce a specific type of part. Below is a precedence table that lists the operations that need to be performed during the development and production of these machines.
|
Operation code |
Description of operation |
Immediately preceding operation |
|
A |
Estimating project costs |
|
|
IN |
Coordination of cost estimates |
A |
|
WITH |
Buying your own equipment |
IN |
|
D |
Preparation of design documentation |
IN |
|
E |
Workshop construction |
D |
|
F |
Equipment installation |
WITH, E |
|
G |
Equipment testing |
F |
|
N |
Determining the Model Type |
D |
|
I |
External body design |
D |
|
J |
Creating an external enclosure |
H,I |
|
TO |
Final assembly |
G, J |
|
L |
Control check |
TO |
Network analysis tools are network graphs. There are different types of network graphs, but the most commonly used are arrow graphs.
In arrow graphs, each operation is designated by a letter and represented by an arrow; each operation begins and ends with an event that has a specific number (Fig. 8.2).
Rice. 8.2.
During the planning process, it should be taken into account that many operations will be performed simultaneously, therefore, several operations may correspond to (begin or end with) one event. An event is not considered completed until all operations included in it are completed. An operation leaving an event cannot begin until all the operations included in it have been completed. So, in Fig. 8.3 operation WITH cannot be started until the work is completed A And IN.
Rice. 8.3.
Sometimes, to depict the logical sequence of operations, so-called fictitious transactions, depicted by dotted arrows and having zero duration. They are used when it is necessary to reflect that an event cannot occur before another event, and this cannot be done using ordinary arrows corresponding to actual operations. This situation is shown in Fig. 8.4. Operation WITH cannot start before the operation has completed A, and work D you cannot start before operations are completed A And IN. It is customary to number events so that the number of the final event is greater than the numbers of previous events.
Rice. 8.4.
After an arrow graph is constructed based on the precedence table, it is usually revised to eliminate unnecessary fictitious operations. This can be done based on the following principle - if the only operation that comes out of some event is fictitious, most likely, you can do without it.
The network graph must begin with a single initial event (all operations that do not have previous ones begin with it) and end with a single final event.
Example 8.2
Let's build a network graph for the precedence table from Example 8.1.
After establishing the sequence and logical relationship of the activities, their duration is estimated, and therefore the duration of the entire project.
In addition to arrow graphs, they also use vertex graphs(precedence diagrams), where the nodes contain project operations, and the arrows between them characterize the duration of the operations (Fig. 8.5).
