Plays a major role at the structural planning stage. Development of a project for an Internet company for the sale, installation and maintenance of software products

Labor Relations 25.03.2020
Labor Relations

Laboratory work No. 4.

Project management by means

Microsoft Project2007

The laboratory work is intended to familiarize you with the main stages of project management technology in the environment MicrosoftOffice Project 2007.

A brief description of the theoretical foundations of network and scheduling planning as the foundation of automated project management technology is given. Techniques for drawing up a project plan are discussed.

1. Basic concepts of project management

Project is a set of activities or work distributed over time aimed at achieving a goal. Examples of projects are the construction of buildings, complexes, enterprises, the development of a new type of product, the modernization of production, the development of a software product, etc.

The project has certain properties.

    A project always has a clearly defined goal, which is expressed in obtaining some result. Achieving this result signifies the successful completion and completion of the project. For example, for a building construction project, the result is the building itself, accepted for operation.

    The project has a clearly defined beginning, which coincides with the beginning of the first work aimed at achieving the goal. The beginning can be set prescriptively, or calculated as a result of drawing up a work plan for the project.

    The project has a clearly defined end that coincides with the end last work aimed at obtaining a given result. Like the beginning, the end of the project can be specified prescriptively, or calculated when drawing up a work plan. For example, for a building construction project, the end of the project coincides with the date of its commissioning/acceptance certificate.

    The project is carried out by a team, which includes the project leader, managers, and performers. In addition to the main team, it may involve third-party performers, teams and organizations that are involved on a temporary basis to perform individual work.

    When implementing the project, material resources are used. Their nomenclature and quantity are determined by the nature of the project and the work included in it. So, when building a house, sand, crushed stone, cement, brick, etc. are used.

    The project has a budget. The cost of the project consists of the cost of spent material resources, labor costs for the team implementing it and other expenses associated with the characteristics of specific types of work.

    The project has three types of restrictions.

    Budget restrictions set a limit on the cost of the entire project or individual types of work.

    Time limits set deadlines for completing either the entire project or some work. For example, test trials should be carried out in the presence of a customer representative who will be present for a specified period of time.

    Resource limitations are determined by limited team composition or material resource arrival schedules.

2. Network planning and management

Structural planning. Scheduling. Operational management.

2.1. Structural planning

Structural planning includes several stages:

    dividing the project into a set of individual works, the implementation of which is necessary for the implementation of the project;

    constructing a network diagram describing the sequence of work;

    assessment of the time characteristics of work and analysis of the network diagram.

The main role at the structural planning stage is played by the network diagram.

Network diagram is a directed graph in which the vertices indicate the work of the project, and the arcs indicate the temporary relationships of the work.

The network diagram must satisfy the following properties.

    Each job corresponds to one and only one vertex. No work may be submitted to network graphics twice. However, any job can be divided into several separate jobs, each of which will correspond to a separate vertex of the graph.

    No job can begin before all the jobs immediately preceding it have been completed. That is, if arcs enter a certain vertex, then work can begin only after the completion of all the works from which these arcs emerge.

    No job that immediately follows a job can begin before it ends.

    In other words, if several arcs exit from a job, then none of the jobs that those arcs are part of can begin until that job ends. The beginning and end of the project are indicated by activities with zero duration. Such work is called milestones and indicate the beginning or end of the most important stages

project. Example

. As an example, consider the project “Development of a software package”. Let us assume that the project consists of work, the characteristics of which are given in Table 2.1.2. 1

Table

Work number

Job title

Duration

Start of the project

Formulation of the problem

Interface development

Development of data processing modules

Database structure development

Populating the Database

Debugging the software package

Preparation of program documentation

Completion of the project

Network diagram for of this project shown in Fig. 2.1. On it, the vertices corresponding to normal work are outlined with a thin line, and the project milestones are outlined with a thick line.

Rice.2. 1. Project network diagram

The network diagram allows you to find the critical activities of the project and its critical path using given values ​​of work durations.

Critical is a job for which a delay in its start will delay the completion of the project as a whole. Such work does not have a reserve of time. Non-critical activities have a certain margin of time, and within this margin their start may be delayed.

Critical path– this is the path from the initial to the final vertex of the network diagram, passing only through critical activities. The total duration of the critical path activities determines the minimum project implementation time.

Finding the critical path comes down to finding critical jobs and is performed in two stages.

    Calculation early start time each work of the project. This value shows the time before which work cannot start.

    Calculation late start time each work of the project. This value indicates the time after which work cannot begin without increasing the duration of the entire project.

Critical jobs have equal early and late start times.

Let us denote – the time it takes to complete the work, – early time start of work - late start time. Then

where is the set of jobs immediately preceding the job. Early time initial work project is taken equal to zero.

Since the last activity of the project is a milestone of zero duration, its earliest start time coincides with the duration of the entire project. Let's denote this quantity. Now the late start time of the last job is taken as the later start time, and for the remaining jobs the later start time is calculated using the formula:

Here are a lot of works that immediately follow the work.

Schematic calculations of early and late start times are shown, respectively, in Fig. 2.2 and Fig.2.3.

Rice.2. 2. Scheme for calculating early start time

Rice.2. 3. Scheme for calculating late start time

project.. Let's find the critical work and the critical path for the project "Development of a software package", the network diagram of which is shown in Fig. 1, and the duration of the work is calculated in days and is given in Table 1.

First, we calculate the earliest start time of each job. Calculations start from the initial work and end with the final work of the project. The process and results of the calculations are shown in Fig. 2.4.

The result of the first stage, in addition to the early start time of work, is the total duration of the project.

At the next stage, we calculate the later start time of work. Calculations begin in the last and end in the first work of the project. The calculation process and results are shown in Figure 2.5.

Rice.2. 4. Calculating the earliest start time

Rice.2. 5. Calculating the latest start time for work

The summary results of the calculations are given in Table 2.2. Critical work is highlighted in it. The critical path is obtained by connecting the critical activities on the network diagram. It is shown by dotted arrows in Fig. 2.6.

Table 2.2

Early start time

Late start time

Reserve time

Rice.2.6 . Project Critical Path

After calculating the values ​​and for each job, calculate reserve time:

This value shows how much you can delay the start of work without increasing the duration of the entire project.

For critical work, the slack time is zero. Therefore, the project manager's efforts should be directed primarily at ensuring the timely completion of these works.

For non-critical work, the time slack is greater than zero, which gives the manager the opportunity to maneuver their start time and the resources they use. The following options are possible.

    The start of work is delayed by an amount not exceeding the reserve time, and the resources required for work are directed to perform work on the critical path. This can result in a reduction in the duration of critical work and the project as a whole;

    Underutilization of non-critical work with resources. As a result, its duration increases within the time reserve, and the freed resource is used to perform critical work, which will also lead to a decrease in the duration of it and the entire project.

In the example project, work 3, 4 and 9 have a reserve time according to Table 2.

As well as its internal administrative and economic structure. Each structural unit develops its own plan, which ultimately comes down to overall plan enterprises. A well-functioning system for collecting information from each service is needed for more accurate planning. This is a complex process, but its debugging leads to forecasting with the smallest percentage of deviations in the future from actual data, which reduces the risk of negative factors affecting the decline in financial results as a whole.

As a rule, the situation sometimes develops in such a way that one service of the enterprise is not aware of what is the responsibility of another.

These structural units work according to one task specified in the plan, which binds them. The most effective direction of planning is one that takes into account all the necessary rules, namely:

  1. justification of all elements and stages of the plan;
  2. control over the strict execution of the plan by its participants;
  3. constant accounting and control, as well as making adjustments to the plan and its execution.

Plans can be grouped as follows.

  1. company-wide;
  2. workshop;
  3. work plans of structural units.

By type of product, work, service:

  1. mastered production;
  2. mastered production;
  3. planned for development in the future.

Business plan The enterprise has the following structure:

  1. a brief description of the business plan;
  2. business strategy (managerial structure, business organization, goals regarding quality and types of products, personnel qualifications);
  3. marketing strategy and identification of sales markets (analysis of the competitive environment, consumer demand, identifying the strengths and weaknesses of the business, the efficiency of the economic sector);
  4. operation and production (development plans, evaluation production capacity etc.);
  5. management process (quantitative and qualitative indicator control commands);
  6. financial policy (definition cash flows, level of production profitability, etc.);
  7. certain risk factors (presence of technical and financial risks, calculation of the break-even point and ratios characterizing the financial condition);
  8. applications.

Annotation: Structural planning. Scheduling. Operational management. Practical classes on structural and scheduling. Test assignments.

2.1. Theoretical course

2.1.1. Structural planning

Structural planning includes several stages:

  1. dividing the project into a set of individual works, the implementation of which is necessary for the implementation of the project;
  2. constructing a network diagram describing the sequence of work;
  3. assessment of the time characteristics of work and analysis of the network diagram.

The main role at the structural planning stage is played by the network diagram.

Network diagram is a directed graph in which the vertices indicate the work of the project, and the arcs indicate the temporary relationships of the work.

The network diagram must satisfy the following properties.

  1. Each job corresponds to one and only one vertex. No work can be represented on the network diagram twice. However, any job can be divided into several separate jobs, each of which will correspond to a separate vertex of the graph.
  2. No job can begin before all the jobs immediately preceding it have been completed. That is, if arcs enter a certain vertex, then work can begin only after the completion of all the works from which these arcs emerge.
  3. No job that immediately follows a job can begin before it ends. In other words, if several arcs exit from a job, then none of the jobs that those arcs are part of can begin until that job ends.
  4. The beginning and end of the project are indicated by activities with zero duration. Such work is called The beginning and end of the project are indicated by activities with zero duration. Such work is called and mark the beginning or end of the most important stages of the project.

project.. As an example, consider the project “Development of a software package”. Let's assume that the project consists of work, the characteristics of which are given in Table 2.1.

Table 2.1.
Work number Job title Job title
1 Start of the project 0
2 Formulation of the problem 10
3 Interface development 5
4 Development of data processing modules 7
5 Database structure development 6
6 Populating the Database 8
7 Debugging the software package 5
8 Testing and bug fixing 10
9 Preparation of program documentation 5
10 Completion of the project 0

The network diagram for this project is shown in Fig. 2.1. On it, the vertices corresponding to normal work are outlined with a thin line, and the project milestones are outlined with a thick line.


Rice. 2.1.

The network diagram allows you to find the critical activities of the project and its critical path using given values ​​of work durations.

Critical is a job for which a delay in its start will delay the completion of the project as a whole. Such work does not have a reserve of time. Non-critical activities have a certain margin of time, and within this margin their start may be delayed.

Critical path– this is the path from the initial to the final vertex of the network diagram, passing only through critical activities. The total duration of the critical path activities determines the minimum project implementation time.

Finding the critical path comes down to finding critical jobs and is performed in two stages.

  1. Calculation early start time each work of the project. This value shows the time before which work cannot start.
  2. Calculation late start time each work of the project. This value indicates the time after which work cannot begin without increasing the duration of the entire project.

Critical jobs have equal early and late start times.

Let us denote – the time of work execution, – the early start time of work, – the late start time of work. Then

where is the set of jobs immediately preceding job . The early start time of the project is assumed to be zero.

Since the last activity of the project is a milestone of zero duration, its earliest start time coincides with the duration of the entire project. Let's denote this quantity. Now it is taken as the late start time of the last job, and for the remaining jobs the later start time is calculated using the formula:

Here are many works directly following the work.

Schematic calculations of early and late start times are shown, respectively, in Fig. 2.2 and Fig. 2.3.


Rice. 2.2.


Rice. 2.3.

project.. Let's find the critical work and the critical path for the project "Development of a software package", the network diagram of which is shown in Fig. 2.1, and the duration of the work is calculated in days and is given in Table 2.1.

First, we calculate the earliest start time of each job. Calculations start from the initial work and end with the final work of the project. The process and results of the calculations are shown in Fig. 2.4.

The result of the first stage, in addition to the early start time of work, is the total duration of the project .

At the next stage, we calculate the later start time of work. Calculations begin in the last and end in the first work of the project. The process and results of the calculations are depicted in Figure 2.5.


Rice. 2.4.


Rice. 2.5.

The summary results of the calculations are given in Table 2.2. Critical work is highlighted in it. The critical path is obtained by connecting the critical activities on the network diagram. It is shown by dotted arrows in Fig. 2.6.

Table 2.2.
Job 1 2 3 4 5 6 7 8 9 10
Early start time 0 0 10 16 10 16 24 29 29 39
Late start time 0 0 12 17 10 16 24 29 34 39
Reserve time 0 0 2 1 0 0 0 0 5 0

Structural planning

Structural planning includes several stages:

1. dividing the project into a set of individual works, the implementation of which is necessary for the implementation of the project;

2. construction of a network diagram describing the sequence of work;

3. assessment of the time characteristics of work and analysis of the network diagram.

The main role at the structural planning stage is played by the network diagram.

Network diagram is a directed graph in which the vertices indicate the work of the project, and the arcs indicate the temporary relationships of the work.

The network diagram must satisfy the following properties.

1. Each job corresponds to one and only one vertex. No work can be represented on the network diagram twice. However, any job can be divided into several separate jobs, each of which will correspond to a separate vertex of the graph.

2. No work can begin before all immediately preceding work has been completed. That is, if arcs enter a certain vertex, then work can begin only after the completion of all the works from which these arcs emerge.

3. No work that immediately follows a certain work can begin before it ends. In other words, if several arcs exit from a job, then none of the jobs that those arcs are part of can begin until that job ends.

4. The beginning and end of the project are indicated by activities with zero duration. Such work is called The beginning and end of the project are indicated by activities with zero duration. Such work is called and mark the beginning or end of the most important stages of the project.

project.. As an example, consider the project “Development of a software package”. Let us assume that the project consists of works, the characteristics of which are given in Table 1.

Table 1.

The network diagram for this project is shown in Fig. 1. On it, the vertices corresponding to ordinary work are outlined with a thin line, and with a thick line project milestones.

Rice. 1. Project network diagram

The network diagram allows you to find the critical activities of the project and its critical path using given values ​​of work durations.

Critical is a job for which a delay in its start will delay the completion of the project as a whole. Such work does not have a reserve of time. Non-critical activities have a certain margin of time, and within this margin their start may be delayed.

Critical path– this is the path from the initial to the final vertex of the network diagram, passing only through critical activities. The total duration of the critical path activities determines the minimum project implementation time.

Finding the critical path comes down to finding critical jobs and is performed in two stages.

1. Calculation early start time each work of the project. This value shows the time before which work cannot start.

2. Calculation late start time each work of the project. This value indicates the time after which work cannot begin without increasing the duration of the entire project.

Critical jobs have equal early and late start times.

Let us denote – the time of work execution, – the early start time of work, – the late start time of work. Then

where is the set of jobs immediately preceding job . The early start time of the project is assumed to be zero.

Since the last activity of the project is a milestone of zero duration, its earliest start time coincides with the duration of the entire project. Let's denote this quantity. Now it is taken as the late start time of the last job, and for the remaining jobs the later start time is calculated using the formula:

Here are many works directly following the work.

Schematic calculations of early and late start times are shown, respectively, in Fig. 2 and Fig.3.

Rice. 2. Scheme for calculating early start time

Rice. 3. Scheme for calculating late start time

project.. Let's find the critical work and the critical path for the project "Development of a software package", the network diagram of which is shown in Fig. 1, and the duration of the work is calculated in days and is given in Table 1.

First, we calculate the earliest start time of each job. Calculations start from the initial work and end with the final work of the project. The process and results of the calculations are shown in Fig. 4.

The result of the first stage, in addition to the early start time of work, is the total duration of the project .

At the next stage, we calculate the later start time of work. Calculations begin in the last and end in the first work of the project. The calculation process and results are shown in Figure 5.

Rice. 4. Calculating the earliest start time

Rice. 5. Calculating the latest start time for work

The summary results of the calculations are given in Table 2. Critical work is highlighted in it. The critical path is obtained by connecting the critical activities on the network diagram. It is shown by dotted arrows in Fig. 6.

Table 2.

Rice. 6. Project Critical Path

After calculating the values ​​and for each work, calculate reserve time :

This value shows how much you can delay the start of work without increasing the duration of the entire project.

For critical work, the slack time is zero. Therefore, the project manager's efforts should be directed primarily at ensuring the timely completion of these works.

For non-critical work, the time slack is greater than zero, which gives the manager the opportunity to maneuver their start time and the resources they use. The following options are possible.

1. Delay in the start of work by an amount not exceeding the time reserve, and the resources required for work are directed to perform work on the critical path. This can result in a reduction in the duration of critical work and the project as a whole;

2. Underutilization of non-critical work with resources. As a result, its duration increases within the time reserve, and the freed resource is used to perform critical work, which will also lead to a decrease in the duration of it and the entire project.

In the example project, work 3, 4 and 9 have a reserve time according to Table 2.

Scheduling

At the scheduling stage, a calendar schedule is developed, which is called Gantt chart. The Gantt chart displays the following project parameters:

1. structure of work obtained on the basis of the network diagram;

2. composition of resources used and their distribution between jobs;

3. calendar dates to which the start and completion of work are tied.

Let's consider the construction of a calendar schedule using the example of the project "Development of a software package." First of all, you need to decide on the resources that will be used by this project. Let us assume that only performers act as resources, and they are distributed among jobs according to Table. 3.

Table 3.

Job no. Job title Executor
Start of the project -
Formulation of the problem Stage Director
Interface development Programmer1
Development of data processing modules Programmer1
Database structure development Programmer2
Populating the Database Programmer2
Debugging the software package Programmer1 Programmer2
Testing and bug fixing Programmer1 Programmer2 Director
Preparation of program documentation Stage Director
Completion of the project -

Let's choose the start date of the project - September 7, 2009. (Monday). When drawing up a calendar schedule, only working days are taken into account. All Saturdays and Sundays are considered non-working, as well as official holidays, the nearest of which is November 4.

Calendar schedule(Gantt chart) is shown in Fig. 7, where diamonds indicate milestones, solid lines indicate the duration of work, solid lines with arrows indicate reserve time for work, dotted lines indicate the connection between the end of previous and the beginning of subsequent work.

Rice. 7. Project schedule



Rice. 8. Resource load charts

Based on the Gantt chart, a resource load chart. This graph shows the download percentage of a specific labor resource during the course of the project. The x-axis shows the time interval of the project, and the y-axis shows the total percentage of the contractor’s workload for all project tasks that he is performing at the current time.

Usually the performer is completely occupied with solving a certain task and, upon completion, moves on to the next one. This corresponds to 100% load. However, in some cases, he can be involved in 2 or more tasks in parallel, allocating part of his working time to solve them. For example, two tasks of 50% each, that is, half a working day per task. In this case, the resource load chart allows you to monitor the total workload of the performer and identify possible periods of overload when he is scheduled to do more work than he can complete during the working day. This is evidenced by the total workload of more than 100%.

An example of resource load graphs for the “Software development” project is shown in Fig. 8. It is built on the assumption that each employee is 100% engaged in completing the task planned for him. It is clear from the graphs that the Director is overloaded in the period from October 16 to October 23, since he is assigned two parallel jobs during this period. The area of ​​its overload is highlighted on the corresponding graph by hatching.

Operational management

At the stage operational management work on the project is carried out and the progress of its implementation is continuously monitored. No matter how good the initial plan, life will definitely make its own adjustments to it. Therefore, the manager’s tasks are:

1. tracking the actual work schedule;

2. comparison of the actual schedule with the planned one;

3. making decisions to eliminate emerging deviations from the plan;

4. Re-planning of the project in case of significant deviations.

The first two tasks are solved using a Gantt chart. On it, parallel to the work duration lines, lines are drawn indicating the percentage of actual completion of these works. This makes it easy to detect any deviations that have occurred.

The method for eliminating deviation depends on the available resource manager. To complete the delayed work, you can either involve additional workers(additional resources), or use the same composition of workers overtime. In both cases, eliminating the deviation will have to be paid for by increasing the cost of the project (previously unplanned payment for additional workers, resources and overtime).

If the deviation is such that it cannot be corrected by attracting additional and overtime resources, or the increase in project cost is unacceptable, it needs to be done again reschedule project and do the following:

1. completed jobs are assigned zero duration values;

2. for partially completed work, duration values ​​are set corresponding to the remaining amount of work;

3. structural changes are made to the network schedule in order to eliminate the existing unnecessary work and adding others, previously unplanned;

4. re-calculation of the critical path and re-scheduling of the project.

After creating the adjusted project, it is approved by management and its implementation and operational management begins. This adjustment can be made several times.

Control questions

1. What stages are included in the structural planning methodology?

2. What is a network diagram?

3. What properties does a network diagram have?

4. What is critical work?

5. What is the critical path?

6. What are the steps in finding the critical path?

7. How is the early start time calculated?

8. How is late start time calculated?

9. How to find critical jobs based on the early and late start times?

10. What is the operating time reserve?

11. How can the operating time reserve be used?

12. What is a Gantt chart?

13. Give an example of a Gantt chart.

14. What is the purpose of the resource load graph?

15. How can you find resource overload based on the resource load graph?

16. Give an example of a resource load graph.

17. What is the essence of the operational management process?

18. What actions should be performed when replanning a project in the process of operational management?

Laboratory work 1. Drawing up and calculating a network diagram

Laboratory work 2. Compilation and calculation calendar plan

  • At the end of each topic, it is necessary to form a conclusion from the acquired practical and theoretical knowledge obtained as a result of the internship.

  • Annotation: Structural planning. Scheduling. Operational management. Practical classes on structural and calendar planning. Test assignments.

    2.1. Theoretical course

    2.1.1. Structural planning

    Structural planning includes several stages:

    1. dividing the project into a set of individual works, the implementation of which is necessary for the implementation of the project;
    2. constructing a network diagram describing the sequence of work;
    3. assessment of the time characteristics of work and analysis of the network diagram.

    The main role at the structural planning stage is played by the network diagram.

    Network diagram is a directed graph in which the vertices indicate the work of the project, and the arcs indicate the temporary relationships of the work.

    The network diagram must satisfy the following properties.

    1. Each job corresponds to one and only one vertex. No work can be represented on the network diagram twice. However, any job can be divided into several separate jobs, each of which will correspond to a separate vertex of the graph.
    2. No job can begin before all the jobs immediately preceding it have been completed. That is, if arcs enter a certain vertex, then work can begin only after the completion of all the works from which these arcs emerge.
    3. No job that immediately follows a job can begin before it ends. In other words, if several arcs exit from a job, then none of the jobs that those arcs are part of can begin until that job ends.
    4. The beginning and end of the project are indicated by activities with zero duration. Such work is called The beginning and end of the project are indicated by activities with zero duration. Such work is called and mark the beginning or end of the most important stages of the project.

    project.. As an example, consider the project “Development of a software package”. Let's assume that the project consists of work, the characteristics of which are given in Table 2.1.

    Table 2.1.
    Work number Job title Job title
    1 Start of the project 0
    2 Formulation of the problem 10
    3 Interface development 5
    4 Development of data processing modules 7
    5 Database structure development 6
    6 Populating the Database 8
    7 Debugging the software package 5
    8 Testing and bug fixing 10
    9 Preparation of program documentation 5
    10 Completion of the project 0

    The network diagram for this project is shown in Fig. 2.1. On it, the vertices corresponding to normal work are outlined with a thin line, and the project milestones are outlined with a thick line.


    Rice. 2.1.

    The network diagram allows you to find the critical activities of the project and its critical path using given values ​​of work durations.

    Critical is a job for which a delay in its start will delay the completion of the project as a whole. Such work does not have a reserve of time. Non-critical activities have a certain margin of time, and within this margin their start may be delayed.

    Critical path– this is the path from the initial to the final vertex of the network diagram, passing only through critical activities. The total duration of the critical path activities determines the minimum project implementation time.

    Finding the critical path comes down to finding critical jobs and is performed in two stages.

    1. Calculation early start time each work of the project. This value shows the time before which work cannot start.
    2. Calculation late start time each work of the project. This value indicates the time after which work cannot begin without increasing the duration of the entire project.

    Critical jobs have equal early and late start times.

    Let us denote – the time of work execution, – the early start time of work, – the late start time of work. Then

    where is the set of jobs immediately preceding job . The early start time of the project is assumed to be zero.

    Since the last activity of the project is a milestone of zero duration, its earliest start time coincides with the duration of the entire project. Let's denote this quantity. Now it is taken as the late start time of the last job, and for the remaining jobs the later start time is calculated using the formula:

    Here are many works directly following the work.

    Schematic calculations of early and late start times are shown, respectively, in Fig. 2.2 and Fig. 2.3.


    Rice. 2.2.


    Rice. 2.3.

    project.. Let's find the critical work and the critical path for the project "Development of a software package", the network diagram of which is shown in Fig. 2.1, and the duration of the work is calculated in days and is given in Table 2.1.

    First, we calculate the earliest start time of each job. Calculations start from the initial work and end with the final work of the project. The process and results of the calculations are shown in Fig. 2.4.

    The result of the first stage, in addition to the early start time of work, is the total duration of the project .

    At the next stage, we calculate the later start time of work. Calculations begin in the last and end in the first work of the project. The process and results of the calculations are depicted in Figure 2.5.


    Rice. 2.4.


    Rice. 2.5.

    The summary results of the calculations are given in Table 2.2. Critical work is highlighted in it. The critical path is obtained by connecting the critical activities on the network diagram. It is shown by dotted arrows in Fig. 2.6.

    Table 2.2.
    Job 1 2 3 4 5 6 7 8 9 10
    Early start time 0 0 10 16 10 16 24 29 29 39
    Late start time 0 0 12 17 10 16 24 29 34 39
    Reserve time 0 0 2 1 0 0 0 0 5 0

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