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Organizational tools. Network matrices

Organizational Toolkit project management: network modeling, PERT method, RAZU matrix, information technology management models

The network matrix is ​​a graphical representation of the project implementation processes, where all work (managerial, production) is shown in a certain technological sequence and the necessary relationships and dependencies

One of the most effective tools in project management are the so-called network matrices ( higher level of development of "network diagrams"). They will allow you to present the entire process of project implementation in a very visual form, as well as identify the composition and structure of work and acceptable means and methods for their implementation, analyze the relationship between performers and work, prepare a scientifically based coordinated plan for the implementation of the entire complex of work on the project for more effective use available resources and reducing deadlines.

It is also possible to quickly process using tools computer technology arrays of information and provide project management with timely and comprehensive information about the actual state of work, facilitating the adjustment of decisions made; predict the progress of work on the critical path and focus the attention of project managers on them. Using mathematical apparatus, it is possible to determine the degree of probability of project implementation and correctly distribute responsibility among the hierarchical levels of management.

The basis of the project management system is matrix of division of administrative management tasks. ONCE Using this matrix in the project management system, you can divide the duties, rights and responsibilities of all project participants in the project team and build an organizational-dynamic structure and information system on this basis.

The matrix for the division of administrative management tasks is a table in which the names of positions, departments and services are located, and the tasks performed by these performers are also listed. A conventional sign denotes the attitude of each service unit or specific employee to solving a specific problem.



The activities for implementing management functions when designing a RAZU matrix are as follows:

responsibility for solving a particular project management problem;

I am the sole decision and personal responsibility for solving a particular problem (with signature);
! - personal responsibility for solving a particular problem in a collegial form of decision-making (with signature);
P - participation in the collegial solution of this problem without the right to sign.

P - planning;
O - organization;
K - control;
X - coordination of joint efforts of process participants;
A - activation.

C - approval, approval;
T - performance;
M - preparation of proposals;
+ - settlement operations necessary to carry out the function (task);
- - does not participate in the work.

Design of project management technology, i.e. fixing the sequence and relationship of solving management problems, possibly using the so-called information technology model (ITM).

Main stages of ITM development:

1) development of information tables.



2) Formation of information technology models based on information tables

When developing an ITM for project management, it is necessary to: reflect the relationship of tasks in the decision-making process; ensure clear distribution job responsibilities and responsibility (RAZU matrix); determine the types and forms of documents that are the result of solving problems.

3) Formation of a consolidated project management model. To build this model, it is necessary to: identify target management functions; identify supporting subsystems; establish the place of each task (from information tables) in the model. Project marketing. Marketing plan for the project. Feasibility study of the project: content, purpose. Business plan investment project: content, purpose.

Information technology model (ITM)

The information technology model (ITM) is a table consisting of six blocks:

1) Block 1: Calendar days – deadlines for solving a management task (as a rule, this is the deadline for providing the resulting documentation (all deadlines are taken from the network schedule or work production schedule));

2) 2 block: Input information – accepted based on the second column of the information table;

3) block 3: Performers – filled in based on the fifth column of the information table;

4) block 4: Management task – filled in based on the first column of the information table;

5) block 5: Resulting documentation - filled out based on the fourth column of the information table;

6) block 6: Consumers of the resulting documentation - filled out based on the seventh column of the information table;

Each task (with all its elements: initial information, performers, etc.) has its own vertical bar. All information in the information technology model (ITM) is represented by the following symbols:

1) - incoming information, performers, consumers;

2) - management tasks;

3) – resulting documentation;



74. Project cost management at the stage of its implementation: main and additional indicators of the earned value method.

Project control should include the earned value method to analyze and evaluate the current status and progress of the project and be carried out by comparing actual volume and cost indicators with baseline planned indicators. The main indicators of the earned value method, such as earned volumes, actual costs and planned volumes, allow not only to record actual results, but to predict the future state of the project and, based on these forecasts, make the right management decisions.

The basic indicators of the earned value method are:

Planned volumes (Planned Value - PVj\

Earned volumes (Earned Value - EV)\ Earned volumes show the actual volumes of work completed, expressed in terms of the planned cost of these works, as of the target date.

Actual Cost (AC). Actual costs show the actual (actually established) cost of the volumes of work performed, i.e. the totality of all costs incurred during the execution of work as of the current date. Sometimes actual costs are referred to as the amount of resources that should have been used at the current date or during a certain period of time.

Additional indicators:

Such derived (calculated) indicators usually include the following analytical and forecast indicators:

Variances:

Schedule Variance (SV),

Cost variances (by cost) (Cost Variance - CV),

Variance at Completion (VAC);

Indices:

Schedule Performance Index (SPI),

Budget Performance Index (CPI),

To-Complete Performance Index - TCPI;

Forecasts:

Projected duration of the project (Time Estimate at Completion - EAC t),

Estimated cost of the project (Estimate at Completion - EAC),

Variance at Completion (VAC).

When calculating analytical indicators, the indicator of the total budget of the project (Budget at Completion - BAC) is also used, which characterizes the total sum of all planned volumes of work of the project, the final value of the basic plan for the project.

Issues of operational project management Earned Value Method Indicators
Is the project behind schedule or ahead of it? Schedule deviation (by timing) (SV)
How effectively is time used? Schedule Performance Index (SPI)
What is the likely duration of the project? Forecast duration of the project (EAS()
Is the project on or off budget? Cost Variance (by Value) (CV)
How efficiently are resources used? Budget Performance Index (CPI)
How efficiently must resources be used to successfully complete the project? Needed Performance Index (TCPI)
What is the expected cost of the project? Estimated cost of the project (EAC)
Will the project be completed on or off budget? Variance at Completion (VAC)

The relationship between the business plan and feasibility study.

A business plan is a generally accepted form in world economic practice for presenting business proposals and projects, containing detailed information about production, sales and financial activities the company and assessment of the prospects, conditions and forms of cooperation based on the balance of the company’s own economic interests and the interests of partners, investors, consumers and competitors.

It is obvious that the development of a business plan, a set of calculated indicators, is the initial information for the feasibility study. Thus, an organic relationship between the parameters of the business plan and the parameters of the feasibility study (with the technical and economic parameters of the project) is achieved, and the most full compliance conducted research technical specifications for the project.

Mandatory elements of a business plan are:
1. Development of a project idea
2. Description of the idea (essence) of the project
3. Analysis production capabilities companies in the project implementation
4. Market assessment
5. Development of a marketing plan
6. Development of a production plan
7. Development organizational plan
8. Calculation of feasibility study indicators
9. Development financial plan
10. Risk assessment
11. General conclusions and suggestions (summary)

Thus, in the process of developing sections of the business plan, the initial data for the feasibility study is formed.

Having received all the necessary data for the feasibility study, the feasibility study indicators are calculated ( net profit, profitability, internal efficiency ratio, maximum cash outflow, return period for capital investments, break-even point). If the calculations show technical and economic efficiency, then we begin to formulate the final version of the business plan.

If the feasibility study indicators do not meet the requirements of technical and economic efficiency, then the initial data are clarified or a decision is made about the inappropriateness of the project.

The feasibility study is the main design document for the construction of facilities. Based on the duly approved feasibility study, a feasibility study is prepared tender documentation And tenders are held for the contract , is agreement (contract) contract, opens financing construction and development working documentation .

· Business plan is a program of action for the implementation of entire business projects that are in constant interaction with the external environment.

· Feasibility study is a slightly more localized version of a business plan. The main task of the feasibility study is assessment and description of the economic feasibility of the project , which will be implemented within one enterprise (which may ultimately require the development of a separate business plan).

Parameter Feasibility study Business plan
Performed tasks · Comparison of investment and technical characteristics project · Search for sources of additional funding · Comprehensive assessment of the business project · Establishing communications with interested parties
Potential reader · Management · Owners of the enterprise · Key technical personnel · Banks · Venture funds · Business angels · Owners · Partners
Typical structure · general information about the project · commercial viability of the project · structure and cost items associated with the project · production capabilities/project plan · funding requirements · Concept, overview, summary. · Description of the base enterprise. · Product Description. · Market analysis, marketing and sales. · Production plan. · Organizational plan. · Environment and regulatory information. · Financial plan. · Project risks and their minimization. · Schedule project implementation
In what situations might it be necessary? · Purchase of new automated coffee machines · Upgrade software assembly line · Development of a new mechanism for feeding sheet materials for cutting · Use of a new type of waterproof ink for large format printers · Opening of a new business-format hair salon · Organization of a shoe production plant in China · Opening of a new furniture store specializing in furniture from interchangeable colored modules · Organization of a chain of cafe-restaurants with changing interiors and menus · Opening of a new super-budget grocery store within walking distance · Construction of a polyethylene processing plant

General understanding of corridor network diagrams

In the so-called corridor network diagrams, part of the entire complex of works or individual performing works can be taken as a corridor (Fig. 4.12).

The belonging of a work to a particular corridor is determined by its horizontal position (or segment) in this corridor, as shown in Fig. 4.13.

So, in the figure we see that works 1-2 and 2-4 are performed on node “a”, since the horizontal segments of these works lie in the plane of the corridor of node “a”. Works 1-3 and 3-4 are performed on node “b”, since the horizontal sections of these works lie in the plane of the corridor of node “b”.


Rice. 4.12.


Rice. 4.13.

Thus, Executor 1 is depicted as a triangle on the graph. Performer 2 is indicated by a square. Performer 3 is indicated by a circle. Thus, any figure standing at the beginning of a work denotes a specific performer of this work. So, work 1-2 on node “a” is performed by Contractor 1. Work 3-4 on node “b” is performed by Contractor 2, etc.


Rice. 4.15.

As you can see, corridor network diagram carries significantly more information than a regular network one. This quality allows it to be used in cases where a simple network diagram is not enough to perform management functions.

Network Matrix

The network matrix is corridor-scale network diagram, organized by work performers.

The network matrix allows you to link the logical-time structure and organizational management structure of an organization into a single comprehensive tool.

The use of network matrices in the project management process makes it possible to present this process in a visual form, as well as to identify the features of the situation, the structure necessary work and acceptable means and methods for their implementation, analyze the relationship between performers and work, prepare a scientifically based coordinated plan for performing the entire range of work to solve the task. Such a plan allows for more efficient use of available resources, since analysis of the network matrix and identification of critical work and time reserves for non-critical work make it possible to redistribute resources in order to better use and reduce the time required to complete the assigned tasks. It also becomes possible to quickly process large amounts of reporting data using computer technology and provide company management with timely and comprehensive information about the actual state of work, facilitating the adjustment of decisions made; predict the progress of work on the critical path and focus the attention of managers at various levels on them. Using mathematical apparatus, it is possible to determine the degree of probability of plan implementation and correctly distribute responsibility among the hierarchical levels of management.

The network matrix is ​​a graphical representation of project management processes, where all operations that are necessary to achieve the final goal are shown in a certain technological sequence and interdependence. The network matrix is ​​combined with a calendar-scale time grid, which has horizontal and vertical corridors. Horizontal corridors characterize the level of management, structural unit or an official performing one or another operation of the process of preparing, making and implementing a decision; vertical - the stage and individual operations of the decision-making process that occur over time.

A network matrix is ​​a type of network diagram. Therefore, when constructing a network matrix, the same three basic concepts are used as when constructing network graphs:

  • work (including expectation and dependence);
  • event;
  • path.

All rules for constructing network graphs also apply to network matrices.

Building a network matrix

To properly build a network matrix, in addition to general rules When constructing network graphs, you should adhere to several special rules that directly relate to network matrices as a corridor-scale variety of network models.

The belonging of a work (arrow) to one or another horizontal corridor is determined by its horizontal position or its scale-free horizontal section in this corridor. The belonging of a job (arrow) to a vertical corridor is determined by the vertical boundaries of the corridor, stage or operation, i.e. vertical lines defining the time scale of the matrix.


Rice. 4.17.

After constructing a network matrix, you can apply all known methods for calculating analytical parameters and optimizing the model.

In order to cope with the inherent difficulties and uncertainty of every project, the manager must break the project into separate stages and identify the risk. Then, at each stage, a list of tasks is formed.

Exercise- This is a mandatory part of the work that must be completed in a predetermined manner and within a predetermined time frame. For ease of verification, it should be small (perhaps no more than 10 man-hours). Many tasks tend to be self-evolving rather than self-regulating, so for each task it is necessary to determine the following:

    uniqueness of the task;

    due date(days, hours, etc.), variable and strictly established duration of work;

    start and end dates:

    planned (in accordance with the original plan);

    expected (in accordance with subsequent changes in the plan);

    real;

    constraints and restrictions;

    necessary resources to complete the work(spatial, technical, technological, human, financial, etc.) and their uniqueness, accessibility and alternative use for other works and projects;

    connection with other tasks(preceding and subsequent tasks).

There are two main methods for planning and coordinating large-scale projects:

PERT (program evaluation and review technique) – method of evaluating and reviewing the program) and

CPM (critical path method) – critical path method.

These methods emerged independently of each other. SRM was developed Dupont Corporation in the 1950s 20th century to help draw up a plan to overhaul the corporation's plant. PERT was developed around the same time by the US Department of the Navy to plan a missile development project Polaris. The methods are almost the same; in the literature the term is most often used PERT.

PERT/time - This is a planning and management method that has four features: a network schedule, time estimates, determination of time reserves and the critical path, and the possibility of taking measures to adjust the schedule.

Many projects, be it construction, marketing, development and production of a new product, can be considered as a set of independent operations, the logical sequence of implementation of which can be displayed in the form of a network diagram. It represents chains of works (operations) and events that reflect their sequence and connection in the process of achieving the goal (Fig. 16). The network originates from one node (zero event) and ends with one event when work on the project is completed.

Critical path- the longest chain of interconnected, sequential tasks for which the slack time is zero and which determine the minimum amount of time required to complete the project.

Fig. 16. Project implementation network schedule

Work-event numbers above the arrows show the duration of the work; - work of the critical path;

When analyzing by the critical path method, the following is determined:

    earliest start date for surgery– this is the earliest possible start date, provided that all previous operations on the critical path are performed as quickly as possible. This period for all operations is calculated from left to right by adding the duration of the previous operation to its own earliest start date;

    the latest start date for the operation– the deadline for the start of the operation so that it does not cause a delay in the implementation of the entire project;

    the latest date for completing an operation– the date by which a network operation must be completed so that the next one can start on time, and the project as a whole can be completed in the shortest possible time. To calculate the latest completion date, you first need to calculate the earliest start dates of the operations from left to right in the network diagram. Then, working backwards, based on the earliest possible completion date for the project, determine the latest acceptable time to complete each activity.

Operations on the critical path do not have the slightest slack.

Time reserve– the amount of free time by which the execution of an operation as part of the project can be delayed. There are two ways to calculate reserves:

    full reserve- everything available free time, in which, in general, the project timeline will not be affected (for example, if an operation that takes 2 days can begin on the 3rd day, and the next one must begin on the 9th day of work on the project, then there is a total gap of 4 days (4 = 9 – 2 – 3):

Most deterministic projects use a single estimate of how long it will take to complete a job, based on resource standards (for example, a 40-hour work week). In less certain cases, it is recommended to estimate the duration of each job based on three estimates: optimistic, pessimistic and most likely.

In more complex projects where there is a high degree of uncertainty, PERT the assumption is made that the duration of pioneering work is a random variable that obeys the beta distribution.

Method PERT/cost represents a further development of the method in the direction of optimizing network diagrams by cost and is characterized by:

    structural analysis of project work;

    determination of types of work (R&D, production, marketing);

    construction of network diagrams;

    establishing the functional dependence of work on its duration;

    finding the duration of work that minimizes the cost of completing the project, given the deadlines for completing the entire project;

    monitoring the progress of work;

    development of corrective actions if necessary.

After the timing and cost of completing each work have been determined, the necessary material and labor resources and a budget is drawn up for each type of work, as well as a budget for the entire project.

During the course of the project, periodic estimates of “costs to completion” are made and actual costs are compared with planned ones. In the event of schedule delays or cost overruns, the project manager has the opportunity to take corrective action. Network graphs And cost estimates are revised from time to time to keep them in line with actual and planned project changes.

Thus, this approach allows us to compose detailed plans and schedules, determine the duration of work and their resource provision, describe the sequential relationships that exist between activities and show which of them are critical to completing the project on time, calculate the critical path. By identifying critical activities, managers can ensure they are properly monitored and ensure that all the resources needed for those activities are delivered on time.

The critical path can be adjusted using the following methods:

    increase resources;

    review tasks on the critical path, reduce their duration, and possibly eliminate some;

    loosen restrictions, increasing risk;

    detail tasks, increasing the number of relationships.

Advantages and disadvantages of the method PERT are given in table 56.

Table 56 - Advantages and limitations of the methodPERT

Advantages

Restrictions

    PERT forces you to plan projects carefully. In complex projects, it is almost impossible to plan events and activities without linking them together in a network diagram. The method requires structuring a set of operations and allows you to plan a project;

    The method is based on modeling and, therefore, makes it possible to conduct experiments and variant calculations;

    PERT increases the efficiency of control, because allows you not only to analyze data for the past period, but also to see potential problems in the future.

    Inaccurate estimates reduce the effectiveness of the method.

    Long time automated systems project management due to the high cost of computing resources were used mainly for the analysis of large-scale projects. Now this limitation is becoming less significant due to the development of low-cost application software packages aimed at managing small and medium-sized projects

In addition to the critical path method, there is also a step-by-step control method, which follows the same pattern as the critical path method, but recognizes that the execution time of each operation is difficult to foresee in advance, and therefore makes allowances for this.

For a project containing several dozen works, finding the critical path can be done manually. For management large projects, where the number of works exceeds hundreds and thousands, automatic project management tools are widely used (Project for Windows). For example, the technique PRINCE(Projects in Controlled Environments) is used by the UK Government in the field of information technology.

9.2 Gantt chart and network matrices

Another analysis tool is Gantt chart - a diagram depicting tasks as segments on a timeline. The length of the segment corresponds to the deadline of the task. The entire project is presented in the form of a calendar, which allows you to use it to control and show the percentage of completion of the task.

A type of Gantt chart is network matrices, for the compilation of which the following characteristics are determined (Table 57):

    resource provision;

    sequence of work, taking into account the maximum possible parallelization of work;

    performers of each work.

Table57 - List of works for building a network matrix

The network matrix is ​​a graphical representation of the project implementation processes, where all work (managerial, production, etc.) is shown in a certain technological sequence and relationship. The network matrix is ​​combined with a calendar-scale time grid that has horizontal and vertical “corridors”. Horizontal “corridors” characterize the degree of management, structural unit or official performing this or that work; vertical - stage and individual operations of the project management process that occur over time. When constructing a network matrix, three basic concepts are used: “work” (including wait and dependency), “event” and “path”.

On the graph, work is depicted as a solid arrow. The concept of “work” includes the process of waiting, i.e. a process that requires not labor and resources, but time, which is depicted by a dotted arrow with the duration of the wait indicated above it. Dependency between events indicates that there is a connection between activities and that there is no need to invest time and resources.

The most important advantage of the network matrix is ​​that there is no need to calculate matrix parameters, since they are clearly shown in the figure itself (see Fig. 29).

Divisions

Work code

Duration (days)

Number of personnel

in subdivision, people.

Employed at work, people.

Chief Technologist Department

Chief Design Department

Manufacturing workshop rigging

Mechanical workshop

Foundry shop.

Assembly shop

Drawing29 -Example of a network matrix (fragment)

Network matrices should be used at all stages life cycle project. This will make it possible to present the entire process of project implementation in a visual form, as well as to identify the composition and structure of work and acceptable means and methods for their implementation, analyze the relationship between performers and work, and prepare a scientifically based coordinated plan for the implementation of the entire complex of work on the project for more efficient use of available resources and reducing deadlines. It is also possible to quickly process large amounts of information, predict the progress of work on the critical path and concentrate the attention of project managers on them. Using mathematical tools, you can determine the degree of probability of project implementation and correctly distribute responsibility.

The first part briefly discussed the nature of the project and the activities associated with its implementation. At the same time, the issue of structuring work to achieve the goals of the project was raised. It is obvious that such activities, as noted above, serve to increase efficiency project activities according to various parameters (cost, timing, etc.). Among the elements of project activity one can also name organizational tools. The following types of organizational tools are distinguished http://tww48.narod.ru/slides_03/PM_03.files/frame.htm#slide0040.htm:

1. network matrices (a higher level of scientific development of “network graphs”):

· present the entire project implementation process in a visual form,

· identify the composition and structure of the work, and acceptable means and methods for their implementation;

· analyze the relationship between performers and work;

· prepare a scientifically based coordinated plan for the implementation of the entire range of work on the project for more efficient use of available resources and reduction of time frames.

2. matrix of division of administrative management tasks (RAZU):

· using this matrix in the project management system, you can divide the duties, rights and responsibilities of all project participants in the project team and build an organizational-dynamic structure and information system on this basis.

3. information technology model (ITM):

· helps to design project management technology, that is, fixing the sequence and relationship of solving management problems.

Project planning

The planning process is at the heart of project implementation. Planning in one form or another is carried out throughout the entire duration of the project. "Planning is a continuous process of determining the best way actions to achieve the goals, taking into account the current situation" http://www.betec.ru/index.php?id=6&sid=18. Early in the project life cycle, an informal preliminary plan is usually developed - a rough idea of ​​what will be required to complete the project. The project selection decision is largely based on preliminary plan estimates. Formal and detailed project planning begins after the decision to open is made. Key events - project milestones - are determined, tasks, work and their interdependence are formulated.

The project plan is a single, consistent and agreed document that includes the planning results of all project management functions and is the basis for project execution and control.

Network graphs and network matrices

A project consists of many stages and stages carried out by various performers. This complex process must be clearly coordinated and time-bound. The following requirements apply to planning and control systems:

· ability to assess the current state;

· predict the future progress of work;

· help choose the right direction to influence current problems so that the entire range of work is completed on time according to the budget.

At this stage, the sequence of work that is part of the WBS is determined, resulting in a network diagram. This graph represents an information-dynamic model that reflects the relationships between the activities required to achieve the final goal of the project. A network diagram is also useful in the development of large systems in which many workers are involved, for the operational management of developments.

The network diagram depicts all the relationships and results of all the work necessary to achieve the final development goal in the form of a directed graph, i.e. a graphical diagram consisting of points - the vertices of the graph, connected by directed lines - arrows, which are called the edges of the graph. The duration of work can be determined if labor intensity standards are available - by appropriate calculation; in the absence of labor intensity standards - expertly. Based on the network schedule and an estimate of the duration of the work, the main parameters of the schedule are calculated.

There are two possible approaches to constructing network models. In the first case, arrows on the graph represent work, and vertices represent events. Such models are referred to as the “Work-arrow” type and are called network diagrams. In the second approach, on the contrary, the arrows correspond to events, and the vertices correspond to jobs. Such models are classified as the “Job-top” type and are called precedence networks (each subsequent job is connected to its predecessor). In Fig. Figures 2.1 and 2.2 show examples of these types of models.

Works are any actions leading to the achievement of certain results - events. Events other than the initial one are the results of the work. Between two adjacent events, only one job or sequence of jobs can be performed.

To build network models, it is necessary to determine the logical relationships between activities. The reason for the interconnections is, as a rule, technological limitations (the start of some work depends on the completion of others). The complex of relationships between jobs determines the sequence of work execution over time.

Fig.2.1 Network model of the "Work-arrow" type - Network diagram.


Fig.2.2 Network model of the "Job-top" type - Precedence network

When managing project activities, tools for creating hierarchical network models are often used. “The process of building a network is carried out step by step” http://www.iis.nsk.su/preprints/Monog/MONOGR/node49.html. First of all, the root level of the hierarchical network is created, which consists of structural transitions of the work system representing its modules. Also at this stage, places are created that model interaction points. These places and structural transitions are connected by arcs in accordance with the stage of the project. The next three generation steps are performed sequentially for each module. In the second step, a network implementing the module is generated. This network, in turn, will contain structural transitions. At this stage of construction, arcs are not created, but are completed at the next step, where subnets are created corresponding to structural transitions. After this, individual operators are broadcast. In the process of building such a network, arcs are created for the second-level network. At the fourth step, structural transitions are created that implement procedures and functions, if any. At the final step - network optimization - all empty transitions are removed, that is, transitions that have empty bodies and do not have expressions on the output arcs.

Network matrices, as mentioned above, are a higher level of scientific development of network graphs. They are “a graphical representation of the processes of project implementation, where all work (managerial, production) is shown in a certain technological sequence and the necessary relationships and dependencies” http://tww48.narod.ru/slides_03/PM_03.files/frame.htm#slide0040 .htm.

It is combined with a calendar-scale time grid, which has horizontal and vertical “corridors”: horizontal “corridors” characterize the management level, structural unit or official performing this or that work; vertical - stage and individual operations of the project management process that occur over time (Appendix 1).

The process of constructing a network matrix based on the precedence network (“Job-vertex”) includes the following steps. First of all, this is the identification of participants in the implementation of the project, their distribution hierarchically and their design in the form of a table (for example, as shown in Appendix 1): line by line from top to bottom in accordance with their position in the project. It is determined what everyone can do and what is actually required of them for the needs of the project. Then a list of works is compiled, the implementation of which is necessary to achieve the set goals. Using, for example, the critical path method, the order of work is determined. Then, having marked the work with a symbol (circle, square, etc.), they are distributed into the cells of the calendar-scale grid, into which the model is placed, the elements of which are subsequently connected by arrows, illustrating - in turn - the sequence of work.

When constructing a network matrix, three basic concepts are used: “work” (including wait and dependency), “event” and “path”.

Work is labor process, requiring time and resources; The concept of “work” includes the process of waiting, that is, a process that requires the expenditure not of labor and resources, but of time, which is depicted by a dotted arrow with the duration of the waiting indicated above it.

An event is the result of the execution of all work included in this event, allowing the start of all work coming out of it; On the network matrix, an event is usually indicated in the form of a circle.

Path is a continuous sequence of work, starting from original event and ending with the final one; the path with the longest duration is called critical and is indicated in the matrix by a thickened or double arrow.

The following network diagram parameters are distinguished:

· early start time (ER) of this work;

· early finishing time (EC) of this work;

· late start time (LM) of this work;

· late completion time (LA) of this work;

· full reserve of time for this work;

· private time reserve for this work;

· work intensity factor.

That is, it is clear here that almost all of them are related to the time limitation of work, on the basis of which we can confidently assert that the use of network diagrams in general and network matrices in particular is intended to ensure, first of all, planning the timing of various works. Network planning methods are “methods whose main goal is to reduce the duration of a project to a minimum” http://www.projectmanagement.ru/theory/pm_glos.html. This, in turn, will make it possible to more rationally plan work and resources at the stages of project activities, some or all of which will be identified precisely as a result of constructing a network matrix.

PROJECT

Case No. 1

The figure shows an image of the network model of the “Project to create a new pharmaceutical product»:

Identify the critical path.

Case No. 2

The figure shows an image of the network model of Project Alpha; it is necessary to identify the critical path:

Case No. 3

Case No. 4

The figure shows an image of the network model of the VBB Project; it is necessary to identify the critical path:

Case No. 5

The figure shows an image of the network model of Project “A”; it is necessary to identify the critical path:


PROJECT TEAM MANAGEMENT

Case No. 1

Select the most profitable project for the Aquarium project group (by calculating the rate of return of the projects): Project A requires an investment in the amount of 900, income stream: first year - 350, second year - 425, third year - 650. Project B requires costs in the amount of 325 and will provide income: the first year – 100, the second year – 200, the third year – 300. The discount rate is 10%.

Case No. 2

The credit policy of Investor Bank limits the repayment period of the loan provided to finance investment projects related to the construction materials industry to three years. Will a loan be issued? project team"Alpha" for the construction of a brick factory worth 1300 million rubles, if the income flow is 500 million rubles. annually, discount rate – 8%

Case No. 3

The West project team needs to calculate the net present value of the project's income. Project cost - 2450 million rubles, income stream: in the first year - 100 million rubles, in the second - 550 million rubles, in the third 800 million rubles, in the fourth - 1200 million rubles, in the fifth – 1500 million rubles, discount rate – 10%.

Case No. 4

The Voskhod project group needs to calculate the rate of return for a project worth 1,400 million rubles, if in the first year of operation it brings a loss of 200 million rubles, in the next five years the annual income will be 350 million rubles, the discount rate is 6% .

Case No. 5

Which project should the Alphabet project team prefer? Costs for the Omega project - 800 million rubles, income: in the first year - 200 million rubles, in the second - 350 million rubles, in the third - 400 million rubles, in the fourth year - 500 million. rub., discount rate – 11%. Costs for the Alpha project are 2,100 million rubles, income over five years is 600 million rubles annually, the discount rate is 8%.

PROJECT COMMUNICATION MANAGEMENT



Case No. 1

Case No. 2

The figure shows the organizational structure of management; determine the type of organizational structure and identify its disadvantages and advantages

Case No. 3

The figure shows the organizational structure of management; determine the type of organizational structure and identify its disadvantages and advantages

Case No. 4

The figure shows the organizational structure of management; determine the type of organizational structure and identify its disadvantages and advantages

Case No. 5

The figure shows the organizational structure of management; determine the type of organizational structure and identify its disadvantages and advantages.

PROJECT BUDGETING

Case No. 1

Determine the payback period of the investment project "Ural", which requires an investment of 1000. The projected income flow will be: the first year - 200, the second - 500, the third - 600, the fourth - 800, the fifth - 900. Discount rates - 15%.

Case No. 2

Calculate the net present value of the income of the Ural project, which requires an investment of 1000. The projected income stream will be: the first year - 200, the second - 500, the third - 600, the fourth - 800, the fifth - 900. Discount rates - 15%.

1. Presented project costs – 1000

2. Amount of reduced income – 1851

3. Net present value of income - 851

Case No. 4

Select the most profitable project (by calculating the rate of return of the projects): Project A requires an investment in the amount of 900, income stream: first year - 300, second year - 400, third year - 600. Project B requires costs in the amount of 325 and will provide income: first year – 100, second year – 200, third year – 300. Discount rate – 10%.



Case No. 5

Calculate the payback period for the “Sun” project, which requires costs in the amount of 850 million rubles. and providing income: in the first year - 85 million rubles, in the second - 300 million rubles, in the third - 400 million rubles, in the fourth - 500 million rubles, in the fifth year - 600 million rubles. , discount rate – 12% (business valuation).

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