Network schedule and project schedule. Network planning, scheduling

Annotation: Structural planning. Calendar planning. Operational management. Practical training in structural and scheduling. Tasks for control work.

2.1. Theoretical course

2.1.1. Structural planning

Structural planning includes several stages:

1. splitting the project into a set individual works, the implementation of which is necessary for the implementation of the project;
2. building a network diagram that describes the sequence of work;
3. evaluation of the time characteristics of work and analysis of the network diagram.

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

network diagram is a directed graph, in which the vertices indicate the work of the project, and the arcs indicate the temporal 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 twice on a network diagram. 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 be started until all immediately preceding jobs have been completed. That is, if arcs enter a certain vertex, then the work can begin only after the end of all the works from which these arcs exit.
3. No work that immediately follows some work can begin before the moment of its completion. In other words, if multiple arcs leave a job, then none of the jobs that include those arcs can start before the end of that job.
4. The beginning and end of the project are indicated by works with zero duration. Such work is called milestones and mark the beginning or end of the most important phases of the project.

Example. As an example, consider the project "Development software package". Let's assume that the project consists of works, the characteristics of which are given in Table 2.1.

Table 2.1.

Job number	Job title	Duration
1	Start of the project	0
2	Formulation of the problem	10
3	Interface development	5
4	Development of data processing modules	7
5	Development of the database structure	6
6	Populating the database	8
7	Software debugging	5
8	Testing and bug fixing	10
9	Compilation of program documentation	5
10	Project Completion	0

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

Rice. 2.1.

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

critical is such work for which a delay in its start will lead to a delay in the completion of the project as a whole. Such work does not have a margin of time. Non-critical activities have some slack, and within that slack, 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 works. The total duration of the critical path activities determines the minimum project implementation time.

Finding the critical path is reduced to finding critical activities and is performed in two stages.

1. calculation early start time each work of the project. This value indicates the time before which the job cannot be started.
2. calculation late start time each work of the project. This value indicates the time after which the work cannot be started without increasing the duration of the entire project.

Critical jobs have the same early and late start time value.

Let us designate - the time of the work execution, - the early start time of the work, - the late start time of the work. Then

where is the set of jobs immediately preceding the 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 early start time is the same as the duration of the entire project. Let's denote this value. Now it is taken as the late start time of the last job, and for other jobs, the later start time is calculated by the formula:

Here is a set of works immediately following the work .

Schematically, the calculations of the early and late start times are depicted, respectively, in Fig. 2.2 and fig.2.3.

Rice. 2.2.

Rice. 2.3.

Example. Let's find the critical jobs and the critical path for the project "Development of a software package", the network schedule 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 early start time of each job. Calculations start from the initial and end with the final work of the project. The process and results of calculations are shown in Figure 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 late start time of work. Calculations start in the last job and end in the first job of the project. The process and results of the calculations are shown in Figure 2.5.

Rice. 2.4.

Rice. 2.5.

The summary results of the calculations are given in Table 2.2. Critical works are 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.

Work	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

The project manager, when planning a project, must keep in mind the project triangle of constraints: "duration" - "cost" - "content". Resource and cost constraints determine the quality of the project schedule. Network planning, although it is a fairly routine tool for scheduling, nevertheless, allows you to better optimize the plan in terms of resources and timing. The network diagram, built according to the “top - work” method, provides all the possibilities for applying applied optimization methods.

Glossary of network design

The construction of a network schedule is methodologically based on the general concept of SPM (planning and management systems) of projects. Key aspects of this methodology were discussed in an article on the topic. In this material, we develop the understanding of the theoretical and applied issues of network modeling that we have begun. First of all, we are interested in the development of a network diagram of the “vertex - work” type in the context of its compilation, optimization and adjustment. The network planning logic is quite simple, the method is not mathematically complicated.

However, it is not always possible to fully apply this model in practice. Difficulties arise, largely determined by the psychology of the participants who are not ready to objectively calculate the deadlines for completing the formulated tasks. This method gives a weaker result in conditions of congestion of responsible resources for project tasks. Network diagrams work well in projects where the responsible people are involved in only one project, such as in construction. Below is a model of the scheduling process that serves as a guideline for working with the network planning tool.

Project Schedule Development Scheme

Let's introduce the basic concepts that will be needed to compile the network model of the project and its optimization:

• the relation of precedence is a characteristic of the connection of subsequent work in relation to the previous one;
• a path is a continuous sequence of operations (works) in a network diagram;
• previous path - a section of the full path from the source to the event in question;
• subsequent path - a section of the full path from the event in question to any next one;
• the critical path is the full path characterized by zero slack;
• critical work - an action for which the total reserve has a value of zero;
• pre-critical work - an operation for which the project manager has set a total reserve limit number;
• path reserve - the difference between the time duration of the project and the path length on the graph;
• milestone - work with zero duration, denotes an important, significant event in the project;
• the minimum time from the start of the project to the start of the operation without violating the precedence relation is called the early start date;
• the maximum time from the beginning of the project to the start of the operation, which allows the project to finish on time without violating the precedence relation, is called the late start date;
• the minimum time it takes to complete all the work without violating the precedence relation is called the early end of the project;
• a renewable resource implies a restriction in its use at each step of the planning period;
• a non-renewable resource implies a restriction in its use for the entire period of the project.

Basic algorithm and types of network diagram connections

The network diagram allows you to see the structure of work, present all the stages and relationships with the required level of detail. On its basis, a reasonable action plan is developed, taking into account more effective use resources according to the given criteria. The diagram allows for a polyvariant analysis of alternative solutions to improve the schedule using computer technology. Let us recall the basic rules for constructing a network model of the "vertex-work" method.

1. Elements of a network diagram include activities and dependencies (connections) between them. Events are not displayed on the graph, except for milestones, which are the main most important events, depicted in the form of "diamonds", works with zero duration.
2. Work is an indivisible element of the process that requires time and other resources to complete, is depicted as a rectangle stretched horizontally. Based on this rule, the length of the rectangle may indicate the duration of the operation.
3. The development of the schedule begins with the placement of the original work on it at the leftmost point and ends with the inclusion of the final operation in it, which closes the project. calendar initial moment The initial activity indicates the start of the project.
4. Dependencies (connections) between jobs are drawn with arrows directed from left to right at different angles of inclination. Based this rule links between operations are defined by one of the forms of dependency relations.
5. A network diagram has only one job that has dependencies in but none comes out of, and one job that has no dependencies in it.
6. A network diagram cannot have cycles, i.e. dependencies should not tie jobs in a circle.

View of the network diagram of the "top - work" method

The network graph is built according to the following compilation algorithm.

1. The diagram contains the initial work of the project, which has no predecessors.
2. The location of the operation immediately following the work associated with it by a precedence relation, on the graph to the left of the previous one. Displaying a precedence relationship.
3. Go to step 2 until the work with predecessors ends.

The development of a network diagram is carried out taking into account possible connections between works. The main types of precedence relations are used in four types of links and in two additional varieties. Further, the diagram shows options for linking the next work by identification number to the previous one or, conversely, the next one. The main or basic types of precedence are associated with permutations of the words "beginning" and "ending":

• "end - start" (a simple type of precedence relation);
• "ending - ending";
• "beginning - beginning";
• "beginning - ending".

Examples of variants of precedence relations

Methods for calculating the duration of operations

To ensure the construction, analysis and management of the project schedule, it is necessary to calculate the following network schedule parameters: cost, resources involved and duration of work. The required resources must be calculated before determining the duration of operations, since their duration in time, as a rule, depends on the composition of the resource provision involved. In addition, it is important to understand how resources are calendar-available, which, in turn, affects the timing of work and its duration. Obviously, the key parameter is the duration of operations. To evaluate it, a number of special methods are used, a brief description of which are presented in tabular form below.

Basic methods for estimating the duration of operations

In the absence of statistical data on similar transactions and the impossibility of applying economic and mathematical methods of calculation, expert assessments are often used. This method has a serious advantage - its simplicity, provided that it was possible to attract experienced and objective experts. But this is not easy to achieve, the positions of experts on duration issues may turn out to be opposite. However, this state of affairs is quite acceptable when using weighted average estimates of qualified expert opinions.

In various projects, there are works that are identical in nature. For example, the preparation of a project charter, the development of technical specifications, and the holding of a tender in terms of structure and labor intensity are not much different from each other. This property is used to estimate the duration by analogues. In some cases, information about the parameters of similar work is quite acceptable to use for scheduling. To do this, the similarity of the type and content of operations must be subjected to examination.

Parametric duration estimation is closely related to the normative approach. This approach involves parameters such as productivity (production volume per unit of time) or output. For example, to perform the installation of the I-th level of complexity of equipment "A", it is required, for example, 100 standard hours of work of specialists of the highest qualification category. Such activities are also called fixed-volume work, because their duration is related to the number of allocated resources and can be estimated as the amount of work divided by the number of human resources.

In addition to the variant of a fixed volume, the case of a fixed duration of work is singled out separately. Examples of such work are actions related to the on-duty mode at the facility, equipment maintenance, etc. The duration in such cases is due to the duration of the serviced object. For the parametric method, as we can see, it is important to find a parameter that determines the duration of the operation and causal relationships, on the basis of which it is possible to determine the dependence of the parameter on other values.

Network Graph Optimization Methods

The network schedule of the project implementation is associated with the content of the unique task, the parameters of time and space in which the project is carried out. This activity has all the traditional management functions without exception. From this point of view, the process can be divided into stages, in which planning takes a significant share. The following is a simplified block diagram of the functional stages of project management.

Functional-process block diagram of project management

At the moment, we are interested in the optimization of the network schedule as a sub-stage of the process of planning a project task. This is due to the fact that after collecting information about the work and constraints, the development of a visual model in the form of a network diagram implies its further improvement using scheduling methods. There are two main methods: the critical path method (MCP for short) and schedule analysis using the PERT method.

When using the MCP, a sequential calculation of the earliest and latest terms of work on the project is performed. Next, the size of the total reserve is set, while the activities that have zero total reserve are considered critical work. Finally, the time reserves for performing operations are calculated, and the critical path is chosen as the longest path of the network. There can be multiple critical paths. Network graph optimization using the critical path method is applied to the following diagram models:

• for models with discrete and continuous time;
• for models with a simple precedence relation;
• in networks with generalized connections.

The Program Evaluation and Review Method (PERT) serves as the second method by which network optimization is carried out. Its main differences from the MCP are based on the assumption that the duration of the work is random, and for the purposes of estimation and analysis of the timing, the uncertainty of the time parameter of the project work should be taken into account. An assumption is also made about the independence of all random variables of the duration of the critical path. For these purposes, based on the method of mathematical statistics and probability theory, the β-distribution and the estimation of distribution parameters from three expert positions are used: optimistic, pessimistic and most probable.

Adjusting the network schedule and reducing the overall duration of the project are among the key tasks of the project manager. The MCP makes it possible to calculate the optimal timing of the project, but does not allow finding tools for a more effective reduction in its duration. In this regard, the critical path method is not flexible enough. The PERT method is also not without drawbacks. Firstly, it focuses mainly on the optimistic version of the assessment, and secondly, PERT is less applicable to small project tasks.

For effective correction, these are best suited modern methods, like the critical chain method and compression methods. We intend to pay attention to them in a separate article. All of these models and methods are the subject area of ​​PM competencies, having mastered which it is easier for a manager to demonstrate his effectiveness, achieving project results under time and resource constraints.

Network planning and management (SPM) is commonly understood as a graphical representation of a complex of interconnected design work, reflecting their logical sequence, interdependence and planned duration for the purpose of its use in operational management the progress of work during the implementation of the project.

Network planning and management is based on two methods (developed almost simultaneously and independently of each other): the MCP critical path method ( CPM- Critical Path Method) and method for evaluating and reviewing PERT plans (.PERT - Program Evaluation and Review Technique).

Planning and management in STC systems is carried out using a network diagram (plan, model).

Network diagram (plan, model, network) - graphic representation of a complex of interrelated design works (technological operations) performed in a certain sequence.

On fig. 10.1 presents a simplified calendar plan(line Gantt chart) construction and installation of equipment pumping station. The same plan can be depicted in a different, unusual form - graphic (in the form of graphs, Fig. 10.2).

The main elements of the network diagram are jobs (connections) and events, conventionally depicted by arrows and circles, respectively, for example, event 1 or event 3. Each job has one initial and one final event and is indicated (coded) by the numbers of these events, for example, job 1-2 or job 2-5 (see column “job code” in Figure 10.1).

Rice. 10.2.

Event in the network diagram, it displays only the fact of obtaining (achieving) the result of the previous work (works) and the condition for starting the work (works) following it. For example, event 2 means that the construction of the pumping station building has been completed and the installation of pumps and grounding has begun. There is always one initial (initial) and one (or several) final event in the network, all the rest are intermediate. The numbers inside the circle indicate the sequence numbers of events and are numbered arbitrarily.

Work- a separate process, the implementation of which is associated with the cost of time and resources (cost, material, etc.). The duration of work in time is indicated above the arrow in days (hours, weeks, etc.). According to the nature of the consumption of time and resources, three types of work are distinguished:

• work that requires cost and time and resources;
• waiting - a process that requires only time (for example, hardening of concrete);
• dummy job - a logical relationship (dependency) between two or more jobs, requiring neither time nor resources, but indicating that the ability to start one job directly depends on the results of another. The fictitious work (dependence) is depicted on the graph by a dotted arrow. Continuous sequencing of multiple jobs

forms a path in the network diagram, which is indicated by the numbers of the events through which it passes (for example, the path 1-4-5). Its length is equal to the sum of the duration of the jobs that make up this path.

The path with the longest length (from the start to the end event) is called the critical path. On the graph, it is depicted by a thick line (see Fig. 10.2).

Critical Path - the longest path from the start to the end event of the network. The activities that lie on this path are also called critical. It may seem illogical, but it is the longest duration of the critical path that determines the shortest total duration of work on the project as a whole. The duration of the entire project as a whole can be reduced by reducing the duration of the activities that lie on the critical path. Accordingly, any delay in the completion of critical path activities will result in an increase in the duration of the project.

Used in network planning and management critical path method (CPM) allows you to calculate possible schedules for the implementation of a set of works based on the described logical structure of the network and estimates of the duration of each work, determine the critical path for the project as a whole.

Rules for constructing a network diagram. When constructing a network diagram, they are guided by the rules, the main of which are as follows:

• the network diagram is carried out without scale, it should be simple, without unnecessary intersections;
• work-arrows can have arbitrary length, slopes and are directed from left to right;
• there should be no closed loops in the graphs, that is, it is necessary that the work does not return to the events from which it came out;
• “dead ends” must not be allowed in the network, that is, events from which no work comes out, if this event is not final (final) for this network;
• there should be no events in the network (with the exception of the initial one) that do not include any work.

The elements of the graph in the drawing are arranged in such an order that they depict the logical sequence of the execution of individual works, thereby determining the direction of transition from one event to another (from one work to another) or the sequence of events on a given path.

Network diagram calculation. The purpose of calculating the network schedule is to identify work time reserves that can reduce the duration of the entire complex of work when planning and optimizing the schedule; maneuver resources in the operational management of the progress of work in the implementation of the project.

The calculation of the time schedule (by time parameters) consists in determining the critical path, time reserves for events and work. At the end of the calculation, a check and conclusions are made. To determine the critical path, all possible paths of the schedule are written out, the duration of each of them is set by summing the duration of the activities included in this path.

The time parameters of a network diagram can be calculated in various ways. Manual calculation methods (tabular, sector, analytical, etc.) are used for small network graphs. To calculate network diagrams with more than twenty events, as a rule, special software (computer) software is used.

Time parameters of the network diagram and their calculation. The time parameters include: the reserve time of the event, the early and late dates for the completion of the event, the early and late dates for the start and end of work, the reserve of work time.

Event slack- such a period of time for which the accomplishment of this event can be delayed without violating the deadlines for completing the complex of works as a whole. It is defined as the difference between the late and early dates of the event.

Early completion date of the event- the time required to complete all the work preceding this event. It is determined by the duration of the maximum of all paths (or works) preceding the given event.

Late date of the event - such a deadline for the completion of the event, the excess of which will cause a similar delay in the occurrence of the final event. It is found by subtracting from the duration of the critical path the duration of the maximum path (or work) following a given event.

Working time reserve- a period of time within which it is possible to change the start and end dates of this work (and the completion of the event) without violating the end date of the entire complex of works. In network planning, a distinction is made between full, free and private work time reserves.

Full working time reserve - The maximum period by which the duration of a given activity can be extended without changing the duration of the critical path. It is defined as the difference between the late and early start times or late and early finish times.

Early start time coincides with the early completion date of the initial event for this work.

Late start time is equal to the difference between the late completion date of the end event for this activity and the duration of the activity.

Early end of work is equal to the sum of the early deadline for the completion of the initial event for this work and the duration of the work.

Late end of work coincides with the late completion date of the final event for this work. Individual works, in addition to the full reserve of time, may have free and private reserves of time.

In table. 10.1 and 10.2 show the results of calculating the network graph shown in fig. 10.2.

Table 10.1

Calculation of network events (Fig. 10.2)

Event number	Event dates		Event time reserve, days

Table 10.2

Calculation of the work of the network schedule (Fig. 10.2)

	Duration of work, days	Work start date		Completion date		Total reserve of work time, days.

Network graph optimization. Under the optimization of the network schedule, one should understand the reduction in the duration of the critical path due to the reserves of work time, if it (duration) is greater than the directive (given).

If the initial version of the network schedule does not ensure compliance with the directive (set) deadlines, then the planned parameters of the network model are changed to reduce the planned time for the implementation of the entire set of works. There are the following possible ways (methods) to reduce the planned term for the implementation of the entire complex of works: replacement of sequential execution of works by parallel ones (where it is possible according to the technology conditions); reallocation of resources between jobs - transfer work force, mechanisms and other things from the work of unstressed paths (having a reserve) to the work of the critical path.

The result of optimization should be the adjustment and recalculation of the network diagram.

Optimization problems in network planning do not have a rigorous analytical solution due to the non-linear nature of the dependence of the time to complete the work and the number of workers employed in these jobs, and are solved heuristically, in accordance with the experience and intuition of the manager conducting the optimization. At the same time, these optimization methods give satisfactory results.

Developing project network schedules takes time and therefore money. But is it worth doing these developments? The answer is definitely yes, except for minor and short-term projects. The network diagram is easy to understand, as it is a visual graphical representation of the sequence of work in a project. Once a network schedule has been developed, it is easy to modify and change if something unexpected happens during the project. For example, if there is a delay in the delivery of materials needed to complete some work, the consequences of this can be quickly assessed and the entire project revised in a few minutes using a computer. The information obtained during the network plan revision process can be quickly communicated to all project participants.

The network diagram carries important information, revealing internal communications project. It serves as the basis for scheduling work and equipment use; facilitates the interaction of all managers and performers in the process of achieving the established goals in terms of time, cost and quality of the project; allows you to make a rough estimate of the duration of the project, and not just determine the completion date of the project according to someone's desire. The network schedule makes it possible to estimate the periods during which the execution of work can begin and end, as well as the time of acceptable delay in their execution. It creates the basis for calculating the financial supply flows of the project; allows you to determine which work is "critical" and, therefore, must be carried out strictly on schedule so that the project is completed on schedule; shows which work needs to be revised if a shorter time frame is required to complete the project on time.

There are other reasons why you should pay close attention to a project's network schedule. The network schedule minimizes the risks associated with project execution. It is often said in practice that three-quarters of the project management time is spent on the network scheduling. Perhaps this is an exaggeration, but it shows that the project leaders understand the importance of this work.

Conclusion

Thus, Chapter 10 outlines the classical methods (approaches) for planning and managing innovation, investment and other projects. Of greatest interest are the methods of network planning with the calculation of the parameters of the network schedule (project implementation plan). However, despite the solid history and timing of the practical application of the critical path method (CPM) and the method of evaluation and revision of plans (PERT), they remain relevant at the present time, as they allow quite objectively predicting high performance and efficiency in managing the implementation of innovative and other projects.

• See: Naumov L.F., Zakharova L.L. Decree. op. pp. 141 - 149.

Risk reduction methods.

Personnel management methods.

Work content management methods.

Project cost control methods.

Simulation modeling on a computer.

resource planning. Logistics.

Network planning and management, scheduling.

TOPIC 4. PROJECT MANAGEMENT METHODS (4 hours)

Dolyatovsky Dolyatovsky Research of control systems

Ignatieva, Maksimtsov Research of control systems

Basic concepts

Network diagram.

Methods of network planning.

Critical Path.

Leeway.

Development of a network model.

Calendar planning.

Full reserve.

Schedule calculation.

Network diagram (network, network graph, PERT diagram) - a graphical display of the project work and the dependencies between them. In project planning and management, the term "network" refers to the full range of activities and project milestones with the dependencies established between them.

Network diagrams display a network model graphically as a set of vertices corresponding to jobs, connected by lines representing relationships between jobs. This graph, called a node-work network or a precedence-follower diagram, is the most common representation of a network (Figure D.1).

There is another type of network diagram - a node-event network, which is rarely used in practice. With this approach, work is represented as a line between two events (graph nodes), which, in turn, display the beginning and end of this work. PERT charts are examples of this type of chart (Figure D.2).

A network diagram is not a flowchart in the sense that this tool is used to model business processes. The fundamental difference from the flowchart is that the network diagram displays only logical dependencies between jobs, and not inputs, processes and outputs, and also does not allow repeating cycles or so-called loops (in the terminology of graphs, an edge of a graph emanating from a vertex and returning to the same vertex, Fig. D.3).

Network planning methods are methods whose main goal is to minimize the duration of a project. They are based on the Critical Path Method (CPM) and the PERT (Program Evaluation and Review Technique) developed almost simultaneously and independently.

Critical path - the longest complete path in the network is called critical; jobs along this path are also called critical jobs. It is the duration of the critical path that determines the shortest total duration of work on the project as a whole. The duration of the entire project as a whole can be reduced by reducing the duration of the activities that lie on the critical path. Accordingly, any delay in the completion of critical path activities will result in an increase in the duration of the project.

The critical path method allows you to calculate possible schedules for the implementation of a set of works based on the described logical structure of the network and estimates of the duration of each work, to determine the critical path for the project as a whole.

The network diagram of the critical path can be built as shown in Fig. D.4.

The total reserve of time, or the margin of time, is the difference between the dates of the late and early finishes (starts) of work. The managerial meaning of the reserve of time lies in the fact that, if necessary, to resolve the technological, resource or financial constraints of the project, it allows the project manager to delay work for this period without affecting the completion date of the project as a whole. Activities on the critical path have a slack of zero.

Gantt Chart- a horizontal line chart, on which the tasks of the project are represented by segments extended in time, characterized by start and end dates, delays and, possibly, other time parameters. An example of displaying a Gantt chart is shown in fig. D.5.

The network model development process includes:

Definition of the project work list;

Evaluation of work parameters;

Determine dependencies between jobs.

The definition of a set of works is carried out to describe the activities of the project as a whole, taking into account all possible works.

Evaluation of work parameters is a key task of the project manager, who involves team members responsible for the implementation of individual parts of the project to solve this problem. The value of schedules, cost and resource plans obtained as a result of network model analysis depends entirely on the accuracy of estimates of the duration of work, as well as estimates of the needs of work in resources and financial resources.

Determination of dependencies between works is necessary for calculating the schedule for the project. A precedence relationship displays a logical relationship between activities in a schedule. The most common reason for such dependences is technological limitations (the start of some works depends on the results of others), although there may be limitations dictated by other considerations. These links form the structure of the network. The totality of interrelations between works determines the sequence of work execution.

The final step in determining dependencies is to check the relationships for loops and other logical errors. After building the network structure and performing time estimates, the project team has everything it needs to calculate the schedule.

Scheduling requires certain inputs. After their input, the procedure of forward and backward pass through the network is performed and the output information is calculated.

The following input data is required to calculate the calendar schedule:

- set of works;

- dependencies between jobs;

- estimates of the duration of each work;

- project working time calendar (in the most general case, it is possible to set your own calendar for each job);

- resource calendars;

- restrictions on the start and end dates of individual works or stages;

- calendar start date of the project.

Any change to the project start date will result in a recalculation of the due dates for each activity. For detailed planning processes, start dates for subprojects or work packages are determined based on the master plans. Given the input data, the procedure for calculating the schedule forward and backward is performed and the output information is calculated.

Calculation of the schedule ahead begins with activities that do not have predecessors. In its course, it is determined early dates works, which are understood as the earliest possible start dates and completion of works, provided that the previous works are completed:

Backward scheduling starts with jobs that have no successors. In its course, it is determined late dates works, which are understood as the latest possible dates for the commencement and completion of works, provided that the completion date of the project is not delayed:

Based on the calculated early and late start dates of work, the amount of time reserves for each work is determined.

The full reserve is the most significant of all reserves. It represents the amount of time that the completion date can be delayed without delaying the project's planned completion date. Free slack indicates the amount of time a job can be delayed without affecting the full slack of subsequent network jobs (without delaying their early start).

The results of MCP calculations allow to obtain:

- the total duration of the project and the calendar date of its completion. In order for the team to determine acceptable results in terms of goals, further research on the “what if” scenario is possible;

- activities on the critical path. Any delay in such work will delay the completion date of the project. All critical activities have a lead time that is generally zero, which means that their early and late due dates are the same;

- early and late calendar start and end dates for each job.

MCP analysis (scheduling method) does not require setting hard start dates for activities that are not on the critical path. Unlike critical activities, they can be scheduled at any time between their early and late dates.

PQM calculation and scheduling analysis using computer tools can be carried out as needed, whenever information is updated or the external conditions of the project change.

Information obtained as a result of calculations can be presented either in tabular form (Fig. D.6) or in the form of a calendar-network diagram.

Networked process planning is a general tool for project management. It helps to maximize the potential of the company's employees, carry out innovative developments and bring new brands to the consumer market.

Peculiarities

Network planning and management allows you to determine the approximate end date of the project by analyzing the timing of its implemented and unrealized parts. It is based on simple mathematical modeling complex measures and point actions to solve one specific problem. In fact, planning is a complex of settlement, organizational and graphic methods, which allow not only to carry out high-quality development of the project, but help to rebuild it in real time, depending on changing external conditions.

It allows you to evenly distribute tasks, taking into account:

• limited resources (tangible and intangible);
• regularly updated information;
• tracking deadlines.

This method minimizes risks and eliminates the possibility of a deadline. A systematic approach is widely developed in network planning. Often, the launch of a project requires the work of employees from different departments of the enterprise (sometimes even outsourced specialists are involved), so only their coordinated actions in a single organizational system will make it possible to complete the work on time.

The key goal of network planning in management is to reduce the duration of the project, while maintaining the parameters of quality and volume of production.

Applications

Network methods of business process planning and enterprise management are popular in various fields of activity. They have found the greatest application in those projects in which you must first come up with and create New Product, and only then offer it to the consumer. These business areas include:

• R&D;
• innovative activity;
• technological design;
• pilot production;
• automation of business processes;
• testing of serial samples;
• modernization of equipment;
• market research;
• personnel management and recruiting.

Tasks to be solved

The introduction of network planning and management models at the enterprise allows solving a whole range of tasks:

• time analysis of the project:
  • calculation of terms of performance of works;
  • determination of temporary reserves;
  • finding problematic project areas;
  • search for critical ways to solve problems;
• resource analysis, which allows to draw up a calendar plan for spending available resources;
• project modeling:
  • determination of the scope of the required work;
  • establishing a relationship between them;
  • building a hierarchical business model of processes;
  • determination of the interests of all project participants;
• allocation of available resources:
  • increase in income depending on the existing needs;
  • minimization of terms and volumes of supplied resources in one part of the project and their increase in another.

But the exact formulation of the tasks of planning and rational management depends on the industry for which the business project is being developed. In some industries, the human (non-material) resource is considered the main one, and its spending depends not only on the funds invested by the enterprise for training and licensing, but also on the personal potential of employees, which is extremely difficult to measure.

Tools

Graphs or diagrams are considered the main tools for time and resource planning. They allow you to visually determine the status of the work being performed and the relationship between them. Network planning schedule and effective management shows the timing of operations, the required resources and cash costs. There are two types of charts:

• modeling the project in the form of a set of vertices connected by lines that show the relationship between work;
• displaying work as a line between events (“top-event”).

The first method is used more often, because network planning is more productive to start directly from the work performed and the required resources, and not from the exact start and finish dates of the project.

Step-by-step construction of a network diagram

As part 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;
• setting possible restrictions (resources, finances);
• determination of the set of actions that are needed to achieve the goal (all actions are drawn up in separate files, loaded into a program such as MS Visio or written on ordinary 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 start and end dates of the process);
• calculation of the slack for each activity (the difference between early and late start or end of the project);
• definition of a critical path in which there is no slack for each activity, i.e. all of them are performed smoothly, quickly and without interruptions.

Benefits of using

The first network diagram was applied in the 50s of the last century, but so far it has not lost its relevance. This is due to its undoubted advantages. After all, with the help of diagrams, you can:

1. implement a coherent, reasonable and operational planning critical business processes;
2. choose the optimal duration of the process;
3. identify and use available reserves;
4. promptly adjust the work plan depending on changes in external factors;
5. fully implement a systematic approach in production;
6. apply computer technologies that increase the speed and quality of building network models.

Planning Methods

Within project management, various network planning methods are used. The use of certain technologies is associated with variable or unchanged 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 building deterministic models:

• 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 solving production problems due to rational use resources or reduce design time.

Probabilistic models

These methods are used in cases where the exact duration and sequence of work performed is not known. 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 build them:

• PERT (for program evaluation and analysis);
• Monte Carlo (simulation modeling of project stages);
• GERT( program analysis and graphical evaluation).

Additional Methods

There are also additional models of graphic construction:

• matrix method of the 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 start and end dates of work;
• four-sector method.

The use of certain construction methods is associated with the goals and objectives of planning. 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 the enterprise is to reduce the duration of the project, and not to increase it. Therefore, for effective work only those methods and technologies that will be understood by employees should be used.

network charts