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 of 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 of a software package". Suppose that the project consists of works, the characteristics of which are given in Table 2.1.

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.

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.

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.

Scheduling is one of the key concepts of the organization of construction, it ensures the development of the project in time, just as the construction plan ensures the development of the project in space. Scheduling creates the basis for resource management of all kinds, for work planning and building production efficiency. The calendar schedule is a visual means of representing the development of construction over time, it is convenient for determining the consumption of resources. However, it is difficult, and sometimes impossible, to calculate the total duration of construction from it. It is also difficult to single out processes that are important and unimportant for achieving the final result. To eliminate these shortcomings in the middle of the XX century. a mathematical model of the development of the project was developed, which received the name "network diagram" in construction.

Scheduling tasks

Construction time management is a direct task of a manager of any rank, customer and contractor services, regardless of the scale and type of construction. At the same time, a number of issues fall into the scope of management, including financial and resource planning, control of the timing and cost of work, adjustment of technology and sequence of work. With time management, the duration of construction work and individual production operations may change, resource consumption and construction costs may change.

When adjusting the construction time, it can theoretically be beneficial to both reduce and increase the duration, since there are factors that improve the technical and economic indicators in both cases. For example, shorter construction times reduce overhead costs, reduce the risk of contract defaults, and longer construction times reduce the amount of temporary facilities needed and the number of workers on site at any one time (see paragraph 25.4). Thus, there is some optimal duration of work. However, in the vast majority of cases, construction falls behind the optimal schedule, so reducing construction time is the most pressing issue. This task is equally important for the investor, customer and contractor.

The second task of scheduling is to improve the uniformity of resource spending. This task is most important for non-consumable resources (labor and technical), since the uneven consumption of them immediately leads to downtime and, as a result, financial losses. However, the uniformity of the use of consumable resources (materials) is also useful, since it leads to a decrease in the size of warehouses and the number of vehicles. With a given maximum amount of resource expenditure (for example, the maximum number of skilled workers), it is often necessary to reduce the intensity of their consumption by artificially stretching the duration of work. The solution of this problem is of the greatest importance for contractors.

The third task of scheduling, which is mainly solved by the general contractor, is the optimal distribution of work between subcontractors and departments with the timely preparation of the front of work, the mutual linkage of production activities, the establishment of clear guidelines and delivery stages. At the same time, it is necessary to integrate the planning and administrative functions of subcontractors into a single system, establish control over the timing of the implementation of heterogeneous work, and create reserves both in terms of productivity and work time.

When setting the task of identifying the optimal schedule, the question arises about the criteria for assessing the quality of the plans being developed. Various criteria can be used, the most important of which is the minimum of discounted costs, taking into account various effects from changes in the duration, intensity, sequence of work. At the same time, private criteria for reducing the duration of construction, reducing labor costs, and improving the uniformity of work can be used. In particular, to assess uniformity, the indicator of uneven use of resources (for example, labor) can be used:

where Rmax and R c p - maximum and average intensity of resource use.

Thus, drawing up an optimal schedule is a complex multi-criteria task, ideally solved taking into account the interests of all construction participants. At the same time, the calendar plan, regardless of its type, should be the basis for developing contractual terms and volumes performed by contractors, for establishing mutual sanctions and contractual conditions.

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 of 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 of a software package". Suppose that the project consists of works, the characteristics of which are given in Table 2.1.

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.

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.

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.

A project manager at the planning stage is often faced with a situation where the structure, milestone plan, and responsibility matrix alone are not enough to develop a project schedule. This occurs for very large project tasks, where the content of the planned work needs to be carried out in the most rational way, while reducing the consumption of time resources. Network planning can come to the aid of a project manager as an instrumental solution implemented according to a standard optimization algorithm.

Network modeling method

Network planning and management has been actively developed since the 1950s, first in the USA, then in other developed countries and in the USSR. Such network planning methods as CPM, PERT allowed to significantly raise the "bar" of project management in the direction of optimizing the time and content parameters of work schedules. This made it possible to develop project schedules based on a more efficient network modeling methodology that incorporates all the best practices (a diagram of scheduling methods is given below). The network diagram has various names, among them:

• network chart;
• network model;
• net;
• network graph;
• arrow diagram;
• PERT chart, etc.

Visually, the network model of the project is a graphical diagram of a sequential set of works and links between them. It is worth noting that the project planning and management system is holistically displayed in a graphical form of the composition of operations, their time spans and interrelated events. The basis of the model construction method is a branch of mathematics called graph theory, which was formed in the early 50s - late 60s.

Scheduling and Project Management Methods

In the network planning and management model, a graph is understood as a geometric figure that includes an infinite or finite set of points and lines connecting these lines. The boundary points of a graph are called its vertices, and the points oriented in the directions connecting them are called edges or arcs. The network model includes directed graphs.

Type of directed graph

Let's analyze other basic concepts of the network model of the project.

1. Work is a part of a production or project process that begins and ends in the form of a quantitatively described result, requiring time and other resources. The work is reflected in the diagram in the form of a unidirectional arrow line. We can consider operations, events and actions as the form of work.
2. Event - the fact of completion of work, the result of which is necessary and sufficient to start the implementation of the following operations. The type of event on the model is reflected in the form of circles, rhombuses (milestones) or other figures, inside which the identification number of the event is placed.
3. A milestone is work with zero duration and denotes an important, significant event in the project (for example, the approval or signing of a document, the act of finishing or starting a project stage, etc.).
4. A wait is a procedure that consumes no resources other than time. Displayed as a line with an arrow at the end with a duration mark and an indication of the name of the wait.
5. Dummy job or dependence - a type of technological and organizational connection of works that does not require any effort and resources, including time. Shown as a dotted arrow on a network diagram.

Relationship options and precedence relation

Network planning methods are based on models in which the project is presented as an integral set of interrelated activities. These models are largely formed by the type and type of links between project implementation operations. From the point of view of the type, hard, soft and resource ties are distinguished. The specific difference in the interconnectedness of operations is based on the relation of precedence. Consider the main types of communication.

1. Soft connections. They correspond to a special, "discretionary" logic, which provides a "soft" basis for choosing operations to be placed on the diagram, dictated by technology. While the technology has developed over many cycles for a long time, business rules are being developed that do not require additional fixation and planning. This saves time, model space, cost and does not require additional control from the PM. Therefore, the project manager himself decides whether he needs such a dedicated operation or not.
2. Hard connections. This type of connection is based on technological logic. They prescribe the execution of specific actions strictly after others, which is consistent with the procedural logic. For example, adjustment of equipment can be carried out only after its installation. It is permissible to test technology shortcomings if it has been put into trial operation, etc. In other words, the adopted technology (no matter in what area it is implemented) rigidly imposes a sequence of activities and events of the project, which determines the appropriate type of communication.
3. Resource links. When several tasks are assigned to one responsible resource, it becomes overloaded, which can lead to an increase in the cost of the project. By adding an additional resource to a less critical task, this can be avoided, and such links are called resource links.

At the time of the formation of the project schedule, hard ties are applied first, and then soft ties are applied. Further, if necessary, some soft links are subject to reduction. Due to this, some reduction in the overall duration of the project can be achieved. In conditions of congestion of some responsible resources due to parallel work, it is permissible to resolve the conflicts that have arisen by introducing resource links. However, it should be controlled that new connections do not lead to significant changes in the overall plan.

Associated works as a certain sequence of the design task are connected with each other. Let's call them operations A and B. Let us introduce the concept of a precedence relation, which is considered as a certain restriction on the timing and total duration, since operation B cannot begin until the end of operation A. This means that B and A are connected by a simple precedence relation, while it is not at all necessary that B begins at the same time as A ends. For example, finishing work begins after the construction of the roof of a house, but this does not mean that they should be carried out at the same moment when the specified event occurs.

Network model method number one

Network planning and management (SPM) involves two options for constructing a network diagram of a project: "edge - work" and "top - work". In the first version of the chart display, the critical path method and the PERT method are implemented. The method has a different name - "top - event", which, in fact, reflects the other side of a single content. In the English interpretation, this version of building a network model is called AoA (Activity on Arrow Diagramming) by abbreviation. Project events dominate the method. Events are of three types:

• initial event;
• intermediate event;
• end event.

The structure of the design task is such that in the process of its implementation there is only one initial and one final event. No work is done before the start event and after the end event. At the time of the end event, the project is considered completed. All incoming operations must be completed before the intermediate event occurs. It gives rise to all operations outgoing from it. Dummy jobs are applied after jobs if it is not known which one will be the last one.

An example of a network diagram of the "edge - work" method

Network planning when building an AoA network diagram is guided by the following set of basic rules.

1. Design events are subject to consecutive numbering. Numbers are assigned to events without gaps.
2. There must be only one start and end event.
3. Work cannot be scheduled and placed in the direction of a project event that has a lower number than the original event.
4. A closed sequence of operations is not allowed, and arrow lines are placed in the direction from left to right.
5. Double links between events are not allowed.

The diagram formation algorithm is as follows.

1. Place the start event on the left side of the field.
2. Find in the list works that do not have predecessors, and place their final events on the diagram to the right of the initial event without indicating numbers.
3. Connect the start and just placed events with arrow work lines.
4. From the list of jobs that are not yet on the diagram, select the job for which the predecessor has already been placed.
5. To the right of the previous event, insert a new event without a number and link them to the selected job.
6. Given the precedence relation, connect the start event of the placed job and the event placed on the network diagram with a dummy job.

Network planning and management (SPM) is commonly understood as a graphical representation of a complex of interrelated design works, reflecting their logical sequence, interdependence and planned duration in order to use it in the operational management of the progress of work in 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 shows a simplified schedule (Gantt line chart) for the construction and installation of pumping station equipment. 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 (encoded) 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 that requires neither time nor resources, but indicates 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)

Table 10.2

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

Network graph optimization. The optimization of the network schedule should be understood as the reduction of 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: replacing the sequential execution of works with parallel ones (where this is possible according to the conditions of the technology); reallocation of resources between jobs - the transfer of labor, 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 of work execution and the number of workers employed in these works, 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 the internal connections of the 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 reviewed 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.