Scheduling is one of the key concepts of construction organization; it ensures the development of a project in time, just as a construction plan ensures the development of a project in space. Scheduling provides the basis for resource management of all types, work planning and efficiency. construction production. The calendar schedule is a visual means of presenting the development of construction over time and is convenient for determining the consumption of resources. However, it is difficult and sometimes impossible to calculate the total duration of construction using it. It is also difficult to identify processes that are important and unimportant for achieving the final result. To eliminate these shortcomings in the middle of the 20th century. A mathematical model for the development of the project was developed, which in construction was called a “network diagram”.

Scheduling tasks

Managing construction deadlines is a direct task for managers of any rank, customer services and contractors, 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 timing and cost of work, adjustment of technology and work sequence. When managing deadlines, duration may change construction work and individual production operations, resource consumption and construction costs may change.

When adjusting construction time, theoretically it can be beneficial to either reduce or increase the duration, since there are factors that improve the technical and economic indicators in both cases. For example, by reducing construction duration, overhead costs are reduced and the risk of non-fulfillment of contractual obligations is reduced, and by increasing construction duration, the required volume of temporary structures and the number of simultaneously employed workers on site are reduced (see paragraph 25.4). Thus, there is a certain optimal duration of work. However, in the vast majority of cases, construction is delayed relative to the optimal schedule, so reducing construction duration is the most pressing task. This task is equally important for the investor, customer and contractor.

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

The third task of scheduling, which is solved mainly by the general contractor, is the optimal distribution of work between subcontractors and departments with timely preparation of the scope of work, mutual coordination production activities, establishing clear guidelines and delivery stages. At the same time, it is necessary to integrate the planning and administrative functions of subcontractors into unified system, establish control over the timing of various types of work, create reserves both for productivity and for the time of work.

When setting the problem of identifying the optimal calendar plan 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 discounted costs, taking into account the various effects of changes in the duration, intensity, and sequence of work. At the same time, private criteria can be used to reduce construction duration, reduce labor costs, and improve the uniformity of work. In particular, to assess uniformity, an 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 performers, for establishing mutual sanctions and contractual conditions.

1. Planning and control as one of the functions of project management.
2. Basic methods of calendar and network planning in construction.
   • The main processes of the "Planning" and "Control" groups.
   • The main causes of errors in project planning and control.
3. Construction project scope management.
   • Gathering requirements, assumptions and limitations of the project.
   • Decomposition. Development of ISR.
4. Construction project time management. Development of a project schedule.
   • Schedule and network schedule of the project and the purpose of its development.
   • Logic of chart formation.
   • Initial data for generating a graph. Definition of operations. Decomposition. Planning by the rolling wave method.
   • Sequence of development of the project network schedule.
   • Definition of dependencies, advances and delays.
   • Estimating the duration of operations: tools and methods.
   • The concept of resources, types of resources, main stages of resource planning, methods for eliminating resource conflicts.
   • Critical path, critical chain.
   • Characteristics of the critical path method (CPM).
   • Project time reserve, buffer reserve.
   • Monitoring the project schedule.
   • The main types of reports on the progress of the project, forms for presenting data in reports, forms for presenting a network diagram.

Scheduling software

1. Application tools MS Project 2013. Practical work.
   Introduction to MS Project 2013.
   • Corporate project management system Microsoft Enterprise Project Managemant. Features of MS Project 2013 Professional. Interface. Initial parameters.
   Formation of an enlarged construction schedule.
   • Task scheduling modes.
   • Entering project stages.
   • Determination of target dates for project stages. Formation of an enlarged project budget. Maintain the project baseline.
   Project structure.
   • WBS Work Breakdown Structure. Detailing of project stages. Tasks. Changing the task hierarchy level. Summary and detailed tasks. Setting up WBS codes. Adding and removing fields in a spreadsheet.
   • Dependencies between tasks. Estimating the duration of project tasks.
   • How to create a project schedule in MS Project. Critical tasks, critical path.
   Project resources.
   • Resource assignment, resource calendars, resource sheet, resource leveling.
   Monitoring the implementation of the project.
   • Basic plan. Setting up a workspace for tracking and control. Conclusion of the planned percentage of work completion. Select the status report date. Entering actual data on the progress of the project. Forecast of expected project completion dates.
   Project reporting.
   • Reporting, baseline plan, task control. Generating a cash flow report.
   Additional program features.
   • Interrupted and repetitive work. Insert hyperlinks, pictures, and text fields. Moving a project. Accounts. Global template and organizer. View project statistics. reference system programs.

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

2.1. Theoretical course

2.1.1. Structural planning

Structural planning includes several stages:

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

The main role at the stage structural planning plays network diagram.

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

The network diagram must satisfy the following properties.

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

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

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

Rice. 2.1.

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

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

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

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

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

Critical jobs have equal early and late start times.

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

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

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

Here are many works directly following the work.

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

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

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

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

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

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

Book: Project Management - Lecture Notes (UDPSU)

2. Development of a project plan

3. Work distribution structure (decomposition) (WDS)

4. Detailed calendar and network planning

5. The relationship between budget and scheduling

Detailed project planning determines the structure of functional work packages, timing and features of their implementation. Availability and control of detailed work schedules is one of the main requirements project management after the start of its implementation.

In the process of project implementation, we use Various types detailed plans, which can be classified as follows:

Fig. 13. Classification of calendar plans Schedules (Gantt charts are horizontal linear graphs that quite clearly represent the ratio of the time for completing individual works, loading of specific technological equipment, but do not allow establishing logical relationships and interdependence various types works Therefore, it is advisable to use a Gantt chart for qualitative analysis uniform loading of production areas.

Schedule plans include in the list of works decisions on the results of the work and auxiliary work (transfer of information, control of results, etc.), which allows you to see the mutual dependence of the work that is included in the plan.

Program Estimation and Review Technique (PERT) is an event-driven network analysis method used to estimate the duration of a project with a high degree of non-existence with estimates of the duration of individual activities. PERT uses the critical path method to weight the average duration, it provides an approximate estimate of the likely completion time of activities and is recommended for the analysis of projects with significant risk.

Network diagrams are methods whose main goal is to minimize the duration of a project; they include the critical path method (MCM or CPM - Critical Path Method) and PERT - Program Evaluation and Review Technique).

The network planning process assumes that all activities will be described in the form of a set of works; for this it is necessary to determine:

· list of works;

· main parameters of work;

· identifying interdependencies between activities.

The critical path method (CPM) (CPM) is a network analysis method that is used to predict the duration of a project by analyzing which sequence of activities has the least design flexibility (slack amount).

The critical path is a series of activities that determines the earliest completion of a project. This method allows you to establish logical relationships and interdependence of work, as well as establish the time for completion of the relevant work and the plan as a whole. An important element of the network schedule is the continuous sequence of work.

Depending on the degree of detail, there are: initial, unit and summary grids.

Initial meshes are the most detailed. They are compiled weekly at the level of specific performers, displaying all the works and their relationships.

Unit meshes are more generalized; they combine the initial meshes of a given object.

The summary grid combines the full range of work of all objects. It is developed based on the integration of initial and single grids.

MCS scheduling requires some input data. After they are entered, a forward and reverse pass through the network is carried out and information about the possible completion dates of the project is determined.

To calculate the schedule for MCS, the following data is required:

· set of works;

· interconnectedness of works;

· estimates of the duration of each job;

· project working time calendar (in some cases it is possible to create a calendar for each job);

· resource calendars;

· restrictions on the beginning and end of individual works and stages;

· calendar start date of the project.

Any change in the project start date will result in a change in the deadlines for each job.

Plan for presenting and mastering the material

6.1 Mathematical methods for project planning

6.2 Project network planning

6.3 Project scheduling

6.4 Project optimization

Mathematical methods for project planning

Mathematical methods such as modeling, linear programming, dynamic programming, game theory and others can be used to determine

optimal plan, but in such problems the number of variables and constraints is very large, so it is not always possible to use mathematical capabilities, and then iterative methods are used that use heuristics, which allows one to determine, if not the optimal plan, then at least acceptable.

Network project planning

Together with line graphs and tabular calculations, network planning methods find wide application when developing long-term plans and models for creating complex production systems and other long-term use facilities. Network work plans of an enterprise to create new competitive products contain not only the total duration of the entire complex of design, production and financial and economic activities, but also the duration and sequence of individual processes or stages, as well as the need for the necessary economic resources.

Network planning - one of the forms of graphical reflection of the content of work and the duration of implementation of plans and long-term complexes of design, planning, organizational and other activities of the enterprise, ensures further optimization of the developed schedule based on economic-mathematical methods and computer technology.

Application of network planning helps answer the following questions:

1. How long does it take to complete the entire project?

2. Within what time should individual works begin and end?

3. What work is “critical” and must be completed exactly on schedule so as not to miss the deadlines for the project as a whole?

4. How long can the execution of “non-critical” work be postponed so that it does not affect the project deadlines?

Network planning consists primarily of constructing a network diagram and calculating its parameters.

Network model - a set of interconnected elements to describe the technological dependence of individual works and stages of future projects. The main planning document of the network planning system is network diagram , which is an information-dynamic model that reflects all the logical relationships and results of work necessary to achieve ultimate goal planning.

Works in a network diagram any production processes or other actions that lead to the achievement of certain results or events. Work should also include possible expectations of starting following processes associated with interruptions or additional time costs.

Events the final results of previous work are called. An event represents the moment at which a planned action is completed. Events are beginning, ending, simple, complex, intermediate, antecedent, consequent, etc. at all

In network graphs, an important indicator is the path that defines the sequence of activities or events in which the result of one stage coincides with the initial indicator of the next phase. On any graph it is common to distinguish several paths:

The full path from the start to the end event;

The path preceding this event from the initial one;

The path following the given event to the final one;

A path between several events;

The critical path from the initial to the final event of maximum duration.

Network graphs are plotted from left to right with a graphical image design work and determining the logical connections between them. Depending on the method of representation, there are the following types of network diagrams: arrow diagrams; graphs of the previous one.

Arrow charts began to be used in the 50s. They looked like an image of a job in the form of an arrow, and the connections between the jobs were depicted in the form of circles and events that had serial numbers were named (Fig. 6.1).

Rice. 6.1. arrow chart

Previous graphs began to be used in the 60s of the last century. Unlike arrows, works are presented in the form of rectangles, and arrows indicate logical connections (Fig. 6.2).

Previous graphs have their advantages, since such graphs are easier to create by first drawing all the rectangles - the work, and then indicating the logical connections between them. For antecedent graphs it is easier to create computer programs which are in use today. It is easier to move from the previous charts to Gantt charts, which are a form of scheduling.

The idea of ​​graphically depicting the relationships between works is not new. New are the method of optimizing hourly and cost parameters, the critical path and information processing when using a computer. The combination of new methods with old ones led to the creation of the Perth system (method of evaluation and revision of plans). With Perth, managers can quickly identify bottlenecks in schedule performance and allocate resources appropriately to eliminate backlogs. The Perth system can be implemented in several options:

Perth / hour

Perth / expenses.

Rice. 6.2. Previous schedule

The first method has the following features: network schedule, time-based estimates, determination of time reserves and the critical path, taking, if necessary, operational measures to adjust the schedule.

The Perth network diagram shows the sequence of steps required to achieve a goal. It includes events, jobs, and dependencies.

Each job typically requires one to three time-based estimates.

The first is carried out for the critical path.

The second determines the expected date of occurrence of any event.

The third estimate is to find the latest "late" date that does not delay the entire project.

The Perth/Cost method is a further development of the Perth/Hour method in the direction of optimizing network schedules by cost. It is characterized by the following stages:

1. Conducting a structural analysis of the project work.

2. Determination of types of work.

3. Construction of network diagrams.

4. Establishing relationships between the duration of work and cost.

5. Periodic adjustments to the grid and estimates.

6. Monitoring the progress of work.

7. Carrying out, if necessary, measures that would ensure the execution of work according to plan.

Total costs are broken down into elements until they reach such a size that they can be planned and controlled. These elements are the cost of individual works, while individual works are assigned cost values, which allows summing up the cost of groups of works at all levels of the work structure.

As A. Ilyin notes, there are about 100 varieties of the Pert method, but they have General characteristics; These include the following features of the use of this method:

The system forces you to carefully plan the projects for which it is used;

Perth provides the opportunity to model and experiment;

The use of the method expands the participation of lower-level specialists in planning;

Increases control efficiency;

The method is used to solve diverse planning problems;

For complex networks, the cost of using the Perth system is significant, which is a limitation in its use at small sites;

Inaccurate estimates reduce the effectiveness of the method;

If the occurrence of events cannot be predicted (as, for example, in scientific research), then the system cannot be used.

Network models are widely used at domestic enterprises when planning pre-production and developing new products. Network planning allows not only to determine the needs of various production resources in the future, but also to coordinate their rational use at the moment.

The most important stages of network planning are:

Distribution of a set of works into separate parts and assigning them to performers;

Identification and description by each performer of all events and work necessary to achieve the goal;

Construction of primary network diagrams and clarification of the content of planned work;

Combining individual parts of the grids and constructing a consolidated network schedule for the implementation of a set of works;

Justification or clarification of the execution time of each work in the network schedule.

At the beginning of network planning for the release of a new product, it is necessary to identify what events will characterize the work package. Each event must establish the completion of previous actions. It is recommended to list all events and work included in a given complex in the order in which they are performed, but some of them can be performed simultaneously.

The final stage of network planning is to determine the duration of individual work or cumulative processes. To establish the duration of any work, it is necessary, first of all, to use the appropriate standards or labor cost standards. And in the absence of initial regulatory data, the duration of all processes and work can be established by various methods, including with the help of expert assessments.

For each job, as a rule, several time estimates are given: minimum, maximum and probable.

The resulting probable estimate of time cannot be accepted as a standard indicator of the time required to complete each job, since this estimate is mainly subjective and largely depends on the experience of the person in charge. Therefore, to determine the time to complete each job, expert estimates are subject to statistical processing.

The simplified diagram depicts the process of developing a new product, which is the subject of planning and covers the period from the moment the idea is conceived to trial sales and promotion of the product to the market.

The graph shows the sequence of operations to launch a new product on the market. The moments of completion of stages are indicated by circles called “events”

and the periods of time between specific events are depicted as arrows and are called “works”.

An event occurring at a certain moment may depend either on a single event or on a complex of previous interrelated events. No event can occur without the completion of previous operations.

The graph shows that the longest full planning cycle new products includes the following sequence of events: 1, 2, 3, 4, 5, 6,7, 8, 9, 10, 11, 12. It is depicted on the graph as a “thick” line. The cycle covers the period from the moment a decision is made about the need to manufacture a product until the moment it is released onto the national market, provided that all stages of product planning occur in a clear sequence. Delay in any activity along this path causes the planning process to fall behind schedule.

However, the enterprise may also neglect measures such as testing the product with the help of consumers (events 1, 2, 3, 4) or trial sales (events 5, 6, 7, 8, 9, 10) before deciding to immediately release the product to the market (events 1, 11, 12).

In order to simplify the network diagram, all possible options development of a new product is not shown on it. For example, the decision to release a product to the market (event 11) may be made after testing (event 4). In this case, a line should be drawn on the graph from event 4 to event 11. In all these options, the development cycle for a new product is significantly reduced.

Experience shows that the greatest market success with a new product usually comes to manufacturers who consistently go through the entire planning cycle, while losses from shortening the cycle can be significant. The duration of the entire cycle can be reduced, but subject to the involvement of additional resources and the application of additional efforts at critical Imam (for example, during market research or conducting test sales).

In general, there are three types of network models that are used for relay projects, namely:

Models of the "vertex-work" type. The works are presented in the form of rectangles connected by logical dependencies (Fig. 6.3);

Rice. 6.3. A simple vertex-work mesh

Models of "vertices - events" (each work is determined by a number - start - finish). The work is determined by arrows between two nodes and the numbers of the nodes that it connects (Fig. 6.4))

Rice. 6.4. Grid type "vertices - events"

Mixed (the work is presented in the form of a rectangle (node) or line (arrow)). In addition, there are boxes and lines that represent work: simultaneous events and logical dependencies. Lines are not used to connect rectangles at the beginning and end, but to show a point in time before, during, or after the work is completed.

Duration is the time it takes to complete a job.

Early and late dates. These dates can be determined based on the estimated durations of all activities. The beginning and end of one job depends on the end of another. Thus, there is the earliest date that work can begin - the early start date.

The early start date and the estimated duration of the work constitute the early finish date. If the late start date is different from the early start date, the period during which the work can be started is called slack.

Algorithm for calculating the network model

Early start and finish are calculated during the forward mesh pass step. The early start of the first job is 0, the early finish is calculated by adding the duration of the job. Early ending turns into next job for an early start by subtracting advance or adding delay, which provide for the “finish-beginning” dependence. For a start-end relationship, the start time becomes the end time.

Give late start, late finish, slack time are calculated when performing the reverse pass. The late end of the last job is taken to be equal to its early finish.

By subtracting the work duration, the late start is calculated. A late start turns into a late finish for previous work. The converted start or end date is taken as the new start or end time according to the dependency type.

When a job has two or more previous jobs, the job with the lowest start time is selected (after subtracting the tardiness and adding the lead). The process is repeated throughout the grid. The slack time of the first and last job must be 0.

Determining the Critical Path

Activities with zero slack are called critical; their duration determines the duration of the project as a whole.

Critical duration- the minimum duration during which the entire range of project work can be completed.

Critical path - a path in a grid model whose duration is equal to the critical one. The critical path is a sequence of activities with zero slack.

Activities on the critical path are called critical works.

Calculations of the main parameters of network diagrams should be used in the analysis and optimization of network strategic plans.

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