## Wednesday 16 February 2022

Duration is the time it takes to complete the work. Usually, in deterministic plans, the duration of work is considered unchanged. In fact, it depends on external factors and is a random variable, given by the law of distribution (or distribution density). Often the duration changes due to the change in the number of labor resources in this job.

Before starting to draw up a plan for each work, its estimated duration is known. After the work begins, but before it is finished, you can calculate the remaining duration. It can be equal to the planned duration minus the time elapsed since the start of work, or you can overestimate the remaining duration based on the knowledge gained when performing the work at a given point in time.

Once the work is finished, you can record the actual duration. The actual duration is useful to know, because comparing it with the planned one, you can calculate deviations from the plan, which is used to control the progress of work and calculate the trend.

The purpose of duration management is to ensure that the project is implemented within its planned time. To do this, on the basis of long-term aggregate plans of operations, the organization needs to develop more detailed plans, coordinating production capacities with consumer requests, for more and shorter periods of time. As a result, the output should be a schedule of cases for each day, showing how the available resources will be distributed.

### Methods of planning operations.

Network analysis and project scheduling. Definition of the concept of "network model". Critical Pathway Method (CPM) and its analysis. Gantt chart

When analyzing the work of project managers, it is advisable to distinguish three sides of the case: drawing up a plan, drawing up a schedule, management.

Scheduling a project is complex, so many support tools have been developed to help project managers. Two of them are the network graph and the Gantt chart.

Network analysis is a method of planning work of a project nature, i.e. work in which, as a rule, operations are not repeated.

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

The network model of the complex of works is called an oriented graph used to describe the dependencies between the works and the stages of the project. Network models should be used only for complex projects.

In accordance with the types of graphs used, three types of networks are also defined:

•  networks of the type "vertex - work";
•  "vertex-event" networks;
•  mixed networks.

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

Network diagrams display a network model graphically as a set of vertices corresponding to works connected by lines representing relationships between works. This graph, called a vertex-work network or an precedence-follow diagram, is the most common representation of the network.

There is another type of network diagram, a vertex-event network, which is used less frequently in practice. In this approach, the work is represented as a line between two events (graph nodes), which, in turn, reflect the beginning and end of this work. PERT charts are examples of this type of chart.

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

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

Critical path — the longest full path in the network is called critical; works lying along the way are also called critical. 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 project as a whole can be reduced by reducing the duration of work lying on the critical path. Accordingly, any delay in the execution of the work of the critical path will entail an increase in the duration of the project.

The critical path method allows you to calculate possible calendar 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.

A Gantt chart is a horizontal line chart in which project tasks are represented by extended time periods characterized by start and end dates, delays, and possibly other time parameters. An example of displaying a Gantt chart using modern computer tools.

The network planning process assumes that all activities will be described in the form of a set of works or works with certain relationships between them. To calculate and analyze a network diagram, a set of network procedures known as critical path method procedures is used.

The process of developing a network model includes:

•  define a list of project works;
•  evaluation of work parameters;
•  identify dependencies between works.

The network model is formed as a result of defining dependencies between works and adding connecting works and events. In general, this approach is based on the assumption that each work is aimed at achieving a particular result. Binding works may not require any material end result.

Determining the dependencies between works is necessary to calculate the calendar schedule. The precedence relationship displays the logical relationship between the works in the schedule. The most common cause of such dependencies is technological limitations (the beginning of some works depends on the results of others), although limitations dictated by other considerations are also possible.

### These connections form the structure of the network.

The totality of the relationships between the works determines the sequence of work. In accordance with the established connections, the works are divided into previous and subsequent. The preceding work is the providing for the subsequent one; thus, all previous work is required to begin performing subsequent work.

The main methods for determining dependencies between works are:

1. The method of precedence (PDM), or "top-work". It operates with four types of precedence-following dependencies:

• "start after end". This is a standard sequence in which the previous work must be completed before the subsequent one begins;
• "the beginning after the beginning". This is the most common sequence when modeling work that must be performed simultaneously. In this case, you do not need to complete the previous work until the next one begins. To begin, it is necessary that the previous work has just begun;
• "ending after graduation". This type of dependency is also used to simulate parallel jobs. In this case, the end of the subsequent work is controlled by the end of the predecessor's work;
• "ending after beginning". This type of dependency is used quite rarely and is used primarily for work performed on a rotational basis.

2. Method of plotting arrow charts (graphs) (ADM), or "vertex-event". This method operates only with the "Start after the end" dependencies and in some cases requires the use of fictitious works to correctly reflect the technology.

3. Methods of constructing conditional diagrams (graphs).

4. Network Templates.

The final step in defining dependencies is to check the relationships for loops and other logical errors. After building the structure of the network and completing estimates of the duration of work, the project team has everything necessary to calculate the calendar schedule for the ITC.

The PERT method differs from CPM in that here the duration of the processes is characterized by three estimates.

1) an optimistic assessment of the time when it is assumed that the execution of the process will occur as quickly as possible.
2) the most likely estimate of the time when it is assumed that the execution of the process will occur normally.
3) a pessimistic estimate of the time when it is assumed that the process will be very slow.

Drawing. PERT Network – Program Evaluation and Review Technique (PERT).