The critical path method. The critical path - what is it?

2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16

Project management has long been an element of everyday life for businesses of all shapes and sizes. Such a management structure is used to improve the efficiency of decisions made and the implementation of quality control at all stages of the production cycle. Among the wide range of methods and tools for project management, the Critical Path method is especially popular, the main principles of which are proposed to be considered in more detail.

What is project management?

Many definitions of the term “project” are similar in one thing: it is a time-limited set of interrelated actions aimed at achieving a goal that is unique in its kind. Uniqueness, temporality and fixed targets are what distinguishes a project from a company's operations.

Project management is a dynamically developing area of management with its own methodology and tools.

Among all stages of project management, the main ones are distinguished: initiation, planning, implementation and completion. However, project planning is one of thekey stages. Within its framework, the main target indicators are formed, the duration and sequence of operations performed are determined. This stage involves work in various areas, including: the scope, timing, budget and risks of the project.

The time management phase at the planning stage has a special function of forming and predicting the key scheme of actions for all members of the project team.

Network planning: basic approaches

Network planning techniques have been actively developed since the 1950s. It involves the creation of project models that would reflect the relationship between the elements of the overall production chain and would take into account the factors of time, costs and the availability of the necessary resources.

A network diagram is a graphical display of the logical sequence of certain project operations with a reflection of the relationships between them and constraints (terms, availability of resources, etc.). Such a graph is presented, as a rule, in the form of a table or diagram, which reflects the main characteristics of the project.

Sometimes when building a network diagram, it is not possible to accurately determine the duration of each operation. Depending on this factor, there are two main methods for calculating network diagrams. The described method was the first to be developed - the critical path, which involves calculation with unambiguous estimates of the duration of the work. Later, the PERT method was also used, which included the calculation of probabilistic characteristics of the duration of operations.

In both methods, thetask of the critical path: calculating its duration and determining the activities included in it.

Main elements of the project network diagram

In project management, network planning is very often used, so there are many forms of such schedules nowadays.

The elements of a classic network diagram are Work and Event.

Works are indicated by arrows and always "lead" from one event to another.

Works (or operations) that require time and resources are called real, and dependencies between events that do not require real actions (for example, indicating a necessary condition for starting the next job that does not need additional time or workers), are fictitious. Waiting is also distinguished as a separate type of work that takes time, but does not need resources (for example, a person is not involved in this operation).

Events are the result, denoted by a circle (or other closed geometric figure). Separately define the initial event (having no previous work, the beginning of the project) and the final one (end of the project).

The graph itself looks like a network, in the nodes of which there are events connected by works indicating the main characteristics.

The essence of the method

The essence of the critical path method is to calculate the length of the longest chain of project operations, from the beginning to the end.

The critical path is not the only one in the network diagram, but the longest in time. Histhe time span corresponds to the time required to complete all project activities (including parallel work).

The critical path is often mistakenly called the shortest path - this is not true. The confusion is due to the fact that the length of the critical path does not contain reserves (reserves) of time, that is, each subsequent operation begins at the moment the previous one is completed. However, at every opportunity, the project manager tries to reduce this length by increasing or reallocating resources (for example, the number of employees).

The critical path method of the project involves the calculation of the parameters of events and work for each network schedule separately. For this, specialized software products are often used, which reduce the time required to complete all the necessary iterations to a few seconds. It does not require special education and additional training. However, for further analysis of network diagrams, it is worth studying the essence of the calculations below.

Calculate the earliest timing of network events

Early deadline for the event Tr - the time required to complete all the work preceding the event in question.

Early timing of events Tr(i) is calculated from the initial (start) to the final (finish) event as follows:

• for the initial event (start): Тр(s)=0;
• for other events i: Тр(i)=max [Тр(i) + t(k, i)], where t(k, i) is the duration of work (k, i) included in event i.

Thus, in order to calculate the earliest date of occurrence of an event, you need to determine what works are included in this event, and add the time when the previous event occurred and the duration of the work emanating from it and included in the event in question. From the received amounts, you must choose the largest.

The physical meaning of the formula is that until all the work included in a particular event is completed, it will not happen. For example, the "estimate" event includes three parallel actions: calculation of the cost of work, calculation of the cost of equipment, calculation of overhead costs. Each action lasts a different amount of time and depends on different factors (preceding events). After calculating the time when each of the three jobs will be completed, you can determine the time of completion of the "estimate" event - this is the latest of the three, that is, when all three jobs are completed. Before this period, the "estimate" event will not occur. Therefore, the largest is selected from the sums.

Early dates are usually located on the left side of the event circles.

Calculation of the latest network schedule event dates

The late deadline for the completion of the event Tp is the time for which it can be delayed without disrupting the deadlines of the entire project.

Latest timing of events Tr(i) are calculated from the final (finish) to the initial (start) as follows:

• for the final event (finish): Тp(f)=Тр (f);
• for all other i: Tp(i)=min [Tp(j) - t(i, j)], where t(i, j) -duration of work (i, j) coming out of event i.

Thus, to calculate the latest date, you need to determine which jobs come out of this event, and find the difference between the time of the next event and the duration of the work entering and leaving it. From the received differences it is necessary to choose the smallest. In other words, the entire calculation described for the early dates of the completion of events must be performed exactly the opposite.

The physical meaning of the formula lies in the fact that the late dates of the occurrence of events make it possible to model the location of work in the chain as close as possible to the early (late) date of completion of the entire project set at the previous stage. That is, these values will show how much work can be “draged out” without disrupting the final deadline for completing all work.

Late dates are usually located on the right side of the event circles.

Calculation of event reserves

Calculations in two directions are carried out in order to identify temporary reserves - time reserves. This is such a time margin for which a specific event can be delayed (postponed) without violating the end date of the project. It is defined as the difference between Tp and Tr: R=Tp - Tr.

The method (the path is critical) also includes the calculation of the work of network graphs, performed similarly to the parameters of events.

Calculation algorithm

Calculation of the critical path of the project network diagram consists of several stages, which are implemented according to the above formulas. In this case, the calculations canbe made on any elements of network diagrams.

Calculation steps:

1. Early dates for events/works
2. Latest dates for events/works.
3. Reserves of events/works.
4. Define the activities and events included in the project's critical path.

Already at the 1st stage of this algorithm, the value of the critical path length of the project is known. It is equal to the early (aka late) deadline for the completion of the final event.

The jobs included in this volume can be easily calculated from zero reserves of jobs and events. Remember that the critical path begins with the initiating event and ends with the end event of the project without interruption.

Why consider the critical path?

Project planning anyway involves calculating the critical path length of the network. This value shows the fastest possible deadline for completing all the work included in the project. But the definition of these works is also important.

It is the activities of the critical path that require special attention from the project manager and his team. After all, these works do not contain reserves! They must not be delayed and disrupt the timing of their final events, otherwise the final date of completion of all work (the length of the critical path) will change, which will lead to negative consequences. To mitigate these project risks, managers often artificially increase the time allocated to individual activities during scheduling to provide themselves with buffer zones for unforeseen circumstances and delays. Temporary buffersit is advisable to locate a network of operations in front of high-risk areas to reduce the likelihood of missed deadlines.

The method described - the critical path - is the cornerstone of project time management. It is quite simple to use and can be used to determine the duration and identify stressful sections of the chain of any work, even at the household level.