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

Project management has long become an element of daily business for all forms and sizes. Such a management structure is used to improve the efficiency of decisions made and to carry out quality control at all stages of the production cycle. Among a wide range of methods and tools for project management, the Critical Path method is very popular, and its main principles are to be considered in more detail.

What is project management?

Numerous definitions of the concept of "project" are similar in one: it is a limited-time complex of interrelated actions aimed at achieving a unique goal of its kind. Uniqueness, temporality and fixed targets - this is what distinguishes the project from the company's operational activities.

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

Among all stages of project management, the main ones are: initiation, planning, implementation and completion. At the same time, project planning is one of the key stages. Within its framework, the main target indicators are formed, the duration and sequence of the operations being performed. This stage involves work in various areas, including: the content, timing, budget and risks of the project.

The phase management phase at the planning stage performs a special function of forming and forecasting a key action plan for all members of the project team.

Network planning: basic approaches

The method of network planning has been actively developing since the 1950s. It involves the creation of project models that reflect the relationships between the elements of the overall production chain and take into account the factors of time, costs and availability of the necessary resources.

A network graph is a graphical representation of the logical sequence of certain operations of the project with the reflection of the relationships between them and the constraints (timing, availability of resources, etc.). Such a schedule is presented, usually in the form of a table or chart, which reflects the main characteristics of the project.

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

In both methods, the critical path is set: the calculation of its duration and the definition of the works that enter it.

Main elements of the project network

In project management, very often they resort to network planning, so at the present time there are many forms of similar schedules.

The elements of the classic network graphics are Work and Event.

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

Work (or operations) that require time and resources are called valid, and relationships between events that do not require real action (for example, an indication of the necessary condition for starting the next job that does not need additional time or employees) are fictitious. Waiting is also identified as a separate type of work that requires 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 determine the initial event (not having previous work, the beginning of the project) and the final (end of the project).

The graph itself looks like a network, in the nodes of which there are events connected by works with the indication of 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 initial to final.

The critical path is not the only one in the network graph, but the longest in time. Its time length corresponds to the time it takes to complete all project operations (including parallel work).

The critical path is often mistakenly called the shortest - this is incorrect. 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 when 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 calculating the parameters of events and jobs for each network graph separately. To do this, often use specialized software products that shorten the execution of all the necessary iterations to a few seconds. It does not require special education and additional training. Nevertheless, for further analysis of network graphs it is worthwhile to study the essence of the calculations below.

Calculation of the earliest timing of network events

The early deadline for the event Tp is the time required to complete all the work preceding the event in question.

The early timing of the occurrence of Tr (i) events is calculated from the initial (start) to the finishing (finish) event as follows:

• For the initial event (start): Tp (s) = 0;
• For the remaining events i: Tp (i) = max [Tp (i) + t (k, i)], where t (k, i) is the duration of work (k, i) entering event i.

Thus, in order to calculate the earliest date for an event, it is necessary to determine what works are included in this event, and to add up the time when the previous event occurred and the duration of the work coming from it and entering the event under consideration. From the received sums it is necessary to choose the greatest.

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

Early terms are usually placed on the left in the circles of events.

Calculation of the latest timing of network events

The late term for the event Tp is the time for which it can be detained without disrupting the timing of the whole project.

The later timeframes for the occurrence of Tr (i) events are calculated from the finish (finish) to the initial (start) as follows:

• For the finishing event (finish): Tn (f) = Tp (f);
• For all other i: Tn (i) = min [Tn (j) - t (i, j)], where t (i, j) is the duration of the work (i, j) coming from the event i.

Thus, in order to calculate the latest deadline, it is necessary to determine what works out of this event, and to find the difference between the time of the onset of the subsequent event and the duration of the work entering and exiting it. From the differences obtained, it is necessary to choose the smallest. In other words, all the calculations described for the early timing of the events must be performed to the exact opposite.

The physical meaning of the formula is that the late timing of the occurrence of events makes it possible to simulate the location of work in the chain as close as possible to the date of the early (the same late) date for the completion of the entire project, which was established at the previous stage. That is, these values will show how long it is possible to "drag out" the work without disrupting the final completion date of all the works.

Late terms are usually located on the right in the circles of events.

Calculation of event reserves

Calculations in two directions are conducted in order to reveal temporary reserves - reserves of time. This is such a temporary reserve, which can be postponed (delayed) the commission of a specific event without violating the project completion date. It is defined as the difference between Tn and Tp: R = Tn - Tp.

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

Algorithm of calculation

Calculation of the critical path of the network project schedule consists of several stages, which are implemented according to the above formulas. In this case, calculations can be made on any element of network graphs.

Stages of calculation:

1. Early timing of events / works
2. Late time for events / works.
3. Reserves of events / works.
4. Identify the work and events that are part of the critical path of the project.

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

The works included in this volume can be easily calculated from the zero reserves of tasks and events. Do not forget that the critical path begins with the initial event and ends with the final event of the project without interruptions.

Why count the critical path?

Planning a project in any case involves calculating the length of the critical network path. This value shows the fastest of all possible deadlines for completion of all the works included in the project. But important is the definition of these works.

It is the critical path operations that require special attention from the project manager and his team. After all, these works do not contain reserves! They can not be delayed and disrupt the timing of the completion of their final events, otherwise the final end date of all works (the length of the critical path) will change, which will lead to negative consequences. In order to reduce such project risks, when drawing up the schedule, managers often artificially increase the time allocated for the execution of individual operations in order to secure buffer zones for unforeseen circumstances and delays. Temporary buffers should be located in front of high-risk sections of the network operations in order to reduce the probability of failure of terms.

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