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

Project management has long been a element of everyday life for businesses of all shapes and proportions. Such a management structure is used to improve the effectiveness of decisions and the implementation of quality control at all stages of the production cycle. Among the wide range of methodologies and tools of project management is a particularly popular method of "critical Path" of the basic principles on which it is proposed to consider in more detail.

What is project management?

Numerous definitions of the concept of “project” is similar in one: this time-limited set of interrelated actions aimed at achieving a unique goal. Uniqueness, temporality and fixed targets – this is what distinguishes the project from operating activities of the company.

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

Among all the stages of project management allocate primary: initiation, planning, implementation and completion. The planning of the project – one of the key stages. Within it is the formation of the main targets, determining the length and sequence of operations. This phase involves work in various areas, including: scope, schedule, budget and project risks.

Phase control time in the planning stage performs a specific function for the formation and forecasting of key action plans of all members of the project team.

Network planning: basic approaches

The network planning Technique is actively developed since the 1950-ies. It involves creating models of projects, which would reflect the relationship between elements of the overall production chain and take into account the factors of time, cost, and availability of resources.

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The Network is called the graphic display of the logical sequence of certain operations of the project with the reflection of relationships between them and constraints (deadlines, resource availability, etc.). It seems such a chart, usually in the form of tables or charts, which reflect the main characteristics of the project.

Sometimes when building a network, there is no way to accurately determine the duration of each operation. Depending on this factor there are two main methods of calculating network schedules. The first was developed by the described method the critical path, which implies the calculation with the unambiguous estimates of the duration of the works. Later began to use the PERT technique, including the calculation of the probability characteristics of the duration of operations.

In both methods, the task of the critical path: calculation of duration and definition of the works belonging to it.

Main network elements of the project

Project management is very often resort to network planning, so is now found in many forms such graphs.

Classic network Elements are Working and the Event.

Work are indicated by arrows and are always “lead” from one event to another.

Operation (or operations) that require time and resources, is called valid, and the dependencies between events that do not require real actions (e.g., indicating the necessary condition for the start of the next work, which does not require additional time or personnel) – fictitious. There are also pending as a separate type of work that requires time, but not in need of resources (for example, a person not involved in this operation).

The Event is the result of a, denoted by a circle (or other closed geometric figure). Separately identify the initial event (with no preceding experience, the beginning of the project) and final (end of project).

The schedule looks like a network, the nodes of which are events, United work indicating the main features.

The method

The method the critical path is the calculation of the length of the longest time the chain operations of the project, from the initial to the final.

Critical path – not only in the network, but the longest time. Its temporal duration corresponds to the time required to perform all operations of the project (including parallel operation).

The Critical path often incorrectly referred to as the shortest – that's wrong. The confusion is due to the fact that the length of the critical path does not contain the reserves (reserves) time, that is, each subsequent operation starts when the previous is finished. However, whenever possible, the project Manager tries to reduce this length by increasing or reallocating resources (e.g., number of employees).

Critical path Method of the project involves the calculation of the parameters of events and activities for each network separately. For this often use specialized software products that reduce the timeframe for all the necessary iterations to a few seconds. It does not require special education and additional training. However,for further analysis of network graphs is to explore the meaning of the following calculations.

Calculate the earliest dates of events network

The Early term of accomplishment of event Tr - the time required for the completion of all work prior to the present event.

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

• For the source of the event (start): Tr(s) = 0;
• For all other events i: Tr(i) = max [Tr(i) + t(k,i)], where t(k,i) — the duration of the work (k,i), which is part of the event i.

Thus, to calculate the earliest date of occurrence of the event, you need to determine what works are included in this event, and to lay down the time code for the previous event and duration of the work that comes out of it and included in the event in question. Of the amounts received have to choose the greatest.

The Physical meaning of the formula is that, until you have completed all work included in the specific event, it will not be done. For example, in the event “estimates” consists of three concurrent steps: the calculation of cost of works, calculation of equipment cost, overhead. Each action takes different lengths of time and depends on different factors (previous events). After the time is calculated, when completed, each of the three works, it is possible to determine the time of fulfillment of event “estimates” is the most recent period of three, that is, when all three works are completed. Ahead of this event, “estimates” will not occur. Therefore, from amounts selected the greatest.

The Early stages are usually located to the left in circles.

Calculation of the most the late timing of the occurrence of events network

Later the accomplishment of the event TA is the time at which it is possible to detain without delay the entire project.

Late onset of events Tr(i) is calculated from the final (finish) to the starting (start) the following:

• For the final event (finish): TP(f) = Tr (f);
• For all other i: TP(i) = min [TP(j) - t(i,j)], where t(i,j) — duration of operation (i,j) emerging from the event i.

So to calculate the future, then you need to determine what works out of this event, and to find the difference between the time of occurrence of the subsequent events and the duration of the work, incoming and outgoing. From the resulting difference must always choose the lesser. In other words, all described for the early timing of the occurrence of events calculation it is necessary to perform exactly the opposite.

The Physical meaning of the formula is that the late onset of events allow you to simulate the location of the works in the circuit as close as possible to installed in the previous step date early (he was late) date for completion of the entire project. That is, these values show how much the ‘tighten’ work, not tearing the final completion of all works.

The Later stages are usually located in the right circles.

Calculation of reserves events

Settlements in the two areas were conducted in order to identify the temporary reserves-reserves of time. It's such a time margin, which may be deferred (delayed) commit to specific events without violating the end date of the project. It is defined as the difference between TP and Tr: R = TA-Tr.

Method (critical path) also includes the calculation of work schedules produced similar to the event parameters.

Calculation Algorithm

Calculation of a critical path network diagram of the project consists of several stages, which are implemented on the above formulas. The calculations can be performed on any elements of network graphs.

Calculation Steps:

1. Early dates of events/activities
2. Late dates of events/activities.
3. Reserves events/activities.
4. The definition of the activities and events included in the critical path of the project.

Already at the 1st stage of the algorithm know the length of the critical path of the project. It is equal to early (he was late) due date of the final event.

The Work included in this volume, it is easy to calculate the zero-reserves assignments and events. Don't forget that the critical path starts with the initial event and ends with the final event of the project without interruption.

What is considered a critical path?

Project Planning in any case includes the calculation of the length of the critical path network. This value indicates the most rapid of the possible timing of completion of all works included in the project. But also important is the definition of these operations.

That the operation of the critical path require special attention from the project Manager and his team. Because these works do not contain reserves! They cannot tighten and break the timing of the accomplishment of their end events, otherwise the final date of completion of all works (length of critical path) will change, which will lead to negative consequences. In order to reduce such risks of the project, when scheduling managers often artificially increase the time taken for execution of certain operations to provide a buffer zone for unforeseen circumstances and delays. Temporary buffers should be placed before a high-risk sections of the network operations to reduce the likelihood of missed deadlines.

The Described method - the critical path - is the cornerstone of management of project deadlines. It is fairly simple to use and can be used to determine the duration and identify the tense areas of the chain any work, even at the household level.