Project management has long been an element of everyday life for businesses of all shapes and sizes. Such a management structure is used to increase the efficiency of decisions and quality control at all stages of the production cycle. Among the wide range of project management methods and tools, the “Critical Path” method is especially popular, the basic principles of which are proposed to be considered in more detail.
What is project management?
Numerous definitions of the concept of “project” are similar in one: it is a time-limited set of interrelated actions aimed at achieving a unique goal. Uniqueness, temporality and fixed targets are what distinguishes the project from the company's operations.
Project management is a dynamically developing field of management with its own methodology and tools.
Among all the stages of project management, the main ones are distinguished: initiation, planning, implementation and completion. Moreover, project planning is one of the key stages. Within its framework, the formation of the main target indicators, the determination of the duration and sequence of operations. This stage involves work in various areas, including: the content, timing, budget and risks of the project.
The time management phase at the planning stage has a special function of forming and forecasting a key action plan for all members of the project team.
Network Planning: Key Approaches
The network planning technique has been actively developed since the 1950s. It involves the creation of project models that reflect the relationships between elements of the overall production chain and take into account the factors of time, cost and availability of necessary resources.
A network diagram is a graphical display of the logical sequence of certain project operations with a reflection of the interconnections between them and limitations (timing, resource availability, etc.). Such a schedule 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 - a critical path, involving calculation with unambiguous estimates of the duration of work. Later, the PERT method began to be used, including the calculation of the probabilistic characteristics of the duration of operations.
In both methods, the task of the critical path is posed: calculating its duration and determining the work included in it.
Key elements of the project network
In project management, they often resort to network planning, so now there are many forms of such schedules.
Elements of a classic network diagram are Work and Event.
Works are indicated by arrows and always “lead” from one event to another.
Jobs (or operations) that require time and resources are called valid, and dependencies between events that do not require real actions (for example, an indication of the necessary condition for starting the next job that does not need additional time or employees) are fictitious. They also distinguish waiting 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 indicated by a circle (or other closed geometric shape). Separately determine the initial event (without 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 work indicating the main characteristics.
The essence of the method
The essence of the critical path method is to calculate the length of the project’s longest chain of operations, from initial to final.
The critical path is not the only one in the network graphics, but the longest in time. Its time span 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 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 time the previous one is completed. However, at every opportunity, the project manager tries to reduce this length by increasing or redistributing resources (for example, the number of employees).
The project critical path method involves calculating the parameters of events and activities for each network separately. For this, specialized software products are often used that reduce the time it takes to complete all necessary iterations to a few seconds. Moreover, special education and additional training are not required. Nevertheless, for further analysis of network diagrams, it is worth exploring the essence of the calculations below.
Calculation of the earliest timing of network events
The early completion date of the event Tr is the time required to complete all work preceding the event in question.
The early dates of events Tr (i) are calculated from the initial (start) to the final (finish) event as follows:
- for the initial event (start): Tr (s) = 0;
- for other events i: Tp (i) = max [Tp (i) + t (k, i)], where t (k, i) is the duration of the work (k, i) included in event i.
Thus, in order to calculate the earliest possible date of occurrence of an event, it is necessary to determine what kind of work is included in this event, and add up the time when the previous event occurred and the duration of the work emanating from it and included in the event in question. Of the amounts received, you need to choose the largest.
The physical meaning of the formula is that until all the works included in a particular event are completed, it will not be completed. For example, the event “estimate” 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 (previous events). After calculating the time when each of the three works 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 works 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 in the circles of events.
Calculation of the latest completion dates of network events
The late date for the completion of the TP event is the time for which it can be delayed without disrupting the timing of the entire project.
The late dates of events Tr (i) are calculated from the final (finish) to the initial (start) as follows:
- for the final event (finish): Tn (f) = Tp (f);
- for all other i: (i) = min [ (j) - t (i, j)], where t (i, j) is the duration of the work (i, j) coming out of event i.
Thus, in order to calculate the latest deadline, you need to determine what kind of work comes out of this event, and find the difference between the time the next event occurred and the duration of the work coming in and out of it. From the received differences it is necessary to choose the smallest. In other words, all the calculations described for the early dates of the events must be performed exactly the opposite.
The physical meaning of the formula lies in the fact that the late timing of the onset of events allows us to simulate the location of work in the chain as close as possible to the date set at the previous stage for the early (aka late) deadline for completing the entire project. That is, these values will show how much you can “tighten” the work without breaking the final deadline for completing all the work.
Late dates are usually located on the right in the circles of events.
Event Reserves Calculation
Calculations in two directions are carried out in order to identify temporary reserves - time reserves. This is such a temporary reserve for which the completion of a specific event can be delayed (delayed) without violating the project end date. It is defined as the difference between Tn and Tp: R = Tn - Tp.
The method (critical path) also includes the calculation of network work performed in the same way as the event parameters.
Calculation algorithm
The calculation of the critical path of the project network schedule consists of several stages that are implemented according to the above formulas. In this case, calculations can be performed on any elements of network diagrams.
Calculation stages:
- Early dates for events / work
- Late dates for events / work.
- Reserves of events / work.
- Identification of activities and events that are part of the critical path of the project
Already at the 1st stage of this algorithm, the value of the length of the critical path of the project is known. It is equal to the early (aka late) deadline for the execution 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 take the critical path?
In any case, project planning includes calculating the length of the critical path of the network. This value shows the fastest of the possible deadlines for the completion of all work included in the project. But the definition of these works is also important.
It is critical path operations 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 the deadlines for the completion of their final events be delayed, otherwise the final date for the completion of all work (the length of the critical path) will change, which will lead to negative consequences. In order to reduce such project risks, when scheduling, managers often artificially increase the time allotted for certain operations to provide themselves with buffer zones for unforeseen circumstances and delays. It is advisable to place temporary buffers in front of high-risk sections of the network of operations to reduce the likelihood of failure to meet deadlines.
The described method - 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 stressed sections of the chain of any work, even at the household level.