# Coefficient of tension of work. Analysis and optimization of...

## Coefficient of tension of work. Analysis and optimization of network graphics

After finding the critical path and work time reserves and assessing the likelihood of the project being completed within a specified time, a comprehensive analysis of the network schedule should be carried out and measures taken to optimize it. This very important stage in the development of network graphs reveals the main idea of ​​the STC. It consists in adjusting the network schedule in accordance with the specified terms and capabilities of the organization that is developing the project.

First, consider the analysis and optimization of calendar networks, in which only estimates of the duration of work are specified.

The analysis of the network schedule begins with the analysis of the network topology, including control over the construction of the network schedule, determination of the expediency of the selection of works, the degree of their dismemberment.

Then the classification and grouping of works by the size of the reserves are carried out. It should be noted that the magnitude of the total reserve of time can not always sufficiently accurately characterize how intense is the performance of a particular work of a non-critical path. It all depends on what sequence of work the calculated reserve is spreading, what is the duration of this sequence.

It is possible to determine the degree of difficulty in performing a non-critical path in time for each group of works by using the coefficient of work intensity.

The coefficient of intensity K n works ( i, j ) is the ratio of the duration of non-coincident (concluded between the same events) path segments, one of which is the path of maximum duration passing through this work, and the other - the critical path:

(14.29)

where - duration of the maximum path passing through the work (i, j);

- duration (length) of the critical path;

- the length of the segment of the path in question that coincides with the critical path.

The formula (14.29) can easily be reduced to the form

(14.30)

where - full runtime reserve

The coefficient of tension K and ( i, j ) can vary from zero (for works, in which the segments of the maximum of paths that do not coincide with the critical path consist of fictitious works of zero duration) to unity (for works of the critical path).

14.4. Find the performance ratio ( 1 , 4) for the network graph (see Figure 14.6).

Solution. In paragraph 14.5, we determined that the length of the critical path t = 61 (day), and the maximum path passing through the job ( 1 4), - path 14 0 → 1 → 4 → 6 → 9 → 10 → 11 - has a duration of i (Imax) = t (Z.4) = 49 (days). The maximum path L A coincides with the critical path (see Figure 14.6) on the segment 6 -> 9 → 10 → 11 duration t = 13 + 6 + 13 = 32 (day). Using the formula (14.29), we find

Or else: knowing the full operational reserve of R n (1.4) = 12 (see. (see Table 14.3), according to the formula (14.30), we find

The closer to unity the coefficient of tension K H (i, j), in a timely manner. The closer to K and ( i, j ) to zero, the greater relative reserve has the maximum path passing through this work.

Works may have the same total reserves, but the degree of intensity of the terms of their fulfillment, expressed by the coefficient of intensity K and (i, j), can be different. Conversely, the same total energy reserves may correspond to different total reserves.

So, the total work reserves (3, 6) and (6, 7) for the network are: R n (3, 6) = R u (6, 7) = 10 (days) (see Table 14.3), and their tension coefficients are different:

Note that the larger full reserve of one job (compared to the other) does not necessarily indicate a lesser degree of tension in its performance. Thus, in the network under consideration (see Figure 14.6), although the work (2, 7) has a large total reserve in comparison with the work (6 , 10) , Rn (2, 7) = 23 & gt; R n (6, 10) = 14, but has twice the coefficient of intensity K and {2, 7 ) = || = 0.52 against K n (6, /0) = ^ 0.26. This is explained by the different relative weight of the total reserves of work in the duration of the segments of the maximum paths that do not coincide with the critical path.

The calculated coefficients of tension make it possible to further classify works by zones. Depending on the value of K and (i, j) three zones are identified: critical (K H (i, j)>; 0.8); subcritical (0.6 & lt; (/, y) & lt; 0.8); reserve (K and (? ', j) 0.6).

Optimizing network graphics represents the process of improving the organization of the execution of a set of jobs, taking into account the duration of one hundred times. Optimization is carried out in order to reduce the length of the critical path, equalize the work intensity coefficients, rational use of resources.

First of all, measures are taken to reduce the duration of work on a critical path. This is achieved:

• Redistribution of all types of resources, both temporary (using time reserves of non-critical paths), and labor, material, energy (for example, transferring part of the executors, equipment from non-critical paths to critical path work); in this case, the redistribution of resources should, as a rule, proceed from less stressful zones to zones combining the most intense work;

• Reduction of the laboriousness of critical works by transferring part of the work to other ways that have time reserves;

• parallel execution of critical path jobs;

• revision of the network topology, changing the composition of work and the structure of the network.

In the process of reducing the duration of work, the critical path may change, and in the future the optimization process will be aimed at reducing the duration of the new critical path, and this will continue until a satisfactory result is obtained. Ideally, the length of any of the complete paths can become equal to the length of the critical path or at least the path of the critical zone. Then all works will be conducted with equal tension, and the project completion time will be significantly reduced.

It is very effective to use the statistical modeling method , based on multiple successive changes in the duration of the work (within the given limits) and playback on the computer of various variants of the network diagram with calculations of all its time parameters and work intensity coefficients. The playback process continues until an acceptable version of the plan is received or until it is determined that all available options for improving the plan have been exhausted and the conditions imposed on the project developer are not feasible.

So far, we have talked only about compliance with the guidelines for the implementation of the set of works and did not directly address the cost of project development. However, in practice, when trying to effectively improve the plan, it is inevitable to introduce an additional cost factor in addition to the estimates of the terms.

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