Solving a multi-criteria problem in the logistics of special rail transport

. Under the present conditions, there is a need to assess the effectiveness of the functioning of the technical base of railway transport involved in the performance of special (military) transportation, taking into account the current operational and transport situation. To make a management decision on the choice of the option for further following of a special cargo (reloading, following its course, a combined method, as well as following a detour route [4]), when an obstacle occurs along the route, it is necessary to find an option that best meets the requirements of the planned deadlines. This is possible with a systematic approach to finding an alternative way of transportation. For a reasonable choice of the method when making a decision, it is proposed to use the method of hierarchy analysis [5], which allows a comprehensive assessment of all transportation options, taking into account factors affecting the priorities of possible solutions when assessing the effectiveness of the functioning of the railway network when transporting special (military) cargo. The purpose of making a decision is to choose the option of deciding on the method of transportation of special (military) cargo during a break in the movement of trains with available alternatives (B) (4 methods of transportation) the main indicators (K) are the time of arrival of cargo to the designated area, the consumption of material resources (hereinafter-MS) when following their course or using other modes of transport (in particular - fuel), operational losses of automotive equipment (hereinafter - AT) during forced unloading, as well as the consumption of motor resources Kc = f (T, S, N, M)→min (see figure).


Introduction
It should be noted that at the stage of operational management, the indicator of the time of delivery of special (military) cargo to the destination (T) acquires the main importance. However, when carrying out transportation for the management bodies, the remaining indicators will also be important. The choice of the significance (weight) of the indicators largely depends on the current operational and transport situation, the tasks facing the transported troops, as well as their logistical support, and the ability to overload special (military) cargo en route. By the scaling system [5], a procedure is performed for pairwise comparisons of hierarchy elements by degrees of importance, from 1 to 9, with the compilation of a matrix (based on expert opinions). Comparing the transportation indicators, it is necessary to determine the importance of each of them to the other. Based on the determination of the importance of each indicator (w_i), a matrix is formed. If the indicator T is more important than the indicator C, then the cell (T, C) corresponding to row T and column C is filled with an integer, and the cell (C, T) corresponding to row C and column T is filled with an inverse number (fraction). If the value is the same, 1 is put down.

Method of transportation of special cargo
Arrival time (T)

Alternatives(В)
Overload Following your own pace To determine the "weight" of each of the indicators, it is necessary to find an eigenvector and normalize it. To do this, you need to find the geometric mean for each i-th row of the matrix.
The eigenvector is defined as the geometric mean by the formula: where n-the index that characterizes the indicator number; aij-evaluation of the element of the i-th row and the j-th column. The component of the normalized priority vector ai is found.
= ∑ To assess the uniformity of judgments on the prioritization of transportation indicators, it is necessary to determine the consistency index (CI) by the deviation of the eigenvalue (λmax) from the order of the matrix (n).
To determine how accurately the consistency index reflects the consistency of judgments, it must be compared with a random consistency index (CIS), thus we obtain a consistency ratio (CR). The obtained value of CR<0.1 characterizes an acceptable consistency of judgments, otherwise, the estimates need to be revised. Determination of the best method of transportation of special (military) cargo is carried out through the synthesis of the "weights" found at the previous stages for the analyzed methods, taking into account the "weights" of each indicator.

Conclusions
The highest coefficient of the final assessment of significance is a priority and can act as a priority when determining the option of transporting special (military) cargo in the event of a break in traffic or an unscheduled termination of transportation.

Recommendations
The hierarchy analysis method solves the problem and can be adopted as a mathematical tool of a systematic approach to making decisions on the degree of involvement of the railway network and the further option of transporting special (military) cargo.