The sixth chapter presents the procedures for the possible filtering of alternatives that can be implemented on the basis of binary relations in logistics problems. Moreover, various special approaches to the implementation of such filtering are formalized. They are accordingly based on the so-called majority and minority principles for making such decisions. The presented filtering procedures of the analyzed alternatives make it possible to simplify the calculations when choosing solutions according to many criteria, make them more compact and reduce their implementation time in relation to real situations in practice, without compromising optimization goals.
When choosing a vehicle by many criteria, when risks are taken into account as specific criteria, a practicing manager may face the need to analyze a huge number of alternatives, among which one should choose the best. In such situations, preliminary filtering of alternatives may help significantly (in terms of reducing the volume of required procedures for analyzing such alternatives), if it does not lead to a loss of quality of the solution. The article analyzes the features of filtration procedures and their influence on the search for the optimal solution for choosing a vehicle, if such procedures are implemented on the basis of the strict order relation (in the format of the theory of binary relations). It is shown that the following procedures will always precede the tasks of vehicle selection according to many criteria: 1) it will be necessary to provide the same optimization directions for all particular criteria; 2) it will be necessary to eliminate the so-called dimension phenomenon. The article analyzes three possible approaches to eliminating this phenomenon. For the first time it is proved that any of them provides in the future the same result when filtering alternatives based on the considered binary relations. It is shown that for the selection of a vehicle by many criteria, the corresponding filtration procedures can affect the ranking of alternatives. Moreover, it is proved that the undesirable phenomenon can relate to these problems: filtering of this type may not be replaced by alternatives that will be a priori Pareto optimal. Of course, this can affect the quality of the solution found. Therefore, the article notes what precautions are required to be taken into account by the manager so that the choice can correspond to the preferences of the decision maker.