Features of Alternatives Filtration Procedures Based on Binary Relations in the Tasks of Selecting a Vehicle by Many Criteria

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MAGAZINE №6 (83) December 2017


CATEGORY  Optimization and mathematical modelling Analysis in logistics and SCM


When choosing a vehicle by many criteria, when risks are considered 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 eliminate 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 stated problems can be related to this undesirable phenomenon: alternatives that will be a priori Pareto optimal may not go through such type of filtration. This can certainly 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. 

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