OPTIMIZATION OF RESOURCE DISTRIBUTION UNDER THE CONDITIONS OF FUZZY INITIAL DATA
DOI:
https://doi.org/10.20998/2079-0023.2022.01.02Keywords:
problem of rational distribution of a limited resource, fuzzy description of the criterion, mathematical model and solution methodAbstract
The problem of resource distribution in several directions of its spending is considered for the case when the parameters of the distribution efficiency criterion are fuzzy numbers with given membership functions. The purpose of the study is the development of mathematical models and methods for solving the problem of resource allocation for practically the most important criteria, taking into account the fuzziness of the numerical values – of their parameters. An analysis of the well-known approach to solving the problem is carried out and its main shortcomings are identified, which motivate the continuation of research. A method for solving the stated problem is proposed, the computational implementation of which contains three stages. At the first stage, using the membership functions of the fuzzy parameters of the problem, the membership function of the criterion is formed. The function obtained in this case is approximated at the second stage using a four-parameter distribution. An important advantage of this distribution is the possibility, by varying the numerical values – of its parameters over a wide range, to change the mathematical expectation, variance, and asymmetry of the values – specified by this distribution, providing a high quality of approximation. Thus, the criterion for the effectiveness of the task is determined. At the third stage, a mathematical model of the optimization problem of the distribution of a limited resource is formulated. The following three options for constructing an optimality criterion are considered: maximizing the criterion with the maximum possible value of its membership function; maximization of the criterion, provided that the value of its membership function is not lower than the specified one; maximization of the criterion, provided that the value of the membership function of each of its terms is not lower than the specified one. Each of the resulting problems is a standard problem of mathematical programming and is solved by known methods. A possible direction for further research is discussed in order to improve the adequacy of the used analytical descriptions of the membership functions of the fuzzy parameters of the problem.
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