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Authors

Popov V.

Degree
PhD in Physics & Mathematics, Associate Professor, Lobachevsky state university of Nizhni Novgorod
E-mail
victor972993@rambler.ru
Location
Nizhni Novgorod
Articles

An interval approach to optimization of solving of multi-objective task about appointments

We consider the method of conditional optimization of solving of multi-objective task about appointments on the assumption that the number of candidates is equal or more than the number of vacant positions. Whereas eligibility assessments of task is unclear and is based on the judgment of experts we must use elements of fuzzy sets theory and the fuzzy mathematical programming. In our problem the optimization with interval parameter is supposed the solving of two tasks of mathematical programming with upper and lower value boundaries. In both tasks, as the objective functions are used the total score penalty for non-compliance of subjects (candidates) and objects (appointments) for each criterion. The meet of two solving is general solving of optimization problem. In this paper we use interval analysis and interval discrete optimization with Boolean variables, which determine appointment matrix. The Hungarian Method for the assignment problem was used for solving of optimization problems. An appointment matrix must provide the minimum of value of difference between requirements to candidates for appointments and requirements to appointments. It should be noted that it is not always the intersection of the sets of solutions to both problems, and then the task has no decision. In this case the problem should be solved on the basis of indistinct intervals, but the solving will be received in the form of an indistinct appointment matrix. The results of solving of optimization problems are compared with results, which are received on base of fuzzy binary relations ( (max-min) — composition and (max-prod) — composition). This comparison is necessary for more reliable conclusions about the selection of candidates
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