Analytic survey of methods for solving multicriteria mathematical programming problems.

*(Russian)*Zbl 0642.90063The paper is concerned with man-machine interactive procedures (MMIP’s) of decision making in multicriteria mathematical programming problems. The MMIP contains the following two recurring steps: 1) the optimization step, when the computer finds a version of the solution using the available information; 2) the analysis step, when the decision maker (DM), analysing this version, either takes as the desired solution or generates additional information for the computer in the next step. In a book of O. I. Larichev [“Systems research” (Russian), Moscow, Nauka (1982)] the correspondence between requirements imposed on the DM in MMIP, on the one hand, and possibilities of the DM, on the other hand, is used as the criterion of the quality of MMIP. An MMIP is called correct if it satisfies this criterion. To decide whether MMIP is correct, the authors suggest to estimate the possibilities of the DM with respect to the way he realizes standard elementary operations by information processing. These operations are subdivided into complex, admissible and undefined ones. The correct MMIP includes the admissible operations and has small sensitivity with respect to random errors of the DM. Twenty MMIP’s, some of which well known, are analysed. Only six of them can be considered as correct MMIP’s. The other fourteen MMIP’s either use complex operations or have large sensitivity.

Reviewer: A.Kleimenov

##### MSC:

90B50 | Management decision making, including multiple objectives |