Typology of conceptual schemes notation of multi-criterion management decisions optimization problems in aerospace sector

Аuthors

Dmitriev O. N.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: olegdmitriev@yandex.ru

Abstract

The aerospace sector features a highly considerable specifics and types spectrum of management problems. Among these problems the presence of management decisions optimization problems is mandatory. Correspondingly, management goals in aviation and space-rocket sectors are diversified, heterogeneous in dimension, conflict and knowingly irreducible to a single utility measure. Thus, in all cases the multicriteriality occurs.

A certain conceptual idea of a group of optimization criteria notations (interpretations) diversification has the right to existence.

In various fields of mathematical modeling identification and algorithm presentation significant progress can be observed, which may lead to creation of tools allowing newly interpret management situations and find new solutions for management optimization problem, based on conceptually new mathematical methods, namely numerically or even of closed form.

The requirements on presentation include:

— Correspondence to the basic fundamentals of scientific cognition;

— Universality with relation to number and conceptual definition of optimization criterions, as well as procedures applied for their evaluation;

— Keeping the sequence of optimization criteria positioning;

— Keeping the dimensionality of original optimization criterions;

— Keeping mutual priority of original optimization criterions;

— Ensuring representation additivity (componentwise addition feasibility);

— Using such structures of scientific theories within which frameworks the inception of solving optimization problems methods is possible;

— Vector optimization criterion applicability for correct scalarization procedure.

The group of management decisions optimization criterions in aerospace sector can be represented (interpreted) by implementation of the following conceptual schemes:

— Conceptual scheme based on the theory of sets. In this case, the original group of optimization criteria is presented in the form of a set K, such that the original optimization criteria are declared disjoint singleton subsets of this set:

;

— Conceptual scheme based on linear algebra. In this case, the group of optimization criteria is presented in the form of a vector , such that the original optimization criteria are declared components of vector criterion:

;

— Conceptual scheme based on the classical algebra. In this case, the group of optimization criteria is represented as a function K, defined as n-th degree polynomial of conditional argument A without constant term, such that:

;

— Conceptual scheme based on the theory of functions of complex variables. In this case, the group of optimization criteria is presented in the form of functions K of complex variables with parameters , defined as a complex variable without the real part, such that:

.

It is obvious, that all abovementioned interpretations provide for the tend to the extremum, which is also a component (maximum or minimum).

Keywords:

aviation, astronautics, decision substantiation, usefulness, interpretation, formalization, optimization criterion, optimization

References

1. Dmitriev O.N. Sistemnyi analiz v upravlenii (System analysis in management), Moscow, Dobroe slovo, 2005, 197 p.

2. Demchenko O.F. Metodologiya matematicheskogo modelirovaniya organizatsionnykh struktur aviatsionno-promyshlennogo kompleksa Rossiiskoi Federatsii (Methodology of mathematical modeling of organizational structures for aviation industrial complex of the Russian Federation), Moscow, KnoRus, 2011, 315 p.

3. Egorov M.M. Organizatsionno-ekonomicheskii mekhanizm munitsipalnogo inkubatsionnogo upravleniya malymi predpriyatiyami promyshlennosti regiona (na primere goroda Ulan-Ude) (Organizational and economic mechanism of management concerning municipal incubation of small enterprises industry in the region (on the example of the city of Ulan-Ude). Doctors thesis, Moscow, MAI, 2006, 204 p.

4. Pilyugina N.Yu. Mekhanizm byudzhetnogo programmirovaniya promyshlennogo territorialnogo kompleksa munitsipalnogo obrazovaniya Rossii (The mechanism of budgetary programming of territorial-industrial complex of the municipal formation in Russia). Doctors thesis, Moscow, MAI, 2009, 251 p.

5. Dubovik M.V. Metodologiya formirovaniya strategii upravleniya kontragentskoi konkurentospobnostyu promyshlennogo kompleksa goroda na mezourovne (Methodology for developing strategies for managing counterparty competitiveness of the industrial complex of the city at the meso-level). Doctors thesis, Moscow, MAI, 2011, 385 p.

6. Dmitriev O.N. Trudy MAI, 2011, no. 49, available at: http://www.mai.ru/science/trudy/eng/published.php?ID=28122&PAGEN_2=2 (accessed 27.12.2011).

7. Bodrunov S.D., Dmitriev O.N., Kovalkov Yu.A. Aviatsionno-promyshlennyi kompleks Rossii na rubezhe XX veka: problemy effektivnogo upravleniya (Aviation industrial complex of Russia at the turn of XX century: problems of efficient management), St.-Petersburg, Korporatsiya Aerokosmicheskoe oborudovanie, 2002, book 1 — 549 p., book 2 — 475 p.