Poznámky k dekompozici nelineárních rozpočtových vzorců

A note on decomposition of nonlinear budget formula

conference paper

en

The paper focuses on the theoretical problem to find an optimal decomposable representation of the given nonlinear function. The key part of the paper defies necessary functional analysis concepts and reviews their properties. Then the general solution for the studied problem is derived. The paper presents the first results about studied decomposability and identifies the directions for the future research. The paper also shows how to utilize features of a suitable functional space by using a real-world motivating example. Although the presented technique can be widely applied, we focus on this example from the beginning of the paper as it leads to the challenging and important problem of so called nonlinear budget formula decomposition. For public institutions as, e.g., universities, performance indicators based formulas are utilized to construct their budgets. Most of the formulas are linear that allows an easy application of the formula within the institution. However, some weak features of this approach led to the use of nonlinear formula as well. Especially, the formula users often focus on the most profitable performance indicators and omit others. Then, the institution activities tend to degenerate in certain less profitable areas although it is not a public goal. So, the nonlinear formula inspired by Cobb-Douglas function has been introduced a used as well. Its weakness related to problems with its application within institution is discussed in this paper. Because of the nature of the formula, some institution departments financed by it and their performance indicators can be underestimated by this formula. Therefore, abovementioned optimization-related results can be applied to the problem as it is shown.

Příspěvek se zaměřuje na teoretický problém, jak naít optimální rozložitelnou reprezentaci nelineární funkce.

The paper focuses on the theoretical problem to find an optimal decomposable representation of the given nonlinear function. The key part of the paper defies necessary functional analysis concepts and reviews their properties. Then the general solution for the studied problem is derived. The paper presents the first results about studied decomposability and identifies the directions for the future research. The paper also shows how to utilize features of a suitable functional space by using a real-world motivating example. Although the presented technique can be widely applied, we focus on this example from the beginning of the paper as it leads to the challenging and important problem of so called nonlinear budget formula decomposition. For public institutions as, e.g., universities, performance indicators based formulas are utilized to construct their budgets. Most of the formulas are linear that allows an easy application of the formula within the institution. However, some weak features of this approach led to the use of nonlinear formula as well. Especially, the formula users often focus on the most profitable performance indicators and omit others. Then, the institution activities tend to degenerate in certain less profitable areas although it is not a public goal. So, the nonlinear formula inspired by Cobb-Douglas function has been introduced a used as well. Its weakness related to problems with its application within institution is discussed in this paper. Because of the nature of the formula, some institution departments financed by it and their performance indicators can be underestimated by this formula. Therefore, abovementioned optimization-related results can be applied to the problem as it is shown.

nelineární rozpočtové vzorce, ukazatele výkonnosti, rozklad, funkční prostory, norma, minimalizace.

nonlinear budget formula, performance indicators, decomposition, functional space, norm, minimization.

2012

27.06.2012

978-80-214-4540-6

1803-3814

MENDEL 2012: 18th International Conference on Soft Computing

2012

1

174–179

6