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Yoneda Kiyoshi (Fukuoka University), Celaschi Walter (Faculdades de Campinas)
A Utility Function to Solve Approximate Linear Equations for Decision Making
Decision Making in Manufacturing and Services, 2013, vol. 7, nr 1/2, s. 5-18, tab., rys., bibliogr. 4 poz.
Słowa kluczowe
Funkcja użyteczności, Równania liniowe, Optymalizacja, Studium przypadku, Browarnictwo, Podejmowanie decyzji
Utility functions, Linear equation, Optimalization, Case study, Brewing industry, Decision making
Suppose there are a number of decision variables linearly related to a set of outcome variables. There are at least as many outcome variables as the number of decision variables since all decisions are outcomes by themselves. The quality of outcome is evaluated by a utility function. Given desired values for all outcome variables, decision making reduces to "solving" the system of linear equations with respect to the decision variables; the solution being defined as decision variable values such that maximize the utility function. This paper proposes a family of additively separable utility functions which can be defined by setting four intuitive parameters for each outcome variable: the desired value of the outcome, the lower and the upper limits of its admissible interval, and its importance weight. The utility function takes a nonnegative value within the admissible domain and negative outside; permits gradient methods for maximization; is designed to have a small dynamic range for numerical computation. Small examples are presented to illustrate the proposed method. (original abstract)
Pełny tekst
  1. Kato, T., Omachi, S., Aso, H., 2002. Asymmetric gaussian and its application to pattern recognition. In: Joint IAPR International Workshops on Syntactical and Structural Pattern Recognition and Statistical Pattern Recognition (S+SSPR2002). Barcelona, pp. 405-413,, viewed 2012-02-15.
  2. R Core Team, 2012. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna,
  3. Wichers, R., 1996. A Theory of Individual Behavior. Academic Press.
  4. Yoneda, K., 2008. A loss function for box-constrained inverse problems. Decision Making in Manufacturing and Services 2 (1-2), pp. 79-98,
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