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Constructing and Applying Objective Functions pp 117–169Cite as

A Unified Model for Cardinally and Ordinally Constructing Quadratic Objective Functions

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 510))

Abstract

A model for constructing quadratic objective functions (= utility functions) from interviewing a decision maker is considered. The interview is designed to guarantee a unique non-trivial output of the model and to enable estimating both cardinal and ordinal utility, depending on the interview scenarios selected.

The model is provided with operational restrictions for the monotonicity of the objective function (= either only growth, or only decrease in every variable) and its quasi-concavity (= convexity of the associated preference). Thereby constructing a monotonic quasi-concave quadratic objective function is reduced to a problem of non-linear programming. To support interactive editing of a quadratic objective function, the stability of the model (the continuous dependence of the output ordinal preference on the input data) is proved.

For illustration, we construct a quadratic objective function of ski station customers. Then it is used to adjust prices of 10 ski stations in the south of Stuttgart.

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Authors and Affiliations

  1. University of Hagen, Feithstr. 140 (ESG), D-58084, Hagen, Germany

    Andranik Tangian

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  1. Andranik Tangian
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Editors and Affiliations

  1. University of Hagen ESG, Feithstrasse 140, 58084, Hagen, Germany

    Andranik S. Tangian  & Josef Gruber  & 

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Tangian, A. (2002). A Unified Model for Cardinally and Ordinally Constructing Quadratic Objective Functions. In: Tangian, A.S., Gruber, J. (eds) Constructing and Applying Objective Functions. Lecture Notes in Economics and Mathematical Systems, vol 510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56038-5_8

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  • DOI: https://doi.org/10.1007/978-3-642-56038-5_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42669-1

  • Online ISBN: 978-3-642-56038-5

  • eBook Packages: Springer Book Archive

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