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A Stackelberg Location Problem on a Tree Network with Fuzzy Random Demands

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Advances in Intelligent Decision Technologies

Part of the book series: Smart Innovation, Systems and Technologies ((SIST,volume 4))

Abstract

This paper focuses on a new Stackelberg location problem on a tree network with demands whose sites are given uncertainly and vaguely. By representing their sites as fuzzy random variables on the tree network, the distance between a facility and a customer can be defined as a fuzzy random number. For solving the Stackelberg location problem with the fuzzy random distances, first we introduce the α-level set for fuzzy random numbers and transfer it to the Stackelberg location problem with random demands. Next, the randomness of demands is represented as scenarios for each demand. Then, by using their expectations and variances, it can be reformulated as a version of conventional Stackelberg location problem on a tree network. Its complexity and solution method are shown based upon the characteristics of the facility location.

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Author information

Authors and Affiliations

  1. Graduate School of Human and Natural Environment Sciences, The University of Tokushima, 1-1, Minamijosanjima-cho, Tokushima-shi, Tokushima, 770-8502, Japan

    Takeshi Uno

  2. Graduate School of Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashihiroshima-shi, Hiroshima, 739-8527, Japan

    Hideki Katagiri

  3. Faculty of Applied Information Science, Hiroshima Institute of Technology, 2-1-1, Miyake, Saeki-ku, Hiroshima, 731-5193, Japan

    Kosuke Kato

Authors
  1. Takeshi Uno
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  2. Hideki Katagiri
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  3. Kosuke Kato
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Editor information

Editors and Affiliations

  1. Sellinger School of Business and Management, Loyola University Maryland , 4501 N.Charles Street, 21210, Baltimore, MD, USA

    Gloria Phillips-Wren

  2. School of Electrical and Information Engineering, University of South Australia Adelaide , Mawson Lakes Campus, 5095, South Australia, SA, Australia

    Lakhmi C. Jain

  3. School of Human Science and Environment, University of Hyogo , 1-1-12 Shinzaike-honcho, 670-0092, Himeji, Hyogo, Japan

    Kazumi Nakamatsu

  4. KES International , Shoreham-by-Sea, P.O. Box 2115, BN43 9AF, UK

    Robert J. Howlett

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© 2010 Springer Berlin Heidelberg

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Uno, T., Katagiri, H., Kato, K. (2010). A Stackelberg Location Problem on a Tree Network with Fuzzy Random Demands. In: Phillips-Wren, G., Jain, L.C., Nakamatsu, K., Howlett, R.J. (eds) Advances in Intelligent Decision Technologies. Smart Innovation, Systems and Technologies, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14616-9_56

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  • DOI: https://doi.org/10.1007/978-3-642-14616-9_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14615-2

  • Online ISBN: 978-3-642-14616-9

  • eBook Packages: EngineeringEngineering (R0)

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