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OR Spectrum

, Volume 38, Issue 1, pp 119–136 | Cite as

Transportation interval situations and related games

  • O. Palancı
  • S. Z. Alparslan Gök
  • M. O. Olgun
  • G.-W. Weber
Regular Article

Abstract

Basically, uncertainty is present in almost every real-world situation, it is influencing and questioning our decisions. In this paper, we analyze transportation interval games corresponding to transportation interval situations. In those situations, it may affect the optimal amount of goods and consequently whether and how much of a product is transported from a producer to a retailer. Firstly, we introduce the interval Shapley value of a game arising from a transportation situation under uncertainty. Secondly, a one-point solution concept by using a one-stage producere depending on the proportional, the constrained equal awards and the constrained equal losses rule is given. We prove that transportation interval games are interval balanced (\(\mathcal {I}\)-balanced). Further, the nonemptiness of the interval core for the transportation interval games and some results on the relationship between the interval core and the dual interval optimal solutions of the underlying transportation situations are also provided. Moreover, we characterize the interval core using the square operator and addressing two scenarios such as pessimistic and optimistic.

Keywords

Cooperative interval games Transportation games  Uncertainty Interval Shapley value Proportional rule 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • O. Palancı
    • 1
  • S. Z. Alparslan Gök
    • 1
  • M. O. Olgun
    • 2
  • G.-W. Weber
    • 3
  1. 1.Department of Mathematics, Faculty of Arts and SciencesSüleyman Demirel UniversityIspartaTurkey
  2. 2.Faculty of Industrial EngineeringSüleyman Demirel UniversityIspartaTurkey
  3. 3.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

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