Transportation interval situations and related games

Date

2016-01-01

Author

PALANCI, Osman
ALPARSLAN GÖK, Sırma Zeynep
OLGUN, MEHMET ONUR
Weber, Gerhard Wilhelm

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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 (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.

Subject Keywords

Cooperative Interval Games, Transportation Games, Uncertainty, Interval Shapley Value, Proportional Rule

URI

https://hdl.handle.net/11511/56518

Journal

OR SPECTRUM

DOI

https://doi.org/10.1007/s00291-015-0422-y

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

O. PALANCI, S. Z. ALPARSLAN GÖK, M. O. OLGUN, and G. W. Weber, “Transportation interval situations and related games,” OR SPECTRUM, pp. 119–136, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56518.