Transportation interval situations and related games

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 con...

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Bibliographic Details
Published in:OR Spectrum 2016-01, Vol.38 (1), p.119-136
Main Authors: Palancı, O., Alparslan Gök, S. Z., Olgun, M. O., Weber, G.-W.
Format: Article
Language:English
Subjects:
Awards
Business and Management
Calculus of Variations and Optimal Control
Optimization
Constraints
Cooperation
Game theory
Games
Intervals
Logistics
Mathematical models
Operations research
Operations Research/Decision Theory
Optimization
Regular Article
Retail stores
Studies
Texts
Transportation
Transportation problem (Operations research)
Uncertainty
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Summary: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.
ISSN:0171-6468
1436-6304
DOI:10.1007/s00291-015-0422-y