Abstract
In this paper, we focus on stochastic two-level integer programming problems with cooperative decision makers. Using the fractile criterion optimization model in chance constrained programming, the formulated stochastic two-level integer programming problems are transformed into deterministic ones. Taking into account vagueness of judgments of the decision makers, we present an interactive fuzzy programming method to derive a satisfactory solution through interactions with the upper-level decision maker in consideration of the cooperative relation to the lower-level decision maker. For solving transformed deterministic problems efficiently, we also introduce genetic algorithms with double strings for nonlinear integer programming problems. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.
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Sakawa, M., Katagiri, H. & Matsui, T. Interactive fuzzy stochastic two-level integer programming through fractile criterion optimization. Oper Res Int J 12, 209–227 (2012). https://doi.org/10.1007/s12351-010-0085-z
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DOI: https://doi.org/10.1007/s12351-010-0085-z