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Comparison of Fuzzy Solution Approaches for a Bilevel Linear Programming Problem
(Springer Science and Business Media Deutschland GmbH, 2023) Altınkaynak, Büşra; Göçken, Tolunay; Yeşilkaya, Murat; Birgören, Burak; Daş, Gülesin Sena
In this study, we consider solution approaches used to solve the proposed bilevel linear programming model for an Industrial Symbiosis network. We first solve this model with the well-known Karush-Kuch-Tucker (KKT) approach. However, transforming a bilevel programming model with the KKT approach increases the number of variables and constraints. For this reason, we use the fuzzy programming approach and the fuzzy goal programming approaches as alternatives to the KKT approach. Next, we compare the results of the KKT approach with these methods and examine the suitability of these approaches to solve our bilevel problem. Unlike previous studies, which claimed that fuzzy approaches mostly outperform the KKT approach, in our case, the best solution is obtained with the KKT approach. This is most probably because these approaches ignore the hierarchical nature of the problem. We believe that more research on fuzzy approaches is needed to evaluate the suitability of these approaches for solving bilevel programming problems. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.