Solution of a bi-level linear programming problem with uncertain parameters and its application

In this paper, a bi-level linear programming problem characterized by interval uncertainty in the coefficients of both objectives and constraints is thoroughly examined. The Karush-Kuhn-Tucker (KKT) optimality conditions for interval nonlinear programming problems have been developed to address this...

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Published in:Operations research and decisions Vol. 35; no. 2; pp. 1 - 22
Main Authors: Kumar Bhurjee, Ajay, Kumar, Pankaj, Kumar, Pavan
Format: Journal Article
Language:English
Published: Wrocław University of Science and Technology 2025
ISSN:2081-8858, 2391-6060
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Abstract In this paper, a bi-level linear programming problem characterized by interval uncertainty in the coefficients of both objectives and constraints is thoroughly examined. The Karush-Kuhn-Tucker (KKT) optimality conditions for interval nonlinear programming problems have been developed to address this challenge. Utilizing these conditions, the interval bi-level programming problem has been transformed into a deterministic nonlinear programming problem. Subsequently, a comprehensive methodology has been developed to solve the transformed problem. The proposed approach has been validated through numerous illustrative examples that demonstrate its successful execution. Furthermore, the developed methodology has been effectively applied to a practical problem in supply chain planning, showcasing its relevance and applicability in real-world scenarios. (original abstract)
AbstractList In this paper, a bi-level linear programming problem characterized by interval uncertainty in the coefficients of both objectives and constraints is thoroughly examined. The Karush-Kuhn-Tucker (KKT) optimality conditions for interval nonlinear programming problems have been developed to address this challenge. Utilizing these conditions, the interval bi-level programming problem has been transformed into a deterministic nonlinear programming problem. Subsequently, a comprehensive methodology has been developed to solve the transformed problem. The proposed approach has been validated through numerous illustrative examples that demonstrate its successful execution. Furthermore, the developed methodology has been effectively applied to a practical problem in supply chain planning, showcasing its relevance and applicability in real-world scenarios. (original abstract)
Author Kumar Bhurjee, Ajay
Kumar, Pankaj
Kumar, Pavan
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