Issue: 2025/Vol.35/No.2, Pages
SOLUTION OF A BI-LEVEL LINEAR PROGRAMMING PROBLEM WITH UNCERTAIN PARAMETERS AND ITS APPLICATION
Ajay Kumar Bhurjee
, Pankaj Kumar, Pavan Kumar 
This is not yet the definitive version of the paper. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article.
Cite as: A. K. Bhurjee, P. Kumar, P. Kumar. Solution of a bi-level linear programming problem with uncertain parameters and its application. Operations Research and Decisions 2025: 35(2). DOI 10.37190/ord250201
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.
Keywords: Bi-level programming problem, interval optimization problem, interval analysis, KKT optimality conditions, supply chain
Received: 23 May 2024 Accepted: 20 December 2024
Published online: 8 February 2025