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

Ajay Kumar Bhurjee (), Pankaj Kumar () and Pavan Kumar ()

Operations Research and Decisions, 2025, vol. 35, issue 2, 1-22

Abstract: 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 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://ord.pwr.edu.pl/assets/papers_archive/ord2025vol35no2_1.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wut:journl:v:35:y:2025:i:2:p:1-22:id:1

DOI: 10.37190/ord250201

Access Statistics for this article

More articles in Operations Research and Decisions from Wroclaw University of Science and Technology, Faculty of Management Contact information at EDIRC.
Bibliographic data for series maintained by Adam Kasperski ().