Bilevel linear programming with ambiguous objective function of the follower

Masahiro Inuiguchi () and Puchit Sariddichainunta ()
Additional contact information
Masahiro Inuiguchi: Osaka University
Puchit Sariddichainunta: Osaka University

Fuzzy Optimization and Decision Making, 2016, vol. 15, issue 4, No 3, 415-434

Abstract: Abstract Bilevel linear optimization problems are the linear optimization problems with two sequential decision steps of the leader and the follower. In this paper, we focus on the ambiguity of coefficients of the follower in his objective function that hinder the leader from exactly calculating the rational response of the follower. Under the assumption that the follower’s possible range of the ambiguous coefficient vector is known as a certain convex polytope, the leader can deduce the possible set of rational responses of the follower. The leader further assumes that the follower’s response is the worst-case scenario to his objective function, and then makes a decision according to the maximin criteria. We thus formulate the bilevel linear optimization problem with ambiguous objective function of the follower as a special kind of three-level programming problem. In our formulation, we show that the optimal solution locates on the extreme point and propose a solution method based on the enumeration of possible rational responses of the follower. A numerical example is used to illustrate our proposed computational method.

Keywords: Bilevel optimization; Robust optimization; Minimax criterion; Enumerative algorithm; Linear programming (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10700-016-9231-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:fuzodm:v:15:y:2016:i:4:d:10.1007_s10700-016-9231-2

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10700

DOI: 10.1007/s10700-016-9231-2

Access Statistics for this article

Fuzzy Optimization and Decision Making is currently edited by Shu-Cherng Fang and Boading Liu

More articles in Fuzzy Optimization and Decision Making from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().