Computational Difficulties of Bilevel Linear Programming

Computational Difficulties of Bilevel Linear Programming

We show, using small examples, that two algorithms previously published for the Bilevel Linear Programming problem (BLP) may fail to find the optimal solution and thus must be considered to be heuristics. A proof is given that solving BLP problems is NP-hard, which makes it unlikely that there is a...

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Veröffentlicht in:Operations research 1990-05, Vol.38 (3), p.556-560
Hauptverfasser: Ben-Ayed, Omar, Blair, Charles E
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
analysis of algorithms
Applied sciences
Bards
computational complexity: bilevel linear programming is NP-hard
Exact sciences and technology
games/group decisions
Heuristic
Integer programming
Integers
Linear programming
Mathematical models
Mathematical programming
multiple criteria: bilevel linear programming
noncooperative: algorithms for solving Stackelberg games
Operational research and scientific management
Operational research. Management science
Operations research
Optimal solutions
Optimization
programming
Technical Notes
Theory
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Beschreibung
Zusammenfassung:We show, using small examples, that two algorithms previously published for the Bilevel Linear Programming problem (BLP) may fail to find the optimal solution and thus must be considered to be heuristics. A proof is given that solving BLP problems is NP-hard, which makes it unlikely that there is a good, exact algorithm.
ISSN:0030-364X
1526-5463
DOI:10.1287/opre.38.3.556