An investigation of the linear three level programming problem

The open-loop Stackelberg game is conceptually extended to p players by the multilevel programming problem (MLPP) and can thus be used as a model for a variety of hierarchical systems in which sequential planning is the norm. In this paper the rational reaction sets for each of the players is first...

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Bibliographic Details
Published in:IEEE transactions on systems, man, and cybernetics Vol. SMC-14; no. 5; pp. 711 - 717
Main Author: Bard, Jonathan F.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.1984
Institute of Electrical and Electronics Engineers
Subjects:
Applied sciences
Cybernetics
Decision support systems
Decision theory. Utility theory
Exact sciences and technology
Games
Generators
Linear programming
Operational research and scientific management
Operational research. Management science
Programming
Vectors
Non linear programming
Multicriteria analysis
Decision making
Decision theory
Game theory
Mathematical programming
ISSN:0018-9472, 2168-2909
Online Access:Get full text
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Summary:The open-loop Stackelberg game is conceptually extended to p players by the multilevel programming problem (MLPP) and can thus be used as a model for a variety of hierarchical systems in which sequential planning is the norm. In this paper the rational reaction sets for each of the players is first developed, and then the geometric properties of the linear MLPP are stated. Next, first-order necessary conditions are derived and the problem is recast as a standard nonlinear program. A cutting plane algorithm employing a vertex search procedure at each iteration is proposed to solve the linear three-level case. An example is given to highlight the results along with some computational experience. Although only a limited number of test problems were examined, the amount of work required to find a solution seems to grow with the square of the row dimensions of the underlying polyhedral constraint set.
ISSN:0018-9472
2168-2909
DOI:10.1109/TSMC.1984.6313291