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Decentralization in Linear Programming Models
Author(s) -
Van De Panne C.
Publication year - 1989
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1989.tb01880.x
Subject(s) - mathematical optimization , decomposition , parametric programming , linear programming , matrix (chemical analysis) , mathematics , basis (linear algebra) , parametric statistics , set (abstract data type) , computer science , ecology , statistics , materials science , geometry , composite material , biology , programming language
This paper proposes a decomposition of a linear programming problem based on the structure of the optimal basis matrix. If this matrix contains a zero matrix of appropriate dimensions, the problem may be decomposed into a price‐setting problem and a quantity‐setting problem. This decomposition is valid for a set of coefficients of the problem to be determined by parametric programming. It can be applied to problems with common constraints or common variables. An application to dairy production planning is discussed and a comparison with the Dantzig‐Wolfe decomposition principle is given.