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A Note on “An Efficient Zero‐One Formulation of the Multilevel Lot‐Sizing Problem”
Author(s) -
Rajagopalan S.
Publication year - 1992
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.1540-5915.1992.tb00433.x
Subject(s) - unimodular matrix , integer programming , integer (computer science) , mathematical optimization , zero (linguistics) , mathematics , constraint (computer aided design) , linear programming , matrix (chemical analysis) , sizing , relaxation (psychology) , linear programming relaxation , integer matrix , computer science , discrete mathematics , symmetric matrix , nonnegative matrix , art , philosophy , materials science , linguistics , visual arts , composite material , psychology , social psychology , geometry , quantum mechanics , programming language , eigenvalues and eigenvectors , physics
In a recent paper, McKnew, Saydam, and Coleman [3] presented a novel zero‐one integer programming formulation of the multilevel dynamic, deterministic lot‐sizing problem in assembly systems. They stated that “the relaxed linear programming solution to this formulation will always be integer’ [3, p. 280] since the constraint matrix is totally unimodular. In this note, we point out that the constraint matrix is not totally unimodular and therefore the authors’claim that a linear relaxation of the zero‐one integer formulation always yields an integer solution is not true.