Min algebraic duality (Q1090352)

The author developes an elimination scheme for inductively solving systems of min-algebraic equations of the form \[ \min_{1\leq j\leq n}(a_{ij}+x_ j)=b_ i,\quad i=1,...,m \] where \(a_{ij}\in Z\), \(b_ i\in Z\) are given. A theorem of alternatives for such systems is proved. This theorem is closely related to one of the duality models described by \textit{A. J. Hoffman} [Nav. Res. Logist. Q. 10, 369-373 (1963; Zbl 0122.153)].