In this note a class of convex polyhedral sets of functions is studied. A set of the considered class is non-emplty if it satisfies certain conditions. Using Theorem 1 of this paper in the case of multi-index transportations problems we obtain necessary conditions for the existence of a feasible solution to this problem.
 J. Morávek M. Vlach: On the Necessary Conditions for the Existence of the Solution of Multi-Index Transportation Problem. Opns. Res. 15 (1967).
 K. B. Haley: A Note to the paper by Moravek and Vlach. Opns. Res. 15 (1967), str. 545-546.