  Efficient resource allocation is one of the main driving forces of human
civilizations. Of the many existing approaches to resource allocation, matrix
completion is one that is frequently applied. In this paper, we investigate a
special type of matrix completion problem concerning the class of
$(0,1)$-matrices with given row/column sums and certain zeros prespecified. We
provide a necessary and sufficient condition under which such a class is
nonempty. The condition is stated in the form of the nonnegativity of a
structure tensor constructed from the information regarding the given
row/column sums and fixed zeros. Moreover, we show that a more general matrix
completion problem can be studied in a similar manner, namely that involving
the class of nonnegative integer matrices with prescribed row/column sums,
predetermined zeros, and different bounds across the rows. To illustrate the
utility of our results, we apply them to demand response applications in smart
grids. Specifically, we address two adequacy problems in differentiated energy
services, namely, the problems of supply/demand matching and minimum purchase
profile.
