Some Optimization Problems and Row Sum of Zero-one Matrices

Assume that A is an matrix, let ; be the i-th row sum of A and ; be the j-th column sum of A. Define, R, the row sum vector of A, and S, the column sum vector of A, as In this article a practical problem will be modeled. Then several constraints, which are related to the vectors R and S, will be considered on this kind of problems, and by the help of combinatorial theorems appropriate solutions will be obtained. At last, for given vectors R and S we discuss the matrices whose row sum and column sum vectors are as close as possible to R and S, respectively, and also will introduce two algorithms to produce such matrices