# algorithms – Assignment Problem – Computer Science Stack Exchange

This is something like assignment problem, we have 2 group of people, first contains $$n$$ person and second contains $$m$$ person. we have a matrix $$C$$ which is an $$n times m$$ matrix and our goal is to find an assignment matrix $$A$$ which is again an $$n times m$$ binary matrix (contains ones and zeros) and if $$A_{ij}$$ is $$1$$ it shows $$i$$-th person from first group has assigned to $$j$$-th person of second group, and maximize $$displaystylesum_{i}sum_{j} C_{ij}X_{ij}$$, subject to following constraints:

$$1);; forall i: ;; displaystylesum_{j} X_{ij} = 1 \ 2);; forall j: ;; displaystylesum_{i} X_{ij} le 2$$

how should I solve this problem?

how should we solve if we have another matrix $$D$$ and we also want $$displaystylesum_{i} D_{ij}X_{ij} le constant$$ ?