I have the following problem
$$\max_{X_{i,j},i\in N_{U},j\in N_{B}}\sum_{i=1}^{N_U}\sum_{j=1}^{N_B}R_{i,j}X_{i,j}$$ $$\text{subject to}$$ $$a_{\min}\le\sum_{j=1}^{N_B}X_{i,j}\le a_{\max}, \forall i$$ $$\sum_{i=1}^{N_U}X_{i,j}\le b_{\max}, \forall j$$
It is a convex problem,b ut I need a heuristic approach to solve this.
Here, $R$ is a knowm matrix. $X$ is a binary matrix. $a_{\min}$, $a_{\max}$ and $b_{\max}$ are also know. and positive
Any suggestions