Given an $m*n$ positive matrix $\mathbf{A}$ and an integer $K$, where $0<K<n$.
Now, I have a $m*n$ binary matrix $\mathbf{B}$. I need to dertermine the value of each element in matrix $\mathbf{B}$. The objective is to
$$\text{minimize} ~~\sum_{0<j \leq n} { (~~\max_{0<i \leq m}\{A_{ij}B_{ij} \}~~) }$$
suject to: $$(\sum_{0<j\leq n}{B_{ij}}) = K~~ \text{for each} ~~i\in \{1, 2, \ldots, m\}$$.
This problem seems to be NP-hard to me## Heading ##. I have checked the NP problems listed here. But I am still not able to know from which problem I should try to reduce. Could anyone give me a hint? Thank you.