I'm trying to solve a problem for human resource allocation that has a function that receives the number of people working on a project and returns the time to finish it. The number of employees in a project has a nonlinear relation with the time to end it, therefore it can be represented as a matrix, the line controlling the number of employees, and the column controlling the project. For example, in the matrix below (in days), if I allocate 3 people in the 1° project, it will end in 5 days.
$$ A=\begin{bmatrix} 10 & 9 & 7\\ 8 & 7 & 6.5\\ 5 & 6.5 & 6\\ \end{bmatrix} $$
I think I can use binary variables, having one of these for each position of the matrix, to transform the problem into a mixed-integer linear problem, which is what I prefer so I can assess a metaheuristic that I used to solve it. But I also think that it isn't the right approach to solve it.