Big \sum instead of small \sum in array environment

By putting a \displaystyle in front of the \sum. You basically want the font to behave like it does in a top-level environment, because it's nested in an array it gets assigned a \textstyle font size.

Why you're not aligning the equations on the equals sign beats me though. It might be better to use two equation environments in this case, the code wouldn't look so bloated as it does now.

I would typeset this as follows:

\begin{align*}
\min \: A &= \min \: \sum_{i\in B} C_i \\
\min \: D &= \min \: \sum_{i\in B} \pi_i \cdot F_i
\end{align*}

Then it is aligned, and the sums are as you want them. If you do not want it aligned, use gather instead of align. If you want more vertical space between the two lines, use \\[1ex] instead of \\. (Incidentally, I would not use \: after the \min.)