Partition array into k subsets We are given an array and a number K. Partition array into K subsets such that 

let MaxSum be the maximum sum of among subsets.

We have to minimize summation =$$\sum_{i=1}^{k}MaxSum-sum(i) $$

Is this problem polynimial time solvable?
I'm assuming by $sum(i)$ you mean that given an ordering of the $k$ partitioned subsets, sum over all elements of the $i$th subset.

The $k=2$ case is the optimization variant of the set partitioning problem (https://en.wikipedia.org/wiki/Partition_problem) which is known to be as hard as subset sum. EDIT: The general case is as difficult by reduction from $k=2$.