invariant of bin packing
Since the number of bins is fixed, the problems boils down to a job shop scheduling with atomic jobs. See https://en.wikipedia.org/wiki/Job_shop_scheduling#Atomic_jobs

A solution is given by $\max\{ 1/m \sum_{i=1}^n t_i, max_i t_i  \}$
where $t_i$ represents the $i$th integer and $m$ represent the set length. The wiki reference above includes a paper with the proof.

EDIT after request on polynomial time
Since it's equivalent to the partition problem, which is NP-hard, this problem is also NP-hard and therefore not solvable in polynomial time.