Since I didn't get reply, I guess there isn't simple solution.
I have an idea where M can be, but I must say I cannot prove it simple.
M would be first point after B on DB.
This is the problem:
In a plane of quadrilateral ABCD find point M such that sum of AM,BM,CM and DM be smallest.
Solution for convex quadrilateral ABCD is simple, M is intersection of diagonals, but for concave quadrilateral I can't see some simple solution.