I thought of one way to do this.
Using the algorithm which determines if a point is inside a parallelogram,
one can determine if the polygon contains the point within a $2N$ step ($N=2$ for parallelogram)
I want to do this for $n$-dimensional parallelotope but I guess it will take $2^N$ check for every vertex of the $n$-parallelotope.
Could somebody can suggest a better way, which is computationally faster (in a polynomial time, not exponential)?