On the bicanonical map of algebraic threefolds of general type

We answer an open problem of the first author and Zhang (see Open Problem 6.4 (3) in Math. Z. 258 (2008), 565-585) and prove that, for any nonsingular projective $3$-fold of general type with the geometric genus greater than 201, the bicanonical system is not composed of any pencil of surfaces.