Shellability of Componentwise Discrete Polymatroids

In the present paper, motivated by a conjecture of Jahan and Zheng, we prove that componentwise polymatroidal ideals have linear quotients. This solves positively a conjecture of Bandari and Herzog. We introduce componentwise discrete polymatroids, as the combinatorial counterpart of componentwise polymatroidal ideals, and show that they are shellable multicomplexes.