In 1977, Orlik-Randell conjectured a distinguished basis of vanishing cycles with a nice combinatorial property in the Milnor fiber associated to an invertible polynomial of chain type. Motivated by their conjecture and HMS, we construct a full exceptional collection in the category of maximally graded matrix factorizations, which is a Lefschetz decomposition with respect to a polarization in the sense of Kuznetsov–Smirnov.