A new class of entanglement witnesses (EWs) called reduction type entanglement witnesses is introduced, which can detect some multi-qudit entangeled states including PPT ones with Hilbert space of dimension d1 ⊗ d2 ⊗ ... ⊗ dn . The novelty of this work comes from the fact that the feasible regions turn out to be convex polygons, hence the manipulation of these EWs reduces to linear programming ...