  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
$d_{_{1}}\otimes d_{_{2}}\otimes...\otimes d_{_{n}}$. 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 which can be
solved \emph{exactly} by using simplex method. The decomposability and
non-decomposability of these EWs are studied and it is shown that it has a
close connection with eigenvalues and optimality of EWs. Also using the Jamio\l
kowski isomorphism, the corresponding possible positive maps, including the
generalized reduction maps of Ref. \cite{Hall1}, are obtained.
