Proof of an integer programming problem

From: Gang Lu (ganglu_at_usc.edu)
Date: 04/08/04 

Date: Wed, 7 Apr 2004 16:50:43 -0700

Hi,

I am trying to prove whether a problem is NP. Can someone give me some
hints?
Here is the problem:

Given Cij, K, V are known and K<<V, Cii=0
Object:
            min SUM SUM Cij*[(Xj-Xi)+Sij]
                     i j
Subject to:
            i, j belong to {0,1,.....V}
            Xi belongs to {0,1,2,.....K}
            Sij belongs to {0, K} i.e. Sij can be only either 0 or K
            Sij+(Xj-Xi)<=K
            Sij+(Xj-Xi)>0

Thanks for your time.

Regards,
Gang