This paper presents a general ILP model for analyzing the supply noise induced worst path delay variation. The proposed model can address various modes of supply noise analysis: function based, two-vector pattern based, or multiple cycle analysis, additionally capable of including user-specified constraints. The formulated ILP problem is solved via a relaxation approach, which produces a conservative upper-bound estimation to the worst path delay variation at any iteration. The paper applies sub-gradient optimization to improve those upper bounds. Experimentations have demonstrated the efficiency of the proposed approach, by comparisons with a commercial ILP solver and traditional supply noise modeling approaches.