Multiple supply voltage (MSV) assignment is a highly effective means of reducing power consumption. Many existing algorithms perform very well for power reduction. However, they do not handle the area issue of level shifters. In some cases, although one gets a superior result to reduce the power consumption, but many extra level shifters are needed to add so that the circuit area will be over the specification. In this paper, we present an effective integer linear programming (ILP)-based MSV assignment approach to solve two problems with different objectives. For the objective of power reduction under timing constraint, compared with GECVS algorithm, the power consumption obtained by our proposed approach can be further reduced 0 to 5.46% and the number of level shifters is improved 16.31% in average. For the objective of power reduction under constraints of both timing and area of level shifters, the average improvement of power consumption obtained by our algorithm is still better than GECVS while reducing the number of level shifters by 22.92% in average. In addition, given a constraint of total power consumption, our algorithm will generate a design having minimum circuit delay. Experimental results show that the proposed ILP-based MSV assignment algorithm solves different problems flexibly.