Efficiency and equity are the two crucial factors to be considered when allocating public resources such as voting machines. Existing allocation models are all single-objective, focusing on maximizing either efficiency or equity despite the fact that the actual decision-making process involves both issues simultaneously. We propose a bi-objective integer program to analyse the tradeoff between the two competing objectives. The new model quantifies the sacrifice in efficiency in order to achieve a certain improvement in equity and vice versa. Using data from the 2008 United States Presidential election in Franklin County, Ohio, we demonstrate that our model is capable of producing significantly more balanced allocation plans, in terms of efficiency and equity, than current practice or other competing methods.