Making valid inferences about network origin-destination (OD) demands from limited link traffic count data requires a carefully structured data collection strategy. Determination of the required number of vehicle detectors (VDs) and their installation in strategic locations for OD estimation purpose is essentially a network location problem. In the present research, an integer programming framework based on the user equilibrium assumption was developed to determine the most desirable locations for the deployment of vehicle detectors. The proposed models were evaluated under a simplified transportation network and hypothetical OD demands. Numerical results indicate that the proposed mathematical programming model framework is able to find the critical VD deployment locations for OD demand estimation purpose under limited budgetary resources. These findings can beneficially contribute to the preparation of a desirable vehicle detector deployment plan in a general transportation network.