Phasor measurement units (PMUs) are preferred for installation at weak buses in a power network. Therefore, the weak buses need to be located and the strategic locations of PMUs identified to ensure network observability. Thus, the primary aim of this work is to identify the placements of the maximum number of PMUs installed at the weak buses in the electrical network. The voltage collapse proximity indicator, line stability index, fast voltage stability index, and a new voltage stability indicator utilizing load flow measurement are used to determine the weak buses. A novel deterministic methodology based on a binary-integer linear programming model is then proposed to determine the optimal locations of PMUs. The effect of a single PMU outage considering the weak buses is also demonstrated. The effectiveness of the developed approach is tested and validated on the standard IEEE 14-, 118-, 300-, and New England 39-bus systems. The obtained results are also compared to those using different weak bus methodologies.