In the face of budgetary limitations in organizations, identifying critical facilities for investing in quality improvement plans could be a sensible approach. Here, hierarchical facilities with specified covering radius are considered. If disruption happens to a facility, its covering radius will be decreased. For this problem, a bi-objective mathematical formulation is proposed. Critical facilities are equivalent to the facilities which attacking them cause the most reduction in the quality of the system performance. Consequently, this problem is studied in the framework of interdiction problem. To solve the multi-objective model, the weighting-sum approach is applied. The first interdictor’s objective function helps decision makers to identify the vulnerability of the system. Moreover, the second objective function may assist in minimizing the cost of applied quality improvement plans

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