Risk management for cyber-infrastructure protection: A bi-objective integer programming approach

Information and communication technology supply chains present risks that are complex and difficult for organizations to manage. The cost and benefit of proposed security controls must be assessed to best match an organizational risk tolerance and direct the use of security resources. In this paper, we present integer and stochastic optimization models for selecting a portfolio of security controls within an organizational budget. We consider two objectives: to maximize the risk reduction across all potential attacks and to maximize the number of attacks whose risk levels are lower than a risk threshold after security controls are applied. Deterministic and stochastic bi-objective budgeted difficulty-threshold control selection problems are formulated for selecting mitigating controls to reflect an organization’s risk preference. In the stochastic problem, we consider uncertainty as to whether the selected controls can reduce the risks associated with attacks. We demonstrate through a computational study that the trade-off between the two objectives is important to consider for certain risk preferences and budgets. We demonstrate the value of the stochastic model when a relatively high number of attacks are desired to be secured past a risk threshold and show the deterministic solution provides near optimal solutions otherwise. We provide an analysis of model solutions.