The Robust Weapon Target Assignment Problem

We study the weapon target assignment problem under target information uncertainty. We propose three stochastic/ robust optimization models that are average case, worst case, and regret oriented. We show that the average-case and worst-case oriented models can be rewritten as equivalent deterministic ones that are relatively easy to solve. We then show that the regret-based approach yields a model that is less conservative but is substantially more computationally demanding to solve as it includes a number of constraints that grow exponentially in the problem size. To address this, we propose three Benders-like decom-position schemes that increase in sophistication and incorpo-rate two linearization schemes to handle nonlinear con-straints. To assess the performance of our numerical schemes, we conduct an extensive numerical study. Our results indicate that our proposed algorithms perform well and solve most problem instances in reasonable time.