Stochastic Weapon Target Assignment Problem under Uncertainty in Targeting Accuracy

Abstract

We consider a model that minimizes the total cost incurred by assigning available weapons to existing targets in order to reduce enemy threats, which is called the weapon target assignment problem (WTAP). This study addresses the stochastic versions of WTAP, in which data, such as the probability of destroying a target, are given randomly (i.e., data are identified with certain probability distributions). For each type of random data or parameter, we provide a stochastic optimization model on the basis of the expected value or scenario enumeration. In particular, when the probabilities of destroying targets depending on weapons are stochastic, we present a stochastic programming formulation with a simple recourse. We show that the stochastic model can be transformed into a deterministic equivalent mixed integer programming model under a certain discrete probability distribution of randomness. We solve the stochastic model to obtain an optimal solution via the mixed integer programming model and compare this solution with that of the deterministic model.

Mixed-Integer Linear Programming Model by Linear Approximation for a Strike Package-to-Target Assignment Problem

“…Furthermore, studies on the solution methodologies for a WTA have been actively performed because Lloyd and Witsenhausen [19] proved that it is a combinatorial optimization problem and is NP-Complete. Some researches, such as those of Chang et al [20], Orlin [21], and Lee and Shin [22], suggested exact solution methods under the assumption of one type of weapon or less than one bomb per target. Kwon et al [23] linearized the WTA model by the logarithmic transformation and proposed the Lagrangian relaxation approach and branch-andbound (B&B) algorithm.…”