Abstract
On the example of the Weapon-Target Assignment (WTA) problem, we present risk management procedures for military applications that address uncertainties in distributions. In the considered formulation, the cumulative damage to the targets is maximized, which leads to Mixed-Integer Programming problems with non-linear objectives. Ву using a relaxation technique that preserves integrality of the optimal solutions, we developed LP formulations for the deterministic and two-stage stochastic WTA problems. The risk of incorrect second-stage decisions due to errors in specified distributions of the second-stage targets is controlled using the Conditional Value-at-Risk risk measure. An LP formulation for the two-stage SWTA problem with uncertainties in distributions has been developed, which produces integer optimal solutions for the first-stage decision variables, and also yields a tight lower bound for the corresponding MIP problem.
This work was supported in part by the Air Force grant F49620–01–1–0338
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Krokhmal, P., Murphey, R., Pardalos, P., Uryasev, S. (2004). Use of Conditional Value-at-Risk in Stochastic Programs with Poorly Defined Distributions. In: Butenko, S., Murphey, R., Pardalos, P.M. (eds) Recent Developments in Cooperative Control and Optimization. Cooperative Systems, vol 3. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0219-3_13
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DOI: https://doi.org/10.1007/978-1-4613-0219-3_13
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