In the future, the arsenal of the U.S. military will include Space-delivered weapons, released by reusable launch vehicles. Entry vehicles released from the launch platforms will be capable of guiding to target locations throughout the world. In order to adequately incorporate these weapons into military plans, theater commanders will require sophisticated planning algorithms to maximize the likelihood of destroying the most important targets. This thesis develops a target assignment algorithm which uses a sequence of linear auctions to optimize the assignment of entry vehicles to weighted targets. This result can be improved over time by use of a directed search method, which uses numerous sequences of linear auctions to improve on solutions by eliminating poor assignments. These methods are compared to greedy methods, showing improvement in the assignment solution.