An approximate dynamic programming approach for comparing firing policies in a networked air defense environment

•The threat of theater ballistic missiles remains an important concern for many nations.•This research examines a networked, defense-in-depth air and missile defense problem.•Two approximate dynamic programming (ADP) algorithms provide firing policy solutions.•Designed experiments yield insights about algorithm performance and problem features.•ADP policies outperform current U.S. policy of firing two interceptors at each missile. An objective for effective air defense is to identify the firing policy for interceptor allocation to incoming missiles that minimizes the expected total damage to defended assets over a sequence of engagements. We formulate this dynamic weapon target assignment problem as a Markov decision process and utilize a simulation-based, approximate dynamic programming (ADP) approach to solve problem instances based on a representative scenario. Least squares policy evaluation and least squares temporal differences algorithms are developed to determine approximate solutions. A designed experiment investigates problem features such as conflict duration, attacker and defender weapon sophistication, and defended asset values. An empirical comparison of the ADP policies and two baseline policies (i.e., firing either one or two interceptors at each incoming theater ballistic missile (TBM)) yields several insights: the ADP policies outperform both baseline polices when conflict duration is short and attacker weapons are sophisticated; firing one interceptor at each TBM (regardless of inventory status) outperforms the tested ADP policies when conflict duration is long and attacker weapons are less sophisticated; and firing two interceptors at each TBM (regardless of inventory status), which is the United States Army’s currently implemented policy, is never the superlative policy for the test instances investigated.