A Two-Sided Optimization for Theater Ballistic Missile Defense

We describe JOINT DEFENDER, a new two-sided optimization model for planning the pre-positioning of defensive missile interceptors to counter an attack threat. In our basic model, a defender pre-positions ballistic missile defense platforms to minimize the worst-case damage an attacker can achieve; we assume that the attacker will be aware of defensive pre-positioning decisions, and that both sides have complete information as to target values, attacking-missile launch sites, weapon system capabilities, etc. Other model variants investigate the value of secrecy by restricting the attacker's and/or defender's access to information. For a realistic scenario, we can evaluate a completely transparent exchange in a few minutes on a laptop computer, and can plan near-optimal secret defenses in seconds. JOINT DEFENDER's mathematical foundation and its computational efficiency complement current missile-defense planning tools that use heuristics or supercomputing. The model can also provide unique insight into the value of secrecy and deception to either side. We demonstrate with two hypothetical North Korean scenarios.

[1]  George B.Richardson The Theory of the Market Economy. , 1995, Revue économique.

[2]  S. Zielinski,et al.  International Court of Justice , 2002, International Organization.

[3]  A. R. Eckler,et al.  Mathematical Models Of Target Coverage And Missile Allocation , 1972 .

[4]  Eric M. Skroch How to optimally interdict a belligerent project to develop a nuclear weapon , 2004 .

[5]  David Kendrick,et al.  GAMS, a user's guide , 1988, SGNM.

[6]  Delbert Ray Fulkerson,et al.  Maximizing the minimum source-sink path subject to a budget constraint , 1977, Math. Program..

[7]  Philip S. Bud Whiteman Improving Single Strike Effectiveness for Network Interdiction , 1999 .

[8]  B. Golden A problem in network interdiction , 1978 .

[9]  Cynthia A. Phillips,et al.  The network inhibition problem , 1993, STOC.

[10]  Jerome Bracken,et al.  Robust preallocated preferential defense , 1987 .

[11]  Bethany L. Nicholson,et al.  Mathematical Programs with Equilibrium Constraints , 2021, Pyomo — Optimization Modeling in Python.

[12]  A. Propoi On the Theory of Max-Min , 1977 .

[13]  John D. Matheson,et al.  Multidimensional Preferential Strategies , 1975 .

[14]  F. W. Lanchester,et al.  Aircraft in Warfare: The Dawn of the Fourth Arm , 1995 .

[15]  Douglas D. Diehl How to Optimize Joint Theater Ballistic Missile Defense , 2004 .

[16]  J. Salmeron,et al.  Analysis of electric grid security under terrorist threat , 2004, IEEE Transactions on Power Systems.

[17]  Jonathan F. Bard,et al.  The Mixed Integer Linear Bilevel Programming Problem , 1990, Oper. Res..

[18]  Guillermo Owen Minimization of Fatalities in a Nuclear Attack Model , 1969, Oper. Res..

[19]  R. Kevin Wood,et al.  Deterministic network interdiction , 1993 .

[20]  R. Kevin Wood,et al.  Shortest‐path network interdiction , 2002, Networks.