01096nas a2200217   4500000000100000000000100001000000100002008004100003653003200044653002700076653003400103653002000137653002200157100001800179700002200197700002000219245007400239300001100313490000700324520054700331       2009                            d10acapabilities-based planning10adefense planning risks10adiscrete dynamic optimization10aforce structure10ascenario planning1 aTodor Tagarev1 aTsvetomir Tsachev1 aNikolay Zhivkov00aFormalizing the Optimization Problem in Long-Term Capability Planning  a99-1140 v233 a<p>In defining future force capabilities, decision makers need to balance objectives, strategy, force capabilities, and risk within a forecasted force develop­ment environment and resource levels. This is commonly a task in long-term de­fense and force planning. This paper presents a mathematical formalization of the planning problem that involves static and dynamic optimization. Several static and dynamic discrete optimization models illustrate the approach. The concluding sec­tion presents a short deliberation on applicability.</p>