Optimizing Military Capital Planning

Abstract

Planning United States military procurement commits a significant portion of our nation's wealth and determines our ability to defend ourselves, our allies, and our principles over the long term. Our military pioneered and has long used mathematical optimization to unravel the distinguishing complexities of military capital planning. The succession of mathematical optimization models we present exhibits increasingly detailed features; such embellishments are always needed for real-world, long-term procurement decision models. Two case studies illustrate practical modeling tricks that are useful in helping decision makers decide how to spend about a trillion dollars.

Prioritization via Stochastic Optimization

“…is the ratio of 360K to 27798. The results, except for the smallest data set (6,10), show a clear superiority of our branch-and-price algorithm over Cplex.…”

“…As indicated above, capital budgeting classically is formulated using variants of a multidimensional knapsack problem [e.g., 4,6,28,45]. Specifically, given a set of candidate projects, and given (point estimates of) the In this section, we first set notation and briefly describe a multidimensional knapsack formulation for the deterministic capital-budgeting problem, and then discuss the implications of instead having stochastic budget levels.…”

“…The notation and formulation of the optimal prioritization model tion of projects may represent mutually exclusive alternatives; some projects are implemented in phases, with opportunities for acceleration or delay; colors, beyond yearly availability, can distinguish types of money; both fixed and variable costs play a role in asset replacement models; resources in addition to monetary budgets can limit project selection; and, demand constraints can drive project selection. See, for instance, Brown et al [6] and Hartman [15] for a discussion of these and related issues. surprising that when prioritizing a small set of candidate projects (in this case consisting of only 9 projects) using multiple heuristics (in this case 12 different heuristics; see Table 4.5) that some of those heuristics find the optimal solution.…”

Optimizing Project Selection at the Department of Public Works, Presidio of Monterey

“…This is where the theory of a knapsack problem comes into play. The projects with the highest combined value within the limitations are chosen to produce the greatest value to the consumer (Brown, Dell, & Newman, 2004).…”

Optimization Tradecraft: Hard-Won Insights from Real-World Decision Support

“…There may be industry rules of thumb or policies on the admissible state of your enterprise (e.g., always have sufficient supply on hand to satisfy the next 90 days of demand). Lacking such guidance, we often plan further into the future than the planning horizon requires because we want to get some realistic representation of the actions up to exactly the end of the planning horizon (and discarding the further future results) (Brown et al 2004).…”