Military medical planners must consider how aerial medical evacuation (MEDEVAC) assets will be dispatched when preparing for and supporting high-intensity combat operations. The dispatching authority seeks to dispatch MEDEVAC assets to prioritized requests for service, such that battlefield casualties are effectively and efficiently transported to nearby medical-treatment facilities. We formulate and solve a discounted, infinite-horizon Markov decision process (MDP) model of the MEDEVAC dispatching problem. Because the high dimensionality and uncountable state space of our MDP model renders classical dynamic programming solution methods intractable, we instead apply approximate dynamic programming (ADP) solution methods to produce high-quality dispatching policies relative to the currently practiced closest-available dispatching policy. We develop, test, and compare two distinct ADP solution techniques, both of which utilize an approximate policy iteration (API) algorithmic framework. The first algorithm uses least-squares temporal differences (LSTD) learning for policy evaluation, whereas the second algorithm uses neural network (NN) learning. We construct a notional, yet representative planning scenario based on high-intensity combat operations in southern Azerbaijan to demonstrate the applicability of our MDP model and to compare the efficacies of our proposed ADP solution techniques. We generate 30 problem instances via a designed experiment to examine how selected problem features and algorithmic features affect the quality of solutions attained by our ADP policies. Results show that the respective policies determined by the NN-API and LSTD-API algorithms significantly outperform the closest-available benchmark policies in 27 (90%) and 24 (80%) of the problem instances examined. Moreover, the NN-API policies significantly outperform the LSTD-API policies in each of the problem instances examined. Compared with the closest-available policy for the baseline problem instance, the NN-API policy decreases the average response time of important urgent (i.e., life-threatening) requests by 39 minutes. These research models, methodologies, and results inform the implementation and modification of current and future MEDEVAC tactics, techniques, and procedures, as well as the design and purchase of future aerial MEDEVAC assets.

We examine the optimal location of Integrated Air Defense System (IADS) missile batteries to protect a country’s assets, formulated as a Defender-Attacker-Defender three-stage sequential, perfect information, zero-sum game between two opponents. We formulate a trilevel nonlinear integer program for this Defender-Attacker-Defender model and seek a subgame perfect Nash equilibrium (i.e., a set of attacker and defender strategies from which neither player has an incentive to deviate). Such a trilevel formulation is not solvable via conventional optimization software, and an exhaustive enumeration of the game tree based on the discrete set of strategies is only tractable for small instances. We develop and test a customized heuristic over a set of small instances having deliberate parametric variations in a designed experiment, comparing its performance to an exhaustive enumeration algorithm. Testing results indicate the enumeration approach to be severely limited for realistically sized instances, so we demonstrate the heuristic on a larger instance from the literature for which it maintains computational efficiency.

In this paper, we model and solve the strategic problem of minimizing the expected loss inflicted by a hostile terrorist organization. An appropriate allocation of certain capability-related, intent-related, vulnerability-related, and consequence-related resources is used to reduce the probabilities of success in the respective attack-related actions and to ameliorate losses in case of a successful attack. We adopt a nested event tree optimization framework and formulate the problem as a specially structured nonconvex factorable program. We develop two branch-and-bound schemes based, respectively, on utilizing a convex nonlinear relaxation and a linear outer approximation, both of which are proven to converge to a global optimal solution. We also design an alternative direct mixed-integer programming model representation for this case, and we investigate a fundamental special-case variant for this scheme that provides a relaxation and affords an optimality gap measure. Several range reduction, partitioning, and branching strategies are proposed, and extensive computational results are presented to study the efficacy of different compositions of these algorithmic ingredients, including comparisons with the commercial software BARON. A sensitivity analysis is also conducted to explore the effect of certain key model parameters.