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.

The United States pediatric vaccine manufacturing market is analyzed using a static Bertrand oligopoly pricing model that characterizes oligopolistic interactions between asymmetric firms in a homogeneous multiple product market. Firms satisfy demand by appropriately pricing and selling its given set of bundles, where each bundle contains one or more products. In analyzing the pediatric vaccine market, a bundle is a vaccine, where each vaccine contains one or more immunogenic antigens. Consumers seek to purchase at least one of each antigen at an overall minimum cost. Demand is captured by defining a weighted set covering optimization problem, with the weights (prices) controlled by firms engaged in Bertrand competition. A repeated game version of the model enables multiple interactions between firms, allowing examination of tacit collusion. An iterative improvement algorithm is defined that constructs a pure strategy Nash equilibrium (some in the limiting sense) for the static game. Sufficient conditions for the existence of pure strategy Nash equilibria are provided, indicating that this class of games always yields at least one pure strategy equilibrium. Practical results of the pediatric vaccine market analysis follow from the difference in the repeated game equilibrium prices between two combination vaccines, Pediarix® and Pentacel®. Assuming the manufacturers of these vaccines agree to share the market equally with respect to volume, the equilibrium prices from the repeated game indicate a price difference of $0.86, whereas the difference in price between Pediarix® and Pentacel® for contract prices ending March 31, 2010 was $2.74. Interestingly, the subsequent public sector vaccine price list (contract prices ending March 31, 2011) shows a price difference of $0.95, with the price of Pentacel® actually reduced from the previous year—an unusual occurrence. The results presented in this paper suggest that a smaller price difference between these two important combination vaccines is appropriate, which is what occurred. In general, such results could serve to inform both manufacturers and purchasers on the appropriate pricing of combination vaccines, given the existence of a reasonable set of collusive agreements.

Network science spans many different fields of study, ranging from psychology to biology to the social sciences. A number of descriptive network measures have been identified for use within these fields; however, little research examines the relationships of these measures for possible statistical dependence. The research presented in this paper uses Spearman's rank correlation coefficient to examine the statistical dependence between pairs of 24 widely accepted social network measures. Confidence intervals are compared to determine whether computation times between measures in the same correlation group are significantly different. We use a three-factor, four-level, full-factorial experimental design to construct a test set of 64 unique network topologies. The three factors of interest are the network structural properties of size, cluster ability, and the scale-free parameter. A set of 320 networks are generated from a power law degree distribution using a random graph generation algorithm. Results indicate that there exists high correlation among 14 of the 24 tested network measures, many of which also exhibit statistically significant differences with respect to computation time. These findings are of interest to analysts seeking to identify measures that provide similar ranked outcomes and where computational efficiency is an important consideration.