Casualty Rates of US Military Personnel During the Wars in Iraq and Afghanistan

Abstract

In Operation Iraqi Freedom, which ended in August 2010, nearly 3500 hostile deaths occurred among US military personnel and 32,000 more were wounded in action (WIA). More than 1800 hostile deaths occurred during Operation Enduring Freedom (in and around Afghanistan) through 2014 and about 20,000 were WIA. A larger proportion of wounded personnel survived in Iraq and Afghanistan than during the Vietnam War, but the increased survival rates were not as high as some studies have asserted. The survival rates were 90.2% in Iraq and 91.6% in Afghanistan, compared with 86.5% in Vietnam. The casualty rates varied between the conflicts in Iraq and Afghanistan and before, during, and after the respective surges. Amputation rates are difficult to measure consistently, but I estimate that 2.6% of all WIA and 9.0% of medically evacuated WIA from the Iraq and Afghanistan theaters combined resulted in the major loss of a limb. Elevated non-hostile death rates (including deaths due to accidents, illnesses, homicides, or suicides) resulted in about 220 more deaths in Iraq and about 200 more deaths in Afghanistan than would have been expected in peacetime among populations of the size deployed to those two conflicts.     

Algorithms for solving the conditional covering problem on paths

Consider the conditional covering problem on an undirected graph, where each node represents a site that must be covered by a facility, and facilities may only be established at these nodes. Each facility can cover all sites that lie within some common covering radius, except the site at which it is located. Although this problem is difficult to solve on general graphs, there exist special structures on which the problem is easily solvable. In this paper, we consider the special case in which the graph is a simple path. For the case in which facility location costs do not vary based on the site, we derive characteristics of the problem that lead to a linear‐time shortest path algorithm for solving the problem. When the facility location costs vary according to the site, we provide a more complex, but still polynomial‐time, dynamic programming algorithm to find the optimal solution. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Non‐zero‐sum nonlinear network path interdiction with an application to inspection in terror networks

A simultaneous non‐zero‐sum game is modeled to extend the classical network interdiction problem. In this model, an interdictor (e.g., an enforcement agent) decides how much of an inspection resource to spend along each arc in the network to capture a smuggler. The smuggler (randomly) selects a commodity to smuggle—a source and destination pair of nodes, and also a corresponding path for traveling between the given pair of nodes. This model is motivated by a terrorist organization that can mobilize its human, financial, or weapon resources to carry out an attack at one of several potential target destinations. The probability of evading each of the network arcs nonlinearly decreases in the amount of resource that the interdictor spends on its inspection. We show that under reasonable assumptions with respect to the evasion probability functions, (approximate) Nash equilibria of this game can be determined in polynomial time; depending on whether the evasion functions are exponential or general logarithmically‐convex functions, exact Nash equilibria or approximate Nash equilibria, respectively, are computed. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 139–153, 2017     

Recruiters,advertising, and navy enlistments

Regression analysis is used to estimate the effects on Navy enlistments of recruiters, advertising, unemployment and other factors. In measuring the effects of these factors on enlistments, changes in both the demand for and supply of enlistments are taken into account. Advertising is treated as a capital investment; its effect is estimated using a maximum likelihood technique that was developed for measuring the effects of capital investments. We find strong evidence that recruiters and unemployment increase enlistments. Advertising also seems to increase enlistments, but its effect is highly uncertain. The results suggest that increases in recruiting resources would have eliminated the enlistment shortfalls experienced by the Navy in FY 1978–79.     

Aircraft weapon budgeting

This article considers the problem of allocating a fixed budget among alternative air-to-ground weapons. The weapon-budgeting problem is high-dimensional, involving all feasible combinations of aircraft, weapons, and targets. The decision maker's utility function is defined over kills of the various target types, but it is unrealistic to expect him to write down the mathematical formula for this function. The article suggests two procedures for reducing the dimension of the maximization problem and operating without exact knowledge of the utility function. The first procedure uses successive linear approximations to generate the set of “efficient” or undominated weapon allocations. The second procedure applies separability restrictions to the utility function, thereby reducing the overall maximization problem to a sequence of low-dimensional subproblems.     

Inspection games with local and global allocation bounds

This article discusses a two‐player noncooperative nonzero‐sum inspection game. There are multiple sites that are subject to potential inspection by the first player (an inspector). The second player (potentially a violator) has to choose a vector of violation probabilities over the sites, so that the sum of these probabilities do not exceed one. An efficient method is introduced to compute all Nash equilibria parametrically in the amount of resource that is available to the inspector. Sensitivity analysis reveals nonmonotonicity of the equilibrium utility of the inspector, considered as a function of the amount of resource that is available to it; a phenomenon which is a variant of the well‐known Braess paradox. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013