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AbstractWe study how changes to the composition and employment of the US Navy combat logistic force (CLF) influence our ability to supply our navy worldwide. The CLF consists of about 30 special transport ships that carry ship and aircraft fuel, ordnance, dry stores, and food, and deliver these to client combatant ships underway, making it possible for our naval forces to operate at sea for extended periods. We have modeled CLF operations to evaluate a number of transforming initiatives that simplify its operation while supporting an even larger number of client ships for a greater variety of missions. Our input is an employment schedule for navy battle groups of ships operating worldwide, extending over a planning horizon of 90–180 days. We show how we use optimization to advise how to sustain these ships. We have used this model to evaluate new CLF ship designs, advise what number of ships in a new ship class would be needed, test concepts for forward at‐sea logistics bases in lieu of conventional ports, demonstrate the effects of changes to operating policy, and generally try to show whether and how the CLF can support planned naval operations. Published 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008

We propose a definition of infrastructure resilience that is tied to the operation (or function) of an infrastructure as a system of interacting components and that can be objectively evaluated using quantitative models. Specifically, for any particular system, we use quantitative models of system operation to represent the decisions of an infrastructure operator who guides the behavior of the system as a whole, even in the presence of disruptions. Modeling infrastructure operation in this way makes it possible to systematically evaluate the consequences associated with the loss of infrastructure components, and leads to a precise notion of "operational resilience" that facilitates model verification, validation, and reproducible results. Using a simple example of a notional infrastructure, we demonstrate how to use these models for (1) assessing the operational resilience of an infrastructure system, (2) identifying critical vulnerabilities that threaten its continued function, and (3) advising policymakers on investments to improve resilience.

Military Operations Research, to appear. ; We formulate and solve aircraft-routing problems that arise when planning missions for military aircraft that are subject to ground-based threats such as surface-to-air missiles. We use a constrained-shortest path (CSP) model that discretizes the relevant airspace into a grid of vertices representing potential waypoints, and connects vertices with directed edges to represent potential flight segments. The model is flexible: It can route any type of manned or unmanned aircraft; it can incorporate any number of threats; and it can incorporate, in the objective function or as side constraints, numerous mission-specific metrics such as risk, fuel consuption, and flight time. We apply a new algorithm for solving the CSP problem and present computational results for the routing of a high-altitude F/A-18 strike group, and the routing of a medium-altitude unmanned aerial vehicle. The objectives minimize risk from ground-based threats while constraints limit fuel consumption and / or flight time. Run times to achieve a near-optimal solution range from fractions of a second to 80 seconds on a personal computer. We also demonstrate that our methods easily extend to handle turn-radius constraints and round-trip routing.

ABSTRACTWe present the Integrated Preference Functional (IPF) for comparing the quality of proposed sets of near‐pareto‐optimal solutions to bi‐criteria optimization problems. Evaluating the quality of such solution sets is one of the key issues in developing and comparing heuristics for multiple objective combinatorial optimization problems. The IPF is a set functional that, given a weight density function provided by a decision maker and a discrete set of solutions for a particular problem, assigns a numerical value to that solution set. This value can be used to compare the quality of different sets of solutions, and therefore provides a robust, quantitative approach for comparing different heuristic, a posteriori solution procedures for difficult multiple objective optimization problems. We provide specific examples of decision maker preference functions and illustrate the calculation of the resulting IPF for specific solution sets and a simple family of combined objectives.

Military Operations Research, 18(1), pp. 21-37. ; The article of record as published may be located at http://dx.doi.org/10.5711/1082598318121 ; This paper shows that no simple, common-sense rule of thumb can be used to identify a most-vital arc, even in a simple maximum-flow problem. The correct answer requires analysis equivalent in difficulty to completely solving the maximum-flow problem, perhaps repeatedly. This insight generalizes to finding a most-vital component, or set of components, in a system whose operations is described by a more general model. Our paper shows how to evaluate the criticality of sets of components, how to assess the worst-case set of components that might be lost to a given number of simultaneous hostile attacks (or engineering failures, or losses to Mother Nature), and how to allocate limited defensive resources to minimize the maximum damage from subsequent attack. Collateral insights include the fact that there is no way to prioritize individual components by critically, and the the analysis that determines critical component sets also yields objective assessments of operations system resilience and can provide constructive advice on how to increase it.

Military Operations Research, 18(3), pp. 35-52. ; The article of record as published may be located at http://dx.doi.org/10.5711/1082598318335 ; The Air Tasking and Efficiency Model (ATEM) has been used since 2006. Its development was motivated by an urgent need to plan and evaluate intratheater airlift of passengers and palletized freight for Operation Iraqi Freedom in Iraq and Operation Enduring Freedom in Afghanistan ATEM plans routes and aircraft configurations (capacity of passenger seats and pallet positions) for heterogeneous fleet of aircraft flying between multiple airfields. ATEM respects limits on crew duty periods, times and abilities of each airfield to handle and fuel each aircraft type, and aircraft speed and carrying capacity. Initially, ATEM advised improving daily and weekly route ensembles, conveying more passengers and pallets and using fewer aircraft than prior manually generated solutions. This early use reduced the required number of ground convoys and thereby exposure to improvised explosive devises. Later, ATEM advised where to advantageously move aircraft to new home airfields, how to shift aircraft between theaters, and when to bring aircraft home from war.