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This appears in PHALANX, Vol. 37, No. 4, pp. 12 ff, and is reprinted with permission of Military Operations Society, 2004. ; The Department of Defense coordinates the activities of millions of people using assets worth trillions of dollars. This is important, complex work. Computer-based decision support is universal, and this has enabled optimization to continue to enhance legacy manual planning methods. The success of real-world applications of optimization turns out to depend on a handful of trade secrets that are essential, but do not appear in textbooks. This short summary reveals ten of these secrets and motivates them by example.

AbstractOn the surface of a sphere, we take as inputs two points, neither of them contained in any of a number of spherical polygon obstacles, and quickly find the shortest route connecting these two points while avoiding any obstacle. The WetRoute method presented here has been adopted by the US Navy for several applications. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 374–385, 2016

Military Operations Research, 12, pp. 33-45. ; The Fast Theater Model (FATHM) is an aggregated joint theater combat model that fuses Air Force Air-to-Found attack sortie optimization with Ground-to-Gound deterministic Lanchester fire-exchange battles using attrition rates derived from the Army's COSAGE model. The modeled FATHM war is conducted in short periods, with Air-to-Ground and Ground-to-Ground actions carried out in parallel. Period-by-period, damaged and destroyed targets may regenerate, and there may be scheduled reinforcements of attacking platforms, munitions, and new targets. The war progresses in phase whose completion depends on threshold levels of target kills in class categories and limits on phase duration. Each phase has a separate COSAGE input file, so the phases may differ strongly from each other. All FATHM inputs and outputs are ASCII flat-files suitable for immediate integration with a host database and spreadsheet analysis. Completion of a full-scale theater scenario requires about ten minutes on a personal computer.

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

AbstractThis paper examines the dependence of the structure of optimal time‐sequential fire‐support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantification of objectives (i.e. criterion functional). We consider the optimal time‐sequential allocation of supporting fires during the "approach to contact" of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester‐type equations of warfare, and the optimal fire‐support policy for each one‐sided combat optimization problem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular difficulty in one of them. For the same combat dynamics, the splitting of supporting fires between two enemy forces in any optimal policy (i.e. the optimality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an "overall" military advantage or a "local" one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths (computed according to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fire‐support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.

Naval Research Logistics Quarterly, 25, 1, pp. 183-211. ; This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantiiication of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the "approach to contact" of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization p~oblem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular di5culty in one of them. For the same combat dynamics, the splitting of supporting &es between t*o enemy forces in any optimal policy (i.e. the optiality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an "overall" military advantage or a "local" one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed accolding to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fie-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.

AbstractAn integral part of the MIL–STD–105D scheme for sampling inspection by attributes is the transfer from normal inspection to reduced or tightened inspection when the historical record of inspected lots suggests unusually good or bad quality. The switching rules in MIL–STD–105D have been criticized, especially by Japanese manufacturers, as being too severe when what is defined as acceptable quality material is submitted. This paper examines the long range fraction of lots rejected for several MIL–STD–105D sampling plans by using the MIL–STD–105D switching rules, using a modification suggested by the Japanese Standards Association, and by using a second modification developed by the authors.The Japanese Standards Association switching rules are more complex than those in MIL–STD–105D. It is demonstrated that they lead to improved long–range properties for Normal–Tightened–Reduced schemes, but to poorer properties for Normal–Tightened schemes.A simplified set of switching rules is suggested, wherein the "limit numbers" in MIL–STD–105D are eliminated. In comparison to MIL–STD–105D, the simpler rules lead to a lower probability of rejection for good lots and a comparable probability of rejection for bad lots.

AbstractMilitary Standard 105D has been almost universally adopted by government and private consumers for the lot‐by‐lot sampling inspection of product which may be inspected on a dichotomoun basisThe plan specifies, for each lot size, a random sample size and set of acceptance numbers (maximum allowable number of defectives in each sample). The acceptance numbers are based upon the binomial distribution and depend upon the quality required by the purchaser. Where several consecutive lots are submitted, a shift to less severe ("reduced") inspection or more severe ("tightened") inspection is specified when the ongoing quality is very high or low. Further experience permits a return to normal sampling from either of these statesThis paper examines the long range costs of such a sampling scheme. The three inspection types are considered as three distinct Markov chains, with periodic transitions from chain to chain. The expected sample size and the expected proportion of rejected product are determined as a function of the two parameters under control of the manufacturer, lot size and product quality. Some numerical examples are given which illustrate how to compute the overall cost of sampling inspection. Suggestions are made concerning the choice of parameters to minimize this cost.

Traditional probabilistic risk assessment (PRA), of the type originally developed for engineered systems, is still proposed for terrorism risk analysis. We show that such PRA applications are unjustified in general. The capacity of terrorists to seek and use information and to actively research different attack options before deciding what to do raises unique features of terrorism risk assessment that are not adequately addressed by conventional PRA for natural and engineered systems—in part because decisions based on such PRA estimates do not adequately hedge against the different probabilities that attackers may eventually act upon. These probabilities may differ from the defender's (even if the defender's experts are thoroughly trained, well calibrated, unbiased probability assessors) because they may be conditioned on different information. We illustrate the fundamental differences between PRA and terrorism risk analysis, and suggest use of robust decision analysis for risk management when attackers may know more about some attack options than we do.