Differential-game examination of optimal time-sequential fire-support strategies

Optimal time-sequential fire-support strategies are studied through a two-person zero-sum deterministic differential game with closed-loop (or feedback) strategies. Lanchester-type equations of warfare are used in this work. In addition to the max-min principle, the theory of singular extremals is required to solve this prescribed-duration combat problem. The combat is between two heterogeneous forces, each composed of infantry and a supporting weapon system (artillery). In contrast to previous work reported in the literature, the attrition structure of the problem at hand leads to force-level-dependent optimal fire-support strategies with the attacker's optimal fire-support strategy requiring him to sometimes split his artillery fire between enemy infantry and artillery (counterbattery fire). A solution phenomnon not previously encountered in Lanchester-type differential games is that the adjoint variables may be discontinuous across a manifold of discontinuity for both players' strategies. This makes the synthesis of optimal strategies particularly difficult. Numerical examples are given.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Force-annihilation conditions for variable-coefficient lanchester-type equations of modern warfare

This paper develops a mathematical theory for predicting force annihilation from initial conditions without explicitly computing force-level trajectories for deterministic Lanchester-type “square-law” áttrition equations for combat between two homogeneous forces with temporal variations in fire effectivenesses (as expressed by the Lanchester attrition-rate coefficients). It introduces a canonical auxiliary parity-condition problem for the determination of a single parity-condition parameter (“the enemy force equivalent of a friendly force of unit strength”) and new exponential-like general Lanchester functions. Prediction of force annihilation within a fixed finite time would involve the use of tabulations of the quotient of two Lanchester functions. These force-annihilation results provide further information on the mathematical properties of hyperbolic-like general Lanchester functions: in particular, the parity-condition parameter is related to the range of the quotient of two such hyperbolic-like general Lanchester functions. Different parity-condition parameter results and different new exponential-like general Lanchester functions arise from different mathematical forms for the attrition-rate coefficients. This theory is applied to general power attrition-rate coefficients: exact force-annihilation results are obtained when the so-called offset parameter is equal to zero; while upper and lower bounds for the parity-condition parameter are obtained when the offset parameter is positive.     

Environmental regulation in project‐based industries

We study the environmental regulation of industrial activities that are organized as projects. Applications arise in construction, ship and aircraft building, and film making, among other industries. Relative to manufacturing, environmental regulation is different in project‐based industries, due to the uniqueness and geographical diversity of projects, and a lack of product takeback programs. Because the amount of waste and pollution generated by project companies can be large, regulators need environmental policies to ensure reduction of waste and pollution. We consider a regulator who attempts to maximize social welfare. We model this problem as a bilevel nonlinear program. The upper level regulator specifies waste reduction targets, which the lower level project companies meet using waste stream reduction and remediation of pollution, while attempting to control their project costs. We find that high waste diversion targets lead to outcomes with little pollution, but excessive project costs and only modest waste stream reduction. Projects that have lower task precedence density, or that have pollutants with different environmental impacts, show larger increases in project cost and time resulting from regulation. We describe a subsidy for waste stream reduction that coordinates the system, and we estimate the value of coordination. We also describe a bonus that encourages truthful reporting by project companies, and evaluate the relative cost and effectiveness of the subsidy and the bonus. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 228–247, 2015     

Scheduling combat logistics force replenishments at sea for the US Navy

The Replenishment at Sea Planner (RASP) is saving the U.S. Navy millions of dollars a year by reducing fuel consumption of its Combat Logistics Force (CLF). CLF shuttle supply ships deploy from ports to rendezvous with underway U.S. combatants and those of coalition partners. The overwhelming commodity transferred is fuel, ship‐to‐ship by hoses, while other important packaged goods and spare parts are high‐lined, or helicoptered between ships. The U.S. Navy is organized in large areas of responsibility called numbered fleets, and within each of these a scheduler must promulgate a daily forecast of CLF shuttle operations. The operational planning horizon extends out several weeks, or as far into the future as we can forecast demand. We solve RASP with integer linear optimization and a purpose‐built heuristic. RASP plans Replenishment‐at‐Sea (RAS) events with 4‐hour (Navy watch) time fidelity. For five years, RASP has served two purposes: (1) it helps schedulers generate a daily schedule and animates it using Google Earth, and (2) it automates reports command‐to‐ship messages that are essential to keep this complex logistics system operating.     

Insurgency and Violent Extremism in Pakistan

Pakistan has an uneven history of dealing with insurgencies and extremism. This article identifies the various campaigns and policies employed to defeat militants and deal with violent extremism. It describes the major anti-state groups and how Pakistan’s military and civilian leaders, relying on the related strategies of selectivity, gradualism and containment, have allowed militancy and terrorism to thrive. This article finds that while the elites and the public may have belatedly come to appreciate the existential internal threats these groups pose to the country, there are strong reasons to doubt the state’s full commitment to its promises to take meaningful action.     

Detecting Problems in Military Expenditure Data Using Digital Analysis

The UN asks governments to report key figures of their annual military budgets with the aim of creating trust among member states. This goal can only be achieved if the data reported is accurate. However, although there are many reasons for governments to falsify data, the UN does not check for manipulation. In this paper, we apply Benford’s law to the military expenditure data of 27 states taken from the UN register. Our analysis of the first digits shows that the states with the greatest deviations from the expected Benford distribution and therefore the lowest data quality are the USA and the UK.     

POWER,INFLUENCE, AND HIERARCHY: DEFENSE INDUSTRIES IN A UNIPOLAR WORLD

The global defense‐industrial sector reflects the hierarchy of power in the post‐Cold War world. As in the larger international system, the United States plays the dominant role in the defense sector as well. It is a comparative advantage often used by US policymakers to influence the foreign policy behavior of other states. Curiously, the radical concentration of the world’s defense industrial sector, as described here, has received relatively little scrutiny from either academia or the media, even though it not only reflects the international order but provides the United States with considerable leverage in it.     

Financial versus human resources in the Greek‐Turkish arms race: A forecasting investigation using artificial neural networks

This paper aims at forecasting the burden on the Greek economy resulting from the arms race against Turkey and at concentrating on the leading determinants of this burden. The military debt and the defence share of GDP are employed alternatively in order to approximate the measurement of the arms race pressure on Greece, and the method used is that of artificial neural networks. The use of a wide variety of explanatory variables in combination with the promising results derived, suggest that the impact on the Greek economy resulting from this arms race is determined, to a large, extent, by demographic factors which strongly favour the Turkish side. Prediction on both miltary debt and defence expenditure exhibited highly satisfactory accuracy, while the estimation of input significance, indicates that variables describing the Turkish side are often dominant over the corresponding Greek ones.