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.     

Incorporating learning curve costs in acquisition strategy optimization

Each year, the U.S. Army procures billions of dollars worth of weapons and equipment. The process of deciding what to buy, when to buy, and in what quantities is extremely complex, requiring extensive analysis. Two techniques used in this analysis are mathematical programming and cost estimation. Although they are related through constraints on available procurement funds, the use of nonlinear cost learning curves, which better represent system costs as a function of quantity produced, have not been incorporated into the mathematical programming formulations that compute the quantities of items to be procured. As a result, the solutions obtained could be either suboptimal, or even infeasible with respect to budgetary limitations. In this paper we present a piecewise linear approximation of the learning curve costs for a more accurate portrayal of budgetary constraints used in a mixed integer linear programming for acquisition strategy optimization. In addition, implementation issues are discussed, and performance results are given. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 255–271, 1999     

Multilinear extensions and quotients of simple games

Studied here is the problem of evaluating the formation of coalitions in cooperative games by considering its internal and external effects. Our analysis is based upon a formal theory of the quotient game and the use of multilinear extensions to compute the Shapley value and the coalitional value. When it applies to simple games, a series of interesting results is obtained. © 1996 John Wiley & Sons, Inc.     

The individual station technique for the analysis of cyclic polling systems

Polling systems are used to model a wide variety of real-world applications, for example, telecommunication and material handling systems. Consequently, there is continued interest in developing efficient algorithms to analyze the performance of polling systems. Recent interest in the optimization of these systems has brought up the need for developing very efficient techniques for analyzing their waiting times. This article presents the Individual Station technique for cyclic polling systems. The technique possesses the following features: (a) it allows the user to compute the mean waiting time at a selected station independent of the mean waiting time computations at other stations, and (b) its complexity is low and independent of the system utilization. In addition the technique provides explicit closed-form expressions for (i) the mean waiting times in a system with 3 stations, and (ii) the second moment of the waiting times in a system with 2 stations, for an exhaustive service system. © 1996 John Wiley & Sons, Inc.     

Printed circuit board family grouping and component allocation for a multimachine,open-shop assembly cell

This article considers a particular printed circuit board (PCB) assembly system employing surface mount technology. Multiple, identical automatic placement machines, a variety of board types, and a large number of component types characterize the environment studied. The problem addressed is that of minimizing the makespan for assembling a batch of boards with a secondary objective of reducing the mean flow time. The approach adopted is that of grouping boards into production families, allocating component types to placement machines for each family, dividing of families into board groups with similar processing times, and the scheduling of groups. A complete setup is incurred only when changing over between board families. For the environment studied, precedence constraints on the order of component placement do not exist, and placement times are independent of feeder location. Heuristic solution procedures are proposed to create board subfamilies (groups) for which the component mounting times are nearly identical within a subfamily. Assignment of the same component type to multiple machines is avoided. The procedures use results from the theory of open-shop scheduling and parallel processor scheduling to sequence boards on machines. Note that we do not impose an open-shop environment but rather model the problem in the context of an open shop, because the order of component mountings is immaterial. Three procedures are proposed for allocating components to machines and subsequently scheduling boards on the machines. The first two procedures assign components to machines to balance total work load. For scheduling purposes, the first method groups boards into subfamilies to adhere to the assumptions of the open-shop model, and the second procedure assumes that each board is a subfamily and these are scheduled in order of shortest total processing time. The third procedure starts by forming board subfamilies based on total component similarity and then assigns components to validate the open-shop model. We compare the performance of the three procedures using estimated daily, two-day, and weekly production requirements by averaging quarterly production data for an actual cell consisting of five decoupled machines. © 1994 John Wiley & Sons, Inc.     

Setting military reenlistment bonuses

The United States military frequently has difficulty retaining enlisted personnel beyond their initial enlistment. A bonus program within each service, called a Selective Reenlistment Bonus (SRB) program, seeks to enhance reenlistments and thus reduce personnel shortages in critical military occupational specialties (MOSs). The amount of bonus is set by assigning “SRB multipliers” to each MOS. We develop a nonlinear integer program to select multipliers which minimize a function of deviations from desired reenlistment targets. A Lagrangian relaxation of a linearized version of the integer program is used to obtain lower bounds and feasible solutions. The best feasible solution, discovered in a coordinate search of the Lagrangian function, is heuristically improved by apportioning unexpended funds. For large problems a heuristic variable reduction is employed to speed model solution. U.S. Army data and requirements for FY87 yield a 0-1 integer program with 12,992 binary variables and 273 constraints, which is solved within 0.00002% of optimality on an IBM 3033AP in less than 1.7 seconds. More general models with up to 463,000 binary variables are solved, on average, to within 0.009% of optimality in less than 1.8 minutes. The U.S. Marine Corps has used a simpler version of this model since 1986. © 1993 John Wiley & Sons, Inc.     

A bivariate pareto model and its applications to reliability

We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed. © 1993 John Wiley & Sons, Inc.     

Tripwires and free-riders: Do forward-deployed U.S. troops reduce the willingness of host-country citizens to fight for their country?

This article investigates the relationship between U.S. overseas troops and the willingness of the citizens of host states to fight for their country. The study joins the long-running debate about burden-sharing and free-riding among U.S. allies. Unlike most previous empirical studies, we focus on non-material or intangible measures of the underlying concepts. Our dependent variable estimates the proportion of citizens expressing a willingness to fight for their country. Scores at the aggregate-national as well as the individual level are shaped by the presence of U.S. military forces, which act as a “tripwire” signaling credible security commitments. This increases opportunities of (non-material) free-riding. We present both bivariate and multivariate analyses covering the period 1981–2014 to test this supposition. Findings indicate that once U.S. troop levels reach a certain threshold (between 100 and 500 troops), citizens’ willingness to fight drops significantly. This likely reflects non-material free-riding.     

Is Shia-Sunni Violence on the Rise? Exploring New Data on Intra-Muslim Organised Violence 1989-2017

This data study provides the first comprehensive empirical overview of organised violence across the Shia and Sunni Muslim divide, 1989–2017. We present a conceptual framework of sectarian dimensions of armed conflicts: sectarian identities; sectarian ideologies; and sectarian alliances. Our analysis demonstrates the extent to which organised violence has been fought across the Shia-Sunni divide. We also explore the sectarian identity dimension in non-state armed conflicts and one-sided violence. Overall, our study shows that most of the organised violence across the Shia-Sunni divide is driven by states, rebel groups, and militias, rather than communities.