Attrition models of the Ardennes campaign

This paper revisits the modeling by Bracken [3] of the Ardennes campaign of World War II using the Lanchester equations. It revises and extends that analysis in a number of ways: (1) It more accurately fits the model parameters using linear regression; (2) it considers the data from the entire campaign; and (3) it adds in air sortie data. In contrast to previous results, it concludes by showing that neither the Lanchester linear or Lanchester square laws fit the data. A new form of the Lanchester equations emerges with a physical interpretation. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 1–22, 1998     

A squared-euclidean distance location-allocation problem

This article is concerned with the analysis of a squared-Euclidean distance location-allocation problem with balanced transportation constraints, where the costs are directly proportional to distances and the amount shipped. The problem is shown to be equivalent to maximizing a convex quadratic function subject to transportation constraints. A branch-and-bound algorithm is developed that utilizes a specialized, tight, linear programming representation to compute strong upper bounds via a Lagrangian relaxation scheme. These bounds are shown to substantially dominate several other upper bounds that are derived using standard techniques as problem size increases. The special structure of the transportation constraints is used to derive a partitioning scheme, and this structure is further exploited to devise suitable logical tests that tighten the bounds implied by the branching restrictions on the transportation flows. The transportation structure is also used to generate additional cut-set inequalities based on a cycle prevention method which preserves a forest graph for any partial solution. Results of the computational experiments, and a discussion on possible extensions, are also presented.     

The shortest queue model with jockeying

In this article we deal with the shortest queue model with jockeying. We assume that the arrivals are Poisson, each of the exponential servers has his own queue, and jockeying among the queues is permitted. Explicit solutions of the equilibrium probabilities, the expected customers, and the expected waiting time of a customer in the system are given, which only depend on the traffic intensity. Numerical results can be easily obtained from our solutions. Several examples are provided in the article.     

Floor layouts using a multifacility location model

A procedure for obtaining a facilities scatter diagram within a rectangular boundary is developed using a multifacility location model. This method gives favorable computational results and has the advantage over other scatter diagram methods of being able to accommodate fixed facility locations. Examples illustrate how this method can be used by a designer/analyst either as a one-step algorithm or iteratively to build a layout.     

Compound poisson approximation in systems reliability

The compound Poisson “local” formulation of the Stein-Chen method is applied to problems in reliability theory. Bounds for the accuracy of the approximation of the reliability by an appropriate compound Poisson distribution are derived under fairly general conditions, and are applied to consecutive-2 and connected-s systems, and the 2-dimensional consecutive-k-out-ofn system, together with a pipeline model. The approximations are usually better than the Poisson “local” approach would give. © 1996 John Wiley & Sons, Inc.     

Exploiting symmetry in the reliability analysis of coherent systems

Components in a complex system are usually not structurally identical. However, in many cases we may find components that are structurally symmetric, and one should make use of this additional information to simplify reliability analysis. The main purpose of this article is to define and study one such class of systems, namely, those having symmetric components, and to derive some reliability-related properties. © 1996 John Wiley & Sons, Inc.     

Scheduling target illuminators in naval battle-group anti-air warfare

We schedule a set of illuminators (homing devices) to strike a set of targets using surface-to-air missiles in a naval battle. The task is viewed as a production floor shop scheduling problem of minimizing the total weighted flow time, subject to time-window job availability and machine downtime side constraints. A simple algorithm based on solving assignment problems is developed for the case when all the job processing times are equal and the data are all integer. For the general case of scheduling jobs with unequal processing times, we develop two alternate formulations and analyze their relative strengths by comparing their respective linear programming relaxations. We select the better formulation in this comparison and exploit its special structures to develop several effective heuristic algorithms that provide good-quality solutions in real time; this is an essential element for use by the Navy. © 1995 John Wiley & Sons, Inc.     

On the design of a tandem queue with blocking: Modeling,analysis, and gradient estimation

We demonstrate here how recent advances in the study of discrete-event stochastic systems provide fruitful results for the modeling, analysis, and design of manufacturing systems. We consider a multistage make-to-stock system where outputs from the final stage are used to satisfy customer demands. We address the problem of finding the appropriate trade-off between reduced order waiting time and increased process speeds. Using the idea of infinitesimal perturbation analysis (IPA), we establish a simple procedure where sample-path derivatives can be obtained along an arbitrary sample path. Under suitable conditions, we demonstrate that these derivative estimators are unbiased and strongly consistent and can be used in a classical stochastic optimization scheme to solve the problem. The role of continuity and convexity on the validity of the estimator is also addressed. Although the focus of this article is not to solve for the optimal solution, we provide a theoretical justification for such a pursuit. The approach is appealing as it is numerically stable, easy to implement, and can be extended to other system performance measures. © 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 parametric-based heuristic program for the quadratic assignment problem

In this article we study the quadratic assignment problem by embedding the actual data in a data space which satisfies an extension of the metric triangle property. This leads to simpler computations for the determination of heuristic solutions. Bounds are given for the loss of optimality which such heuristic solutions would involve in any specific instance. © 1993 John Wiley & Sons, Inc.