Branch and bound methods for a search problem

The problem of searching for randomly moving targets such as children and submarines is known to be fundamentally difficult, but finding efficient methods for generating optimal or near optimal solutions is nonetheless an important practical problem. This paper investigates the efficiency of Branch and Bound methods, with emphasis on the tradeoff between the accuracy of the bound employed and the time required to compute it. A variety of bounds are investigated, some of which are new. In most cases the best bounds turn out to be imprecise, but very easy to compute. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 243–257, 1998     

On reversibility of tandem queues with blocking

We study the effect of the order of service stations on the departure process in a tandem system with finite buffers and blocking. A reversibility result for a twostation system with various types of blocking mechanisms has been shown before. We show that a similar result holds for a three-station tandem system with no buffers between stations and a so-called communication type of blocking. A general conjecture is stated regarding the reversibility of tandem systems with finite buffers and blocking. © 1992 John Wiley & Sons, Inc.     

Evaluation of an integrated supplier-buyer quality-control system

In this article, a quality-control design framework that employs information for the supplier-buyer system is modeled. Significant operational savings may be obtained by using the integrated plans developed under this framework. This is especially true when the cost of a defective is high, and the variable sampling and rework costs are low. Analysis of the interaction of defective, rework, and variable sampling costs reveals that the savings are the result of a shift of control effort from the process-control to the lot-acceptance stage, which is the consequence of tradeoffs involving both stages. The managerial impact of adopting integrated plans is discussed.     

Economic lot scheduling of fully loaded processes with external setups

Without restricting the class of permissible schedules, we derive optimal schedules for economic lot scheduling problems that are fully loaded, have external setups, and have only two products. The fully loaded condition accurately represents certain types of bottlenecks. We show that the optimal schedule must have the Wagner-Whitin property. We also develop a measure of aggregate inventory, derive an optimal steady-state aggregate inventory policy, and provide conditions under which the aggregate inventory level of an optimal schedule must approach a steady state. By restricting the class of permissible schedules to rotation cycle schedules, we extend these results to more than two products.     

Estimating a survival curve when new is better than used in expectation

Let X be a positive random variable. The distribution F of X is said to be “new better than used in expectation,” or “NBUE,” if E(X) ⩾ E(X – t|X > t) for all t ⩾ 0. Suppose X₁, …, X_n, is a random sample from an NBUE distribution F. The problem of estimating F by a distribution which is itself NBUE is considered. The estimator G_n, defined as the NBUE distribution supported on the sample which minimizes the (sup norm) distance between the NBUE class and the empirical distribution function, is studied. The strong uniform consistency of G_n, is proven, and a numerical algorithm for obtaining G_n, is given. Our approach is applied to provide an estimate of the distribution of lifetime following the diagnosis of chronic granulocytic leukemia based on data from a National Cancer Institute study.     

Some two-on-two homogeneous stochastic combats

In this article we consider two versions of two-on-two homogeneous stochastic combat and develop expressions, in each case, for the state probabilities. The models are natural generalizations of the exponential Lanchester square law model. In the first version, a marksman whose target is killed resumes afresh the killing process on a surviving target; in the second version, the marksman whose target is killed merely uses up his remaining time to a kill on a surviving target. Using the state probabilities we then compute such important combat measures as (1) the mean and variance of the number of survivors as they vary with time for each of the sides, (2) the win probabilities for each of the sides, and (3) the mean and variance of the battle duration time. As an application, computations were made for the specific case of a gamma (2) interfiring time random variable for each side and the above combat measures were compared with the appropriate exponential and deterministic Lanchester square law approximations. The latter two are shown to be very poor approximations in this case.     

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.     

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.     

Note: Normal prediction under linear-quadratic loss

The prediction of the value of a normal random variable is considered in the presence of combined linear and quadratic loss. It is shown that the optimal prediction is an additive adjustment to the predictive mean, the adjustment being the product of the predictive standard deviation and an appropriate adjustment factor. An extensive table of adjustment factor values is presented, and it is noted that for given loss parameters the adjustment is positive unless the predictive variance is sufficiently large. © 1996 John Wiley & Sons, Inc.     

The evolution of a selection system

The article is a case study. It describes the initialization and subsequent modifications of the selection process used for the annual Award for Excellence in Teaching at the Naval Postgraduate School (NPS). The method treats highly unbalanced data and utilizes some exploratory data analysis techniques in interesting ways. It leads to a defensible choice for a winner in a very messy setting. The award designates a faculty member as “teacher of the year” and includes a stipend of substantial value. The recipient is chosen by a committee which reviews objective information summarized from ballots submitted by franchised voters. The issues encountered have some general content and the handling of a number of them may have broader interest. ©John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America.