Random disambiguation paths for traversing a mapped hazard field

We consider the problem of safely and swiftly navigating through a spatial arrangement of potential hazard detections in which each detection has associated with it a probability that the detection is indeed a true hazard. When in close proximity to a detection, we assume the ability—for a cost—to determine whether or not the hazard is real. Our approach to this problem involves a new object, the random disambiguation path (RDP), which is a curve‐valued random variable parametrized by a binary tree with particular properties. We prove an admissibility result showing that there is positive probability that the use of an RDP reduces the expected traversal length compared to the conventional shortest zero‐risk path, and we introduce a practically computable additive‐constant approximation to the optimal RDP. The theoretical considerations are complemented by simulation and example. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Influence of a liquid-filled compartment structure on the incoming shaped charge jet stability

Liquid-filled compartment structure consists of a bulk steel plate with matrix blind holes which are filled with liquid and a steel front plate to seal up the liquid with rings and bolts.The liquid-filled compart-ment structure can resist the shaped charge warhead effectively.This paper presents experimental and theoretical investigations of the penetration ability of the residual shaped charge jet emerging from the liquid-filled compartment structure after the penetration process at different impact angles.On the basis of shock wave propagation theory,the influence of the liquid-filled compartment structure on jet sta-bility is analysed.The interferences of the liquid backflow caused by a reflected shock wave and a back plate on jet stability under different impact angles are also examined.In addition,the range of the disturbed velocity segments of the jet at different impact angles and the penetration ability of the re-sidual jet are obtained.A theoretical model is validated against the experimental penetration depths.     

On vibration analysis of functionally graded carbon nanotube reinforced magneto-electro-elastic plates with different electro-magnetic conditions using higher order finite element methods

This article deals with evaluating the frequency response of functionally graded carbon nanotube rein-forced magneto-electro-elastic (FG-CNTMEE) plates subjected to open and closed electro-magnetic cir-cuit conditions. In this regard finite element formulation has been derived. The plate kinematics adjudged via higher order shear deformation theory (HSDT) is considered for evaluation. The equations of motion are obtained with the help of Hamilton's principle and solved using condensation technique. It is found that the convergence and accuracy of the present FE formulation is very good to address the vibration problem of FG-CNTMEE plate. For the first time, frequency response analysis of FG-CNTMEE plates considering the effect of various circuit conditions associated with parameters such as CNT dis-tributions, volume fraction, skew angle, aspect ratio, length-to-thickness ratio and coupling fields has been carried out. The results of this article can serve as benchmark for future development and analysis of smart structures.     

Convex envelope results and strong formulations for a class of mixed-integer programs

In this article we present a novel technique for deriving the convex envelope of certain nonconvex fixed-charge functions of the type that arise in several related applications that have been considered in the literature. One common attribute of these problems is that they involve choosing levels for the undertaking of several activities. Two or more activities share a common resource, and a fixed charge is incurred when any of these activities is undertaken at a positive level. We consider nonconvex programming formulations for these problems in which the fixed charges are expressed in the form of concave functions. With the use of the developed convex envelope results, we show that the convex envelope relaxations of the nonconvex formulations lead to the linear programming relaxations of the strong IP/MIP formulations of these problems. Moreover, our technique for deriving convex envelopes offers a useful construct that could be exploited in other related contexts as well. © 1996 John Wiley & Sons, Inc.     

A class of Bayes-optimal two-stage screens

Items are characterized by a set of attributes (T) and a collection of covariates (X) associated with those attributes. We wish to screen for acceptable items (T ∈ C_T), but T is expensive to measure. We envisage a two-stage screen in which observation of X_ is used as a filter at the first stage to sentence most items. The second stage involves the observation of T for those items for which the first stage is indecisive. We adopt a Bayes decision-theoretic approach to the development of optimal two-stage screens within a general framework for costs and stochastic structure. We also consider the important question of how much screens need to be modified in the light of resource limitations that bound the proportion of items that can be passed to the second stage. © 1996 John Wiley & Sons, Inc.     

Gittins-index heuristics for research planning

The classical work of Gittins, which resulted in the celebrated index result, had applications to research planning as an important part of its motivation. However, research planning problems often have features that are not accommodated within Gittins's original framework. These include precedence constraints on the task set, influence between tasks, stopping or investment options and routes to success in which some tasks do not feature. We consider three classes of Markovian decision models for research planning, each of which has all of these features. Gittins-index heuristics are proposed and are assessed both analytically and computationally. They perform impressively. © 1995 John Wiley & Sons, Inc.     

Discrete equal‐capacity p‐median problem

This paper examines the discrete equal‐capacity p‐median problem that seeks to locate p new facilities (medians) on a network, each having a given uniform capacity, in order to minimize the sum of distribution costs while satisfying the demand on the network. Such problems arise, for example, in local access and transport area telecommunication network design problems where any number of a set of p facility units can be constructed at the specified candidate sites (hence, the net capacity is an integer multiple of a given unit capacity). We develop various valid inequalities, a separation routine for generating cutting planes that are specific members of such inequalities, as well as an enhanced reformulation that constructs a partial convex hull representation that subsumes an entire class of valid inequalities via its linear programming relaxation. We also propose suitable heuristic schemes for this problem, based on sequentially rounding the continuous relaxation solutions obtained for the various equivalent formulations of the problem. Extensive computational results are provided to demonstrate the effectiveness of the proposed valid inequalities, enhanced formulations, and heuristic schemes. The results indicate that the proposed schemes for tightening the underlying relaxations play a significant role in enhancing the performance of both exact and heuristic solution methods for this class of problems. © 2000 John & Sons, Inc. Naval Research Logistics 47: 166–183, 2000.     

Optimizing barge utilization in hinterland container transportation

In hinterland container transportation the use of barges is getting more and more important. We propose a real‐life operational planning problem model from an inland terminal operating company, in which the number of containers shipped per barge is maximized and the number of terminals visited per barge is minimized. This problem is solved with an integer linear program (ILP), yielding strong cost reductions, about 20%, compared to the method used currently in practice. Besides, we develop a heuristic that solves the ILP in two stages. First, it decides for each barge which terminals to visit and second it assigns containers to the barges. This heuristic produces almost always optimal solutions and otherwise near‐optimal solutions. Moreover, the heuristic runs much faster than the ILP, especially for large‐sized instances.     

A model for critical crack size estimation in fatigue failure of gun barrels

With repeated firing, fatigue cracks are produced in a gun barrel, and the barrel is no longer useful when a crack reaches a critical size. The initial crack size and the critical crack size, as well as the number of firings producing the critical crack size, may be considered as random variables. Assuming a proportional damage model for crack growth, a method for estimating the critical crack size distribution is presented. From these results, an estimate of the barrel life, or the residual barrel life once a crack of a given size is measured, can be obtained.