Evaluation of effectiveness of polymer coatings in reducing blast-induced deformation of steel plates

Incorporating elastomers such as polymers in protective structures to withstand high energetic dynamic loads, has gained significant interest. The main objective of this study is to investigate the influence of a Polyurea coating towards the blast-induced response in steel plates. As such, Polyurea coated steel plates were tested under near-field blast loads, produced by the detonation of 1 kg of spherical nitromethane charges, at a standoff distance of 150 mm. Mild steel (XLERPLATE 350) and high-strength steel (BIS80) plates with thicknesses of 10 mm were Polyurea coated with thicknesses of 6 mm and 12 mm on either the front (facing the charge) or the back face. The deformation profiles were measured using 3D scanning. Numerical simulations were performed using the non-linear finite element code LS-DYNA. The strain-dependent behaviour of the steel and Polyurea were represented by Johnson-cook and Money-Rivlin constitutive models, respectively. The numerical models were validated by comparing the plate deflection results obtained from the experiments and were then used in the subsequent parametric study to investigate the optimum thickness of the Polyurea coating. The results indicate that back face coating contributes towards an approximately 20% reduction in the residual deformation as well as the absence of melting of the Polyurea layer, while the front-face coating can be used a means of providing additional standoff distance to the steel plates.     

Balancing and optimizing a portfolio of R&D projects

A mathematical formulation of an optimization model designed to select projects for inclusion in an R&D portfolio, subject to a wide variety of constraints (e.g., capital, headcount, strategic intent, etc.), is presented. The model is similar to others that have previously appeared in the literature and is in the form of a mixed integer programming (MIP) problem known as the multidimensional knapsack problem. Exact solution of such problems is generally difficult, but can be accomplished in reasonable time using specialized algorithms. The main contribution of this paper is an examination of two important issues related to formulation of project selection models such as the one presented here. If partial funding and implementation of projects is allowed, the resulting formulation is a linear programming (LP) problem which can be solved quite easily. Several plausible assumptions about how partial funding impacts project value are presented. In general, our examples suggest that the problem might best be formulated as a nonlinear programming (NLP) problem, but that there is a need for further research to determine an appropriate expression for the value of a partially funded project. In light of that gap in the current body of knowledge and for practical reasons, the LP relaxation of this model is preferred. The LP relaxation can be implemented in a spreadsheet (even for relatively large problems) and gives reasonable results when applied to a test problem based on GM's R&D project selection process. There has been much discussion in the literature on the topic of assigning a quantitative measure of value to each project. Although many alternatives are suggested, no one way is universally accepted as the preferred way. There does seem to be general agreement that all of the proposed methods are subject to considerable uncertainty. A systematic way to examine the sensitivity of project selection decisions to variations in the measure of value is developed. It is shown that the solution for the illustrative problem is reasonably robust to rather large variations in the measure of value. We cannot, however, conclude that this would be the case in general. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 18–40, 2001     

Sequential and systematic sampling plans for the Markov‐dependent production process

Acceptance sampling plans are used to assess the quality of an ongoing production process, in addition to the lot acceptance. In this paper, we consider sampling inspection plans for monitoring the Markov‐dependent production process. We construct sequential plans that satisfy the usual probability requirements at acceptable quality level and rejectable quality level and, in addition, possess the minimum average sample number under semicurtailed inspection. As these plans result in large sample sizes, especially when the serial correlation is high, we suggest new plans called “systematic sampling plans.” The minimum average sample number systematic plans that satisfy the probability requirements are constructed. Our algorithm uses some simple recurrence relations to compute the required acceptance probabilities. The optimal systematic plans require much smaller sample sizes and acceptance numbers, compared to the sequential plans. However, they need larger production runs to make a decision. Tables for choosing appropriate sequential and systematic plans are provided. The problem of selecting the best systematic sampling plan is also addressed. The operating characteristic curves of some of the sequential and the systematic plans are compared, and are observed to be almost identical. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 451–467, 2001     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

Minimizing weighted mean absolute deviation of flow times in single machine systems

We discuss the problem of scheduling several jobs on a single machine with the objective of minimizing the weighted mean absolute deviation of flow times around the weighted mean flow time. We first show that the optimal schedule is W-shaped. For the unweighted case, we show that all optimal schedules are V-shaped. This characterization enables us to show that the problem is NP-hard. We then provide a pseudopolynomial algorithm for the unweighted problem. Finally, we consider three heuristic algorithms for the unweighted problem and report computational experience with these algorithms. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 297–311, 1998     

Bayesian inference for a Lanchester type combat model

We undertake inference for a stochastic form of the Lanchester combat model. In particular, given battle data, we assess the type of battle that occurred and whether or not it makes any difference to the number of casualties if an army is attacking or defending. Our approach is Bayesian and we use modern computational techniques to fit the model. We illustrate our method using data from the Ardennes campaign. We compare our results with previous analyses of these data by Bracken and Fricker. Our conclusions are somewhat different to those of Bracken. Where he suggests that a linear law is appropriate, we show that the logarithmic or linear‐logarithmic laws fit better. We note however that the basic Lanchester modeling assumptions do not hold for the Ardennes data. Using Fricker's modified data, we show that although his “super‐logarithmic” law fits best, the linear, linear‐logarithmic, and logarithmic laws cannot be ruled out. We suggest that Bayesian methods can be used to make inference for battles in progress. We point out a number of advantages: Prior information from experts or previous battles can be incorporated; predictions of future casualties are easily made; more complex models can be analysed using stochastic simulation techniques. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 541–558, 2000     

Nonpreemptive scheduling of independent tasks with prespecified processor allocations

In this article we study the problem of scheduling independent tasks, each of which requires the simultaneous availability of a set of prespecified processors, with the objective of minimizing the maximum completion time. We propose a graph-theoretical approach and identify a class of polynomial instances, corresponding to comparability graphs. We show that the scheduling problem is polynomially equivalent to the problem of extending a graph to a comparability graph whose maximum weighted clique has minimum weight. Using this formulation we show that in some cases it is possible to decompose the problem according to the canonical decomposition of the graph. Finally, a general solution procedure is given that includes a branch-and-bound algorithm for the solution of subproblems which can be neither decomposed nor solved in polynomial time. Some examples and computational results are presented. © 1994 John Wiley & Sons, Inc.     

An inventory model of incentives for on-time delivery in just-in-time purchasing contracts

This article formulates an analytic model of just-in-time purchasing contracts and compares the minimum cost solution with the cost attainable through vertical integration. The models use standard inventory theory cost parameters and decision variables. The results quantify the increase in cost of buying an item rather than making it. Optimal incentives are characterized when JIT purchasing contracts are used. When JIT purchasing is implemented, buffer inventories are typically reduced. This inventory reduction makes on-time delivery critical to the buyer; yet timeliness is controlled by the supplier. As an incentive to provide on-time delivery, the buyer offers the supplier a bonus for on-time delivery. The supplier chooses a flow time allowance based upon the bonus offered. First- and second-order conditions are characterized in general, and examples are provided for exponentially and uniformly distributed flow times. The delivery timeliness obtainable in a vertically integrated firm is determined and compared with timeliness obtainable between separate firms. This comparison indicates that buyers who choose to purchase materials from a separate firm are more likely to experience late deliveries. The relationship between the value of the bonus and the proportion of on-time deliveries is also considered. The bonus required to achieve the same probability of on-time delivery as under vertical integration is also determined. © 1993 John Wiley & Sons, Inc.     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.