Asymptotic analysis of periodic policies for the inventory routing problem

In this article, a distribution system is studied where the sum of transportation and inventory costs is to be minimized. The inventory holding cost is assumed to be the same for all retailers. A fixed partition (FP) periodic policy is proposed with tight asymptotic worst‐case performance of 3/2 with respect to the best possible policy. This bound cannot be improved in the class of FP periodic policies. In partition‐based PB policies, the retailers are first partitioned into sets and then the sets are grouped in such a way that sets of retailers within a group are served together at selected times. A PB periodic, policy is presented with tight worst‐case asymptotic performance of with respect to the best possible policy. This latter performance improves the worst‐case asymptotic performance of of the previously best known policy for this problem. We also show that the proposed PB periodic policy has the best worst‐case asymptotic performance within the class of PB policies. Finally, practical heuristics inspired by the analyzed policies are designed and tested. The asymptotic worst–case performances of the heuristics are shown to be the same of those of the analyzed policies. Computational results show that the heuristics suggested are less than 6.4% on average from a lower bound on the optimal cost when 50 or more retailers are involved. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 00: 000–000, 2013     

Effects of nano-sized aluminum on detonation characteristics and metal acceleration for RDX-based aluminized explosive

Nano-sized aluminum(Nano-Al)powders hold promise in enhancing the total energy of explosives and the metal acceleration ability at the same time.However,the near-detonation zone effects of reaction between Nano-Al with detonation products remain unclear.In this study,the overall reaction process of 170 nm Al with RDX explosive and its effect on detonation characteristics,detonation reaction zone,and the metal acceleration ability were comprehensively investigated through a variety of experiments such as the detonation velocity test,detonation pressure test,explosive/window interface velocity test and confined plate push test using high-resolution laser interferometry.Lithium fluoride(LiF),which has an inert behavior during the explosion,was used as a control to compare the contribution of the reaction of aluminum.A thermochemical approach that took into account the reactivity of aluminum and ensuing detonation products was adopted to calculate the additional energy release by afterburn.Combining the numerical simulations based on the calculated afterburn energy and experimental results,the param-eters in the detonation equation of state describing the Nano-Al reaction characteristics were calibrated.This study found that when the 170 nm Al content is from 0％to 15％,every 5％increase of aluminum resulted in about a 1.3％decrease in detonation velocity.Manganin pressure gauge measurement showed no significant enhancement in detonation pressure.The detonation reaction time and reaction zone length of RDX/Al/wax/80/15/5 explosive is 64 ns and 0.47 mm,which is respectively 14％and 8％higher than that of RDX/wax/95/5 explosive(57 ns and 0.39 mm).Explosive/window interface velocity curves show that 170 nm Al mainly reacted with the RDX detonation products after the detonation front.For the recording time of about 10 μs throughout the plate push test duration,the maximum plate velocity and plate acceleration time accelerated by RDX/Al/wax/80/15/5 explosive is 12％and 2.9 μs higher than that of RDX/LiF/wax/80/15/5,respectively,indicating that the aluminum reaction energy significantly increased the metal acceleration time and ability of the explosive.Numerical simulations with JWLM explosive equation of state show that when the detonation products expanded to 2 times the initial volume,over 80％of the aluminum had reacted,implying very high reactivity.These results are significant in attaining a clear understanding of the reaction mechanism of Nano-Al in the development of aluminized explosives.     

Combustion characteristic and aging behavior of bimetal thermite powders

Nanothermites have been employed as fuel additives in energetic formulations due to their higher en-ergy density over CHNO energetics. Nevertheless, sintering and degradation of nanoparticles signifi-cantly limit the practical use of nanothermites. In this work, combustion characteristic and aging behavior of aluminum/iron oxide (Al/Fe2O3) nanothermite mixtures were investigated in the presence of micron-scale nickel aimed to produce bimetal thermite powders. The results showed that the alumina content in the combustion residue increased from 88.3％ for Al/Fe2O3 nanothermite to 96.5％ for the nanothermite mixture containing 20 wt％nickel. Finer particle sizes of combustion residue were obtained for the nanothermite mixtures containing nickel, indicative of the reduced agglomeration. Both results suggested a more complete combustion in the bimetal thermite powders. Aging behavior of the nano-thermite mixture was also assessed by measuring the heat of combustion of the mixture before and after aging process. The reduction in heat of combustion of nanothermite mixtures containing nickel was less severe as compared to a significant decrease for the nanothermite mixture without nickel, indicating better aging resistance of the bimetal thermite powders.     

应用抗差无迹卡尔曼滤波的再入弹道处理技术

针对现有无迹卡尔曼滤波在再入弹道处理中可能出现的异常观测、观测随机误差模型不准确以及动力学模型不合理等问题,在无迹卡尔曼滤波中引入自适应与抗差估计理论,研究适用于再入弹道处理的自适应抗差滤波方法。该方法可以自适应地估计测量噪声等价协方差阵和状态噪声等价协方差阵,并可实现异常值的分离和维纳模型方差的自适应调整。数值仿真结果表明:该方法计算简单,并能有效减弱测量误差和动力学模型误差对弹道处理精度的影响。     

Analysis of practical policies for a single link distribution system

In this paper we consider a transportation problem where several products have to be shipped from an origin to a destination by means of vehicles with given capacity. Each product is made available at the origin and consumed at the destination at the same constant rate. The time between consecutive shipments must be greater than a given minimum time. All demand needs to be satisfied on time and backlogging is not allowed. The problem is to decide when to make the shipments and how to load the vehicles with the objective of minimizing the long run average of the transportation and the inventory costs at the origin and at the destination over an infinite horizon. We consider two classes of practical shipping policies, the zero inventory ordering (ZIO) policies and the frequency‐based periodic shipping (FBPS) policies. We show that, in the worst‐case, the Best ZIO policy has a performance ratio of . A better performance guarantee of is shown for the best possible FBPS policy. The performance guarantees are tight. Finally, combining the Best ZIO and the Best FBPS policies, a policy that guarantees a performance is obtained. Computational results show that this policy gives an average percent optimality gap on all the tested instances of <1%. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

An algorithm for a class of loading problems

The loading problem we consinder is to assign a set of discrete objects, each having a weight, to a set of boxes, each of which has a capacity limit, in such a way that every object is assigned to a box and the number of boxes used is minimized. A characterization of the assignments is offered and used to develop a set of rules for generating nonredundant assignments. The rules are incorporated into an implicit enumeration algorithm. The algorithm is tested against a very good heuristic. Computational experience shows that the algorithm is highly efficient, solving problems of up to 3600 0-1 variables in a CPU second.     

An algorithm for 0-1 multiple-knapsack problems

The 0-1 multiple-knapsack problem is an extension of the well-known 0-1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized. A branch-and-bound algorithm for solving the problem is developed and tested. Branching rules that avoid the search of redundant partial solutions are used in the algorithm. Various bounding techniques, including Lagrangean and surrogate relaxations, are investigated and compared.     

Nonexistence of the maximum likelihood estimates in the weibull process

With incomplete data the maximum likelihood estimates of the parameters of the Weibull process can only be obtained by solving the likelihood equations iteratively. In this article we show that the solution of the likelihood equations may lie outside of the parameter space if none of the processes can be observed from time zero.     

Planning gamma accelerated degradation tests with two accelerating variables

Gamma accelerated degradation tests (ADT) are widely used to assess timely lifetime information of highly reliable products with degradation paths that follow a gamma process. In the existing literature, there is interest in addressing the problem of deciding how to conduct an efficient, ADT that includes determinations of higher stress‐testing levels and their corresponding sample‐size allocations. The existing results mainly focused on the case of a single accelerating variable. However, this may not be practical when the quality characteristics of the product have slow degradation rates. To overcome this difficulty, we propose an analytical approach to address this decision‐making problem using the case of two accelerating variables. Specifically, based on the criterion of minimizing the asymptotic variance of the estimated q quantile of lifetime distribution of the product, we analytically show that the optimal stress levels and sample‐size allocations can be simultaneously obtained via a general equivalence theorem. In addition, we use a practical example to illustrate the proposed procedure.