Technical note: An improved range chart for normal and long‐tailed symmetrical distributions

The distribution of the range of a sample, even in the case of a normal distribution, is not symmetric. Shewhart's control chart for range and other approximations for range from skewed distributions and long‐tailed (leptokurtic) symmetrical distributions assume the distribution of range as symmetric and provide 3 sigma control limits. We provide accurate approximations for the R‐chart control limits for the leptokurtic symmetrical distributions, using a range quantile approximation (RQA) method and illustrate the use of the RQA method with a numerical example. As special cases, we provide constants for the R‐chart for the normal, logistic, and Laplace distributions. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Technical note: Reexamination of all‐or‐none inspection policies in a supply chain with endogenous product quality

This note studies the optimal inspection policies in a supply chain in which a manufacturer purchases components from a supplier but has no direct control of component quality. The manufacturer uses an inspection policy and a damage cost sharing contract to encourage the supplier to improve the component quality. We find that all‐or‐none inspection policies are optimal for the manufacturer if the supplier's share of the damage cost is larger than a threshold; otherwise, the manufacturer should inspect a fraction of a batch. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

DEA models for two‐stage processes: Game approach and efficiency decomposition

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs). This tool has been utilized by a number of authors to examine two‐stage processes, where all the outputs from the first stage are the only inputs to the second stage. The current article examines and extends these models using game theory concepts. The resulting models are linear, and imply an efficiency decomposition where the overall efficiency of the two‐stage process is a product of the efficiencies of the two individual stages. When there is only one intermediate measure connecting the two stages, both the noncooperative and centralized models yield the same results as applying the standard DEA model to the two stages separately. As a result, the efficiency decomposition is unique. While the noncooperative approach yields a unique efficiency decomposition under multiple intermediate measures, the centralized approach is likely to yield multiple decompositions. Models are developed to test whether the efficiency decomposition arising from the centralized approach is unique. The relations among the noncooperative, centralized, and standard DEA approaches are investigated. Two real world data sets and a randomly generated data set are used to demonstrate the models and verify our findings. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Parallel machine scheduling with batch deliveries to minimize total flow time and delivery cost

Motivated by the flow of products in the iron and steel industry, we study an identical and parallel machine scheduling problem with batch deliveries, where jobs finished on the parallel machines are delivered to customers in batches. Each delivery batch has a capacity and incurs a cost. The objective is to find a coordinated production and delivery schedule that minimizes the total flow time of jobs plus the total delivery cost. This problem is an extension of the problem considered by Hall and Potts, Ann Oper Res 135 (2005) 41–64, who studied a two‐machine problem with an unbounded number of transporters and unbounded delivery capacity. We first provide a dynamic programming algorithm to solve a special case with a given job assignment to the machines. A heuristic algorithm is then presented for the general problem, and its worst‐case performance ratio is analyzed. The computational results show that the heuristic algorithm can generate near‐optimal solutions. Finally, we offer a fully polynomial‐time approximation scheme for a fixed number of machines. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 492–502, 2016     

Minimal LST representations of MAP(n)s: Moment fittings and queueing approximations

A Markovian arrival process of order n, MAP(n), is typically described by two n × n transition rate matrices in terms of rate parameters. While it is straightforward and intuitive, the Markovian representation is redundant since the minimal number of parameters is n² for non‐redundant MAP(n). It is well known that the redundancy complicates exact moment fittings. In this article, we present a minimal and unique Laplace‐Stieltjes transform (LST) representations for MAP(n)s. Even though the LST coefficients vector itself is not a minimal representation, we show that the joint LST of stationary intervals can be represented with the minimum number of parameters. We also propose another minimal representation for MAP(3)s based on coefficients of the characteristic polynomial equations of the two transition rate matrices. An exact moment fitting procedure is presented for MAP(3)s based on two proposed minimal representations. We also discuss how MAP(3)/G/1 departure process can be approximated as a MAP(3). A simple tandem queueing network example is presented to show that the MAP(3) performs better than the MAP(2) in queueing approximations especially under moderate traffic intensities. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 549–561, 2016     

Convolutions and generalization of logconcavity: Implications and applications

Additive convolution of unimodal and α‐unimodal random variables are known as an old classic problem which has attracted the attention of many authors in theory and applied fields. Another type of convolution, called multiplicative convolution, is rather younger. In this article, we first focus on this newer concept and obtain several useful results in which the most important ones is that if is logconcave then so are and for some suitable increasing functions ?. This result contains and as two more important special cases. Furthermore, one table including more applied distributions comparing logconcavity of f(x) and and two comprehensive implications charts are provided. Then, these fundamental results are applied to aging properties, existence of moments and several kinds of ordered random variables. Multiplicative strong unimodality in the discrete case is also introduced and its properties are investigated. In the second part of the article, some refinements are made for additive convolutions. A remaining open problem is completed and a conjecture concerning convolution of discrete α‐unimodal distributions is settled. Then, we shall show that an existing result regarding convolution of symmetric discrete unimodal distributions is not correct and an easy alternative proof is presented. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 109–123, 2016     

固定翼无人机航迹跟踪抗风性研究

无人机作为一种新型军事装备,具有广泛的作战应用场景。无人机的航迹跟踪性能和抗干扰能力是其安全完成飞行任务的保障,随着现代战争作战环境日益复杂,无人机飞行将面临更大的挑战。针对目前固定翼无人机在飞行过程中受风扰影响严重的问题,设计了一种具有抗风性的航迹跟踪方法。利用非线性导引原理实现对航迹的跟踪,并通过引入反馈消除了风扰条件下飞行轨迹与期望航迹之间存在的静差。最后通过仿真验证了该方法的可行性和有效性。     

Potential impact of recharging plug‐in hybrid electric vehicles on locational marginal prices

Plug‐in hybrid electric vehicles (PHEVs), upon market penetration, will create additional recharging loads to the electric power systems. This article considers different recharging scenarios and uses game theoretic models to study the potential impact of the recharging loads on locational marginal prices (wholesale electricity prices). Computational results from a Pennsylvania‐New Jersey‐Maryland Interconnection case study show that, under the existing recharging infrastructures, even a small magnitude of load increase caused by PHEV recharging could have a significant undesirable impact on locational marginal prices. The impact could be mitigated to a varying extent by the availability of possible future recharging infrastructures, including realtime pricing recharging meters, battery stations, or vehicle‐to‐grid technology.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Decomposing inventory routing problems with approximate value functions

We present a time decomposition for inventory routing problems. The methodology is based on valuing inventory with a concave piecewise linear function and then combining solutions to single‐period subproblems using dynamic programming techniques. Computational experiments show that the resulting value function accurately captures the inventory's value, and solving the multiperiod problem as a sequence of single‐period subproblems drastically decreases computational time without sacrificing solution quality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

一种用于SEAD任务的改进型Voronoi图

根据雷达所在位置构造Delaunay三角形,取它的外心作为Voronoi图的顶点,构造常规Voronoi图,使用随机搜索算法可以为无人战斗机规划安全路径。由于战场环境威胁各异,使用常规Voronoi图不再能表征真实的SEAD任务,增大了无人战斗机的威胁,本文提出了一种新的Voronoi图的改进方法,以提高无人战斗机在执行SEAD任务时的生存概率。首先,根据可能出现的各种情况进行了分析,提出了改进型Voronoi图的构图原则。然后,提出了在不同威胁体下,基于"Delaunay多边形"构造改进型Voronoi图的方法。最后,进行了仿真。仿真算例的结果验证此方法可以明显地提高无人战斗机的生存概率。