On partial orderings of life distributions

Various partial orderings of life distributions have been studied in a unified way with the help of some functions. Two new partial orderings have been defined. Relevance of these partial orderings, for comparing life of a new unit with residual life of a used unit, is discussed.     

Optimal allocation of minimal repairs in parallel and series systems

In reliability engineering, the concept of minimal repair describes that the repair brings the failed unit (eg, system or component) to the situation which is same as it was just before the failure. With the help of the well‐known Gamma‐Poisson relationship, this paper investigates optimal allocation strategies of minimal repairs for parallel and series systems through implementing stochastic comparisons of various allocation policies in terms of the hazard rate, the reversed hazard rate, and the likelihood ratio orderings. Numerical examples are presented to illustrate these findings as well. These results not only strengthen and generalize some known ones in the seminal work of Shaked and Shanthikumar, but also solve the open problems proposed by Chahkandi et al.'s study and Arriaza et al.'s study.     

Terrorist choice: a stochastic dominance and prospect theory analysis

The paper explores terrorist choice by applying two well-known theoretical frameworks: stochastic dominance and prospect theory (PT). We analyse each pair of attack methods that can be formed from the RAND-MIPT database and the Global Terrorism Database. Instances of stochastic dominance are identified. PT orderings are computed. Attention is accorded to the identification of ‘trigger points’ and the circumstances that may lead to an increased likelihood that a terrorist will select an attack method associated with a higher expected number of fatalities, i.e. a potentially more damaging attack method.     

Replacing nonidentical vital components to extend system life

We consider a system that depends on a single vital component. If this component fails, the system life will terminate. If the component is replaced before its failure then the system life may be extended; however, there are only a finite number of spare components. In addition, the lifetimes of these spare components are not necessarily identically distributed. We propose a model for scheduling component replacements so as to maximize the expected system survival. We find the counterintuitive result that when comparing components' general lifetime distributions based on stochastic orderings, not even the strongest ordering provides an a priori guarantee of the optimal sequencing of components. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Some comparison results of system availability

System availability is a measure which is used to evaluate the performance of a system which can be in one of the two states: operational or nonoperational. It indicates the proportion of the time the system is available to perform its function. This paper discusses the concepts of stable point availability, stable interval availability, and long-run availability for the case of complete/minimal repair. Comparisons of these measures are made based on stochastic orderings and classifications of lifetime distributions. These comparisons are useful in determining policies for improving or maximizing the proportion of time the system is operational. The effect of using a burn-in procedure for maximizing these measures is also discussed. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 205–218, 1998     

Partial orderings of life distributions with respect to their aging properties

New partial orderings of life distributions are given. The concepts of decreasing mean residual life, new better than used in expectation, harmonic new better than used in expectation, new better than used in failure rate, and new better than used in failure rate average are generalized, so as to compare the aging properties of two arbitrary life distributions.     

On lifetimes in random environments

For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented. Some applications to the case of repairable components are finally provided. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 365–375, 1998     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.     

Decomposition algorithms for the maximum-weight connected graph problem

Given a positive integer R and a weight for each vertex in a graph, the maximum-weight connected graph problem (MCG) is to find a connected subgraph with R vertices that maximizes the sum of their weights. MCG has applications to communication network design and facility expansion. The constrained MCG (CMCG) is MCG with a constraint that one predetermined vertex must be included in the solution. In this paper, we introduce a class of decomposition algorithms for MCG. These algorithms decompose MCG into a number of small CMCGs by adding vertices one at a time and building a partial graph. They differ in the ordering of adding vertices. Proving that finding an ordering that gives the minimum number of CMCGs is NP-complete, we present three heuristic algorithms. Experimental results show that these heuristics are very effective in reducing computation and that different orderings can significantly affect the number of CMCGs to be solved. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 817–837, 1998     

A dynamic,nonstationary inventory problem for a price/quantity setting firm

A dynamic and nonstationary model is formulated for a firm which attempts to minimize total expected costs over a finite planning horizon. The control variables are price and production. The price p and the demand ζ are linked through the relationship ζ = g(p) + η, where g(p) is the riskless demand curve and η is a random variable. The general model allows for proportional ordering costs, convex holding and stockout costs, downward sloping riskless demand curve, backlogging, partial backlogging, lost sales, partial spoilage of inventory, and two modes of collecting revenue. Sufficient conditions are developed for this problem to have an optimal policy which resembles the single critical number policy known from stochastic inventory theory. It is also shown what set of parameters will satisfy these sufficiency conditions.     

部分服务台同步多重休假的GI/M/c稳态队长

在经典GI/M/c排队中引入部分服务台同步多重休假策略,利用拟单生过程和矩阵几何解的方法,求解系统的稳态队长分布及其条件随机分解。     

随机快速光滑二阶滑模末制导律设计

针对目标随机机动、惯性延迟、参数变化等因素降低导弹末制导精度的问题,提出新型随机快速光滑二阶滑模控制方法。将目标机动简化为零均值高斯白噪声过程,制导系统成为带加性噪声随机不确定非线性系统。考虑到该系统不存在平衡点,提出有限时间二阶均方实用收敛概念,并基于此证明了所设计控制律的收敛特性。根据直接命中条件设计滑模面,得到随机快速光滑二阶滑模制导律。在尾追和迎头两种态势下,将该新型制导律与扩展比例导引、一般滑模制导律及确定性光滑二阶滑模制导律进行仿真比较,验证了该方法的正确性和有效性。     

基于Langevin型随机共振的水中目标线谱检测

将Langevin型双稳态随机共振系统应用于水声时变线谱信号的检测,提出了设计水声线谱检测系统可以利用的外在参数。在水听器端建立了时变线谱模型,考查了随机共振系统对水声环境的适应能力。实验发现在信噪比变化、声压起伏、线谱漂移等情况下,系统都能较好的工作,为水声领域新型线谱检测系统的设计提供了依据。     

Generation and storage dispatch in electricity networks with generator disruptions

We present methods for optimizing generation and storage decisions in an electricity network with multiple unreliable generators, each colocated with one energy storage unit (e.g., battery), and multiple loads under power flow constraints. Our model chooses the amount of energy produced by each generator and the amount of energy stored in each battery in every time period in order to minimize power generation and storage costs when each generator faces stochastic Markovian supply disruptions. This problem cannot be optimized easily using stochastic programming and/or dynamic programming approaches. Therefore, in this study, we present several heuristic methods to find an approximate optimal solution for this system. Each heuristic involves decomposing the network into several single‐generator, single‐battery, multiload systems and solving them optimally using dynamic programming, then obtaining a solution for the original problem by recombining. We discuss the computational performance of the proposed heuristics as well as insights gained from the models. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 493–511, 2015     

Some order relations in closed networks of queues with multiserver stations

Consider a closed network of queues of the “product-form” type, where each station has s servers (s ≥ 1 is identical for all stations). We show that the throughput function of the network is Schur concave with respect to the loading of the stations and arrangement increasing with respect to the assignment of server groups. Consequently, different loading/assignment policies can be compared under majorization/arrangement orderings and their relative merits decided according to the yields of throughput. The results can be used to support planning decisions in computer and production systems which are modeled as closed networks of queues.     

Scheduling stochastic jobs with asymmetric earliness and tardiness penalties

We consider a stochastic counterpart of the well-known earliness-tardiness scheduling problem with a common due date, in which n stochastic jobs are to be processed on a single machine. The processing times of the jobs are independent and normally distributed random variables with known means and known variances that are proportional to the means. The due dates of the jobs are random variables following a common probability distribution. The objective is to minimize the expectation of a weighted combination of the earliness penalty, the tardiness penalty, and the flow-time penalty. One of our main results is that an optimal sequence for the problem must be V-shaped with respect to the mean processing times. Other characterizations of the optimal solution are also established. Two algorithms are proposed, which can generate optimal or near-optimal solutions in pseudopolynomial time. The proposed algorithms are also extended to problems where processing times do not satisfy the assumption in the model above, and are evaluated when processing times follow different probability distributions, including general normal (without the proportional relation between variances and means), uniform, Laplace, and exponential. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44, 531–557, 1997.     

加权随机模拟的时变可靠性分析方法

针对结构时变可靠性的随机模拟分析方法计算代价大的问题,在极值方法的基础上提出基于加权随机模拟的时变可靠性分析策略.时变可靠性分析需要计算在不同时间处的失效概率,通常需要进行多次可靠性分析,计算代价巨大.所提方法通过对常规静态可靠性的随机模拟方法进行改进拓展,运用加权策略分别发展了加权蒙特卡洛法和加权重要抽样法,使之能够...     

Inventory systems with imperfect demand information

An inventory system is described in which demand information may be incorrectly transmitted from the field to the stocking point. The stocking point employs a forwarding policy which attempts to send out to the field a quantity which, in general, is some function of the observed demand. The optimal ordering rules for the general n-period problem and the steady state case are derived. In addition orderings of the actual reorder points as functions of the errors are presented, as well as some useful economic interpretations and numerical illustrations.     

Scheduling jobs with random processing times on a single machine subject to stochastic breakdowns to minimize early-tardy penalties

We examine the problem of scheduling n jobs with a common due date on a single machine. The processing time of each job is a random variable, which follows an arbitrary distribution with a known mean and a known variance. The machine is not reliable; it is subject to stochastic breakdowns. The objective is to minimize the expected sum of squared deviations of job completion times from the due date. Two versions of the problem are addressed. In the first one the due date is a given constant, whereas in the second one the due date is a decision variable. In each case, a general form of the deterministic equivalent of the stochastic scheduling problem is obtained when the counting process related to the machine uptime distribution is a generalized Poisson process. A sufficient condition is derived under which optimal sequences are V-shaped with respect to mean processing times. Other characterizations of optimal solutions are also established. Based on the optimality properties, algorithms with pseudopolynomial time complexity are proposed to solve both versions of the problem. © 1996 John Wiley & Sons, Inc.     

Minimizing the weighted sum of quadratic completion times on a single machine

This article discusses the scheduling problem of minimizing the weighted sum of quadratic completion times on a single machine. It establishes links between orderings of adjacent and nonadjacent jobs that lead to a powerful branch and bound method. Computational results show that this method clearly outperforms the state of the art algorithm. © 1995 John Wiley & Sons. Inc.