对一个重要极限证明中使用循环论证问题的质疑

有的著作认为在极限公式limx→0sinxx=1的证明中,要用到圆(扇形)的面积公式S=21Lr,而对后者的证明中必须要用到重要极限limx→0sinxx=1,从而犯了循环论证的错误。魏晋刘徽的“割圆术”是对无限问题的独特认识和致用的处理方式,是为证明圆面积公式而设计出来的一种方法。刘徽之前,希腊的阿基米德用穷竭法也证明了圆的面积公式。其中,刘徽的证法强调计算的程序性和构造性,而阿基米德则倾向于演绎的严谨性。这两种证明说明limx→0sinxx=1证明所谓的循环论证是可以避免的。     

基于供应链管理的战时装备供应保障业务流程重组

从战时装备供应链管理的要素和相互关系出发,结合我军实际,提出了基于供应链的战时装备供应保障业务流程重组过程,并对相关方法进行了讨论,旨在使战时所需装备以可预见的方式快速、安全、准确地送抵到作战部队。     

Dynamic policy for idling time preservation

This study aims to determine and evaluate dynamic idling policies where an agent can idle while some customers remain waiting. This type of policies can be employed in situations where the flow of urgent customers does not allow the agent to spend sufficient time on back-office tasks. We model the system as a single-agent exponential queue with abandonment. The objective is to minimize the system's congestion while ensuring a certain proportion of idling time for the agent. Using a Markov decision process approach, we prove that the optimal policy is a threshold policy according to which the agent should idle above (below) a certain threshold on the queue length if the congestion-related performance measure is concave (convex) with respect to the number of customers present. We subsequently obtain the stationary probabilities, performance measures, and idling time duration, expressed using complex integrals. We show how these integrals can be numerically computed and provide simpler expressions for fast-agent and heavy-traffic asymptotic cases. In practice, the most common way to regulate congestion is to control access to the service by rejecting some customers upon arrival. Our analysis reveals that idling policies allow high levels of idling probability that such rejection policies cannot reach. Furthermore, the greatest benefit of implementing an optimal idling policy occurs when the objective occupation rate is close to 50% in highly congested situations.     

可修系统可靠性统计分析模型的改进

阐述了复杂可修系统可靠性统计分析的特点及威布尔过程模型的适用性;引入修复影响系数对威布尔过程模型作了改进;给出了一个可供参考的计算示例.     

分段试验的可行性

运用随机点过程方法,从理论上对可修系统能否进行分段试验进行了研究.论证了对于泊松过程模型分段试验的可行性,并研究了分段试验对参数估计的影响.     

Threats and civil–military relations: explaining Singapore’s “trickle down” military innovation

This article explains why Singapore, despite its small size and semi-authoritarian regime, retains one of the best military forces in the Indo-Pacific. It unpacks Singapore’s ability to continuously innovate since the 1960s – technologically, organizationally, and conceptually – and even recently joined the Revolution in Military Affairs bandwagon. Drawing from the broader military innovation studies literature, this article argues evolutionary peacetime military innovation is more likely to occur in a state with a unified civil–military relation and whose military faces a high-level diverse set of threats. This argument explains how the civil–military fusion under the People’s Action Party-led government since Singapore’s founding moment has been providing coherent and consistent strategic guidance, political support, and financial capital, allowing the Singapore Armed Forces to continuously innovate in response to high levels and diversity of threats.     

The Millenials’ war: dilemmas of network dependency in today’s military

This work is about how the United States military has become dependent on networked technology. As arguably the largest contributor to national security, it has become so dependent that its chief doctrine integrates networked technology into nearly every specialty, with particularly intense focus on Network Centric Warfare. As the military’s old guard is replaced by the highly technical Millenial Generation, there is cause to pause when assuming this techno-acuity brings nothing but advantage and success. Vulnerabilities stemming from such extensive dependence offer opportunities for exploitation that have not gone unnoticed. The first step to moving forward from this point is to fully understand the extent to which the military has become dependent on computer networks. It might be the Millenials’ war today, but it would be quite unwise for the United States military to think about it and fight it in a purely Millenial way.     

Determining optimal sizes of bounded batches with rejection via quadratic min‐cost flow

In this article, we consider a single machine scheduling problem, in which identical jobs are split into batches of bounded sizes. For each batch, it is allowed to produce less jobs than a given upper bound, that is, some jobs in a batch can be rejected, in which case a penalty is paid for each rejected job. The objective function is the sum of several components, including the sum of the completion times, total delivery cost, and total rejection cost. We reduce this problem to a min‐cost flow problem with a convex quadratic function and adapt Tamir's algorithm for its solution. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 217–224, 2017     

Optimizing usage and maintenance decisions for k‐out‐of‐n systems of moving assets

We consider an integrated usage and maintenance optimization problem for a k‐out‐of‐n system pertaining to a moving asset. The k‐out‐of‐n systems are commonly utilized in practice to increase availability, where n denotes the total number of parallel and identical units and k the number of units required to be active for a functional system. Moving assets such as aircraft, ships, and submarines are subject to different operating modes. Operating modes can dictate not only the number of system units that are needed to be active, but also where the moving asset physically is, and under which environmental conditions it operates. We use the intrinsic age concept to model the degradation process. The intrinsic age is analogous to an intrinsic clock which ticks on a different pace in different operating modes. In our problem setting, the number of active units, degradation rates of active and standby units, maintenance costs, and type of economic dependencies are functions of operating modes. In each operating mode, the decision maker should decide on the set of units to activate (usage decision) and the set of units to maintain (maintenance decision). Since the degradation rate differs for active and standby units, the units to be maintained depend on the units that have been activated, and vice versa. In order to minimize maintenance costs, usage and maintenance decisions should be jointly optimized. We formulate this problem as a Markov decision process and provide some structural properties of the optimal policy. Moreover, we assess the performance of usage policies that are commonly implemented for maritime systems. We show that the cost increase resulting from these policies is up to 27% for realistic settings. Our numerical experiments demonstrate the cases in which joint usage and maintenance optimization is more valuable. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 418–434, 2017     

Relative Aging of Coherent Systems

In this article, we carry out the stochastic comparison between coherent systems through the relative aging order when component lifetimes are independent and identically distributed. We make use of the signature to characterize the structure of coherent systems, and derive several sufficient conditions under which the compared systems with the common size can be ordered in the sense of relative aging. Specially, we present some scenarios wherein the better a coherent system is, the faster it ages. Moreover, we discuss the relative aging of dual systems as well. Several numerical examples are provided to illustrate the theoretical results. © 2017 Wiley Periodicals, Inc. Naval Research Logistics 64: 345–354, 2017