Analysis of artillery shoot‐and‐scoot tactics

Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.     

三态部件的可靠性分析

本文给出完备的三态部件的可靠性模型类。从静态的观点来看,三态部件的可靠性模型有两类：（１）成功,降格成功,失败;（２）成功,双失败。从动态的观点来看,考虑到三个状态之间的转化关系,其模型类相对复杂;但是在失败率λ、维修率μ为常数的条件下,只需六个参数（λ１λ２λ３μ１μ２μ３）,便可以用马尔可夫模型给出三态部件的可靠性统一模型,并给出部件在三状态的概率函数Ｐｉ（ｔ）的解析表达式（ｔ为时间,ｉ表示状态）。     

基于隐马尔可夫模型的IDS程序行为异常检测

提出一种新的基于隐马尔可夫模型的程序行为异常检测方法,此方法利用系统调用序列,并基于隐马尔可夫模型来描述程序行为,根据程序行为模式的出现频率对其进行分类,并将行为模式类型同隐马尔可夫模型的状态联系在一起。由于各状态对应的观测值集合互不相交,模型训练中采用了运算量较小的序列匹配方法,与传统的Baum Welch算法相比,训练时间有较大幅度的降低。考虑到模型中状态的特殊含义以及程序行为的特点,将加窗平滑后的状态序列出现概率作为判决依据。实验表明,此方法具有很高的检测准确性,其检测效率也优于同类方法。     

Dynamic coordination of production planning and sales admission control in the presence of a spot market

We consider the decision‐making problem of dynamically scheduling the production of a single make‐to stock (MTS) product in connection with the product's concurrent sales in a spot market and a long‐term supply channel. The spot market is run by a business to business (B2B) online exchange, whereas the long‐term channel is established by a structured contract. The product's price in the spot market is exogenous, evolves as a continuous time Markov chain, and affects demand, which arrives sequentially as a Markov‐modulated Poisson process (MMPP). The manufacturer is obliged to fulfill demand in the long‐term channel, but is able to rein in sales in the spot market. This is a significant strategic decision for a manufacturer in entering a favorable contract. The profitability of the contract must be evaluated by optimal performance. The current problem, therefore, arises as a prerequisite to exploring contracting strategies. We reveal that the optimal strategy of coordinating production and sales is structured by the spot price dependent on the base stock and sell‐down thresholds. Moreover, we can exploit the structural properties of the optimal strategy to conceive an efficient algorithm. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Optimal control of a production‐inventory system with both backorders and lost sales

We consider the optimal control of a production inventory‐system with a single product and two customer classes where items are produced one unit at a time. Upon arrival, customer orders can be fulfilled from existing inventory, if there is any, backordered, or rejected. The two classes are differentiated by their backorder and lost sales costs. At each decision epoch, we must determine whether or not to produce an item and if so, whether to use this item to increase inventory or to reduce backlog. At each decision epoch, we must also determine whether or not to satisfy demand from a particular class (should one arise), backorder it, or reject it. In doing so, we must balance inventory holding costs against the costs of backordering and lost sales. We formulate the problem as a Markov decision process and use it to characterize the structure of the optimal policy. We show that the optimal policy can be described by three state‐dependent thresholds: a production base‐stock level and two order‐admission levels, one for each class. The production base‐stock level determines when production takes place and how to allocate items that are produced. This base‐stock level also determines when orders from the class with the lower shortage costs (Class 2) are backordered and not fulfilled from inventory. The order‐admission levels determine when orders should be rejected. We show that the threshold levels are monotonic (either nonincreasing or nondecreasing) in the backorder level of Class 2. We also characterize analytically the sensitivity of these thresholds to the various cost parameters. Using numerical results, we compare the performance of the optimal policy against several heuristics and show that those that do not allow for the possibility of both backordering and rejecting orders can perform poorly.© 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Minimizing the false alarm rate in systems with transient abnormality

We consider a stochastic partially observable system that can switch between a normal state and a transient abnormal state before entering a persistent abnormal state. Only the persistent abnormal state requires alarms. The transient and persistent abnormal states may be similar in appearance, which can result in excess false alarms. We propose a partially observable Markov decision process model to minimize the false alarm rate, subject to a given upper bound on the expected alarm delay time. The cost parameter is treated as the Lagrange multiplier, which can be estimated from the bound of the alarm delay. We show that the optimal policy has a control‐limit structure on the probability of persistent abnormality, and derive closed‐form bounds for the control limit and present an algorithm to specify the Lagrange multiplier. We also study a specialized model where the transient and persistent abnormal states have the same observation distribution, in which case an intuitive “watchful‐waiting” policy is optimal. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 320–334, 2016     

A novel gradient approach for optimal design and sensitivity analysis of EWMA control charts

Conventional control charts are often designed to optimize out‐of‐control average run length (ARL), while constraining in‐control ARL to a desired value. The widely employed grid search approach in statistical process control (SPC) is time‐consuming with unsatisfactory accuracy. Although the simulation‐based ARL gradient estimators proposed by Fu and Hu [Manag Sci 45 (1999), 395–413] can alleviate this issue, it still requires a large number of simulation runs to significantly reduce the variance of gradient estimators. This article proposes a novel ARL gradient estimation approach based on integral equation for efficient analysis and design of control charts. Although this article compares with the results of Fu and Hu [Manag Sci 45 (1999), 395–413] based on the exponentially weighted moving average (EWMA) control chart, the proposed approach has wide applicability as it can generally fit into any control chart with Markovian property under any distributions. It is shown that the proposed method is able to provide a fast, accurate, and easy‐to‐implement algorithm for the design and analysis of EWMA charts, as compared to the simulation‐based gradient estimation method. Moreover, the proposed gradient estimation method facilitates the computation of high‐order derivatives that are valuable in sensitivity analysis. The code is written in Matlab, which is available on request. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 223–237, 2014     

基于马尔科夫决策的目标选择策略

目标选择是军事计划的关键要素之一。基于马尔科夫决策方法,解决具有复杂目标间关联的多阶段目标选择问题。使用与或树描述目标体系各层状态间的影响关联,并以目标体系整体失效为求解目的,建立了基于离散时间MDP的多阶段打击目标选择模型。在LRTDP算法基础上提出一种启发式方法,通过判断从当前目标体系状态到达体系失效状态的演化过程中的可能资源消耗和失败概率,来提供对当前状态的评估值,该方法能有效排除问题搜索空间中不能到达体系失效目的的中间状态,压缩了由于目标间复杂关联而增长的巨大状态空间。用实验验证了该方法有效性,实验结果表明,该方法直观实用,对目标间具有复杂关联关系的目标打击决策有一定参考价值。     

Limiting behavior of the stochastic sequential assignment problem

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

Coordination mechanisms for a three‐stage reverse supply chain to increase profitable returns

In this article, we consider a generic electronic product that can be remanufactured or recycled at the end of its life cycle to generate new profit. We first describe the product return process and then present a customer segmentation model to capture consumers' different behaviors with respect to product return so that the retailer can work more effectively to increase the return volume. In regard to the collaboration between the retailer and the manufacturer, we explore a revenue‐sharing coordination mechanism for achieving a win‐win outcome. The optimality and sensitivity of the critical parameters in four strategies are obtained and examined both theoretically and numerically, which generate insights on how to manage an efficient consumer‐retailer‐manufacturer reverse supply chain, as well as on the feasibility of simplifying such a three‐stage chain structure. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2013