Approximations and empirics for stochastic war equations

The article develops a theorem which shows that the Lanchester linear war equations are not in general equal to the Kolmogorov linear war equations. The latter are time‐consuming to solve, and speed is important when a large number of simulations must be run to examine a large parameter space. Run times are provided, where time is a scarce factor in warfare. Four time efficient approximations are presented in the form of ordinary differential equations for the expected sizes and variances of each group, and the covariance, accounting for reinforcement and withdrawal of forces. The approximations are compared with “exact” Monte Carlo simulations and empirics from the WWII Ardennes campaign. The band spanned out by plus versus minus the incremented standard deviations captures some of the scatter in the empirics, but not all. With stochastically varying combat effectiveness coefficients, a substantial part of the scatter in the empirics is contained. The model is used to forecast possible futures. The implications of increasing the combat effectiveness coefficient governing the size of the Allied force, and injecting reinforcement to the German force during the Campaign, are evaluated, with variance assessments. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Production‐inventory systems with imperfect advance demand information and updating

We consider a supplier with finite production capacity and stochastic production times. Customers provide advance demand information (ADI) to the supplier by announcing orders ahead of their due dates. However, this information is not perfect, and customers may request an order be fulfilled prior to or later than the expected due date. Customers update the status of their orders, but the time between consecutive updates is random. We formulate the production‐control problem as a continuous‐time Markov decision process and prove there is an optimal state‐dependent base‐stock policy, where the base‐stock levels depend upon the numbers of orders at various stages of update. In addition, we derive results on the sensitivity of the state‐dependent base‐stock levels to the number of orders in each stage of update. In a numerical study, we examine the benefit of ADI, and find that it is most valuable to the supplier when the time between updates is moderate. We also consider the impact of holding and backorder costs, numbers of updates, and the fraction of customers that provide ADI. In addition, we find that while ADI is always beneficial to the supplier, this may not be the case for the customers who provide the ADI. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

把目标威胁纳入性能指标的目标分配方法

武器系统目标分配是作战指挥中的一个重要问题。提出了把目标威胁纳入性能指标,建立在马尔可夫动态系统输入过程最优化基础上的目标分配方法     

Dynamic learning,pricing, and ordering by a censored newsvendor

We address the problem of determining optimal ordering and pricing policies in a finite‐horizon newsvendor model with unobservable lost sales. The demand distribution is price‐dependent and involves unknown parameters. We consider both the cases of perishable and nonperishable inventory. A very general class of demand functions is studied in this paper. We derive the optimal ordering and pricing policies as unique functions of the stocking factor (which is a linear transformation of the safety factor). An important expression is obtained for the marginal expected value of information. As a consequence, we show when lost sales are unobservable, with perishable inventory the optimal stocking factor is always at least as large as the one given by the single‐period model; however, if inventory is nonperishable, this result holds only under a strong condition. This expression also helps to explain why the optimal stocking factor of a period may not increase with the length of the problem. We compare this behavior with that of a full information model. We further examine the implications of the results to the special cases when demand uncertainty is described by additive and multiplicative models. For the additive case, we show that if demand is censored, the optimal policy is to order more as well as charge higher retail prices when compared to the policies in the single‐period model and the full information model. We also compare the optimal and myopic policies for the additive and multiplicative models. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

一类马尔可夫人才系统中的工龄和职龄

用马尔可夫模型研究人才系统中工龄和职龄问题的一般方法都要按职务等级、工龄或职龄来划分系统状态。本文在只以职务等级划分系统状态的一类无降级且逐级晋升的齐次马尔可夫人才系统中讨论了工龄和职龄问题,得到直观描述工龄和职龄的计算结果,并通过一实例说明了本方法的应用价值。     

基于马尔科夫链的一种评价方法

应用了数理统计与随机过程理论,从分析动态系统的状态以及状态转移情况给出了一种合理的评价方法,经过实例验证,该方法效果较好.     

具有多类索赔到达保险风险模型的破产问题

应用Markov骨架过程的方法和补充变量技巧研究了索赔为多类一般到达的保险风险模型 ,分别得到了破产时间与破产时刻前后资产盈余的联合分布以及破产时间的分布。使得索赔为一般到达的保险风险问题的研究取得了较大的进展。     

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     

Reliability of a two-dimensional demand-based networked system with multistate components

Existing research on multistate system reliability has mainly focused on one-dimensional systems such as parallel systems, linear sliding window systems, and linearly consecutively connected systems. However, two-dimensional networked systems widely exist in real-world applications such as lighting systems, monitoring systems, and computer network systems. This research considers a two-dimensional networked system consisting of multistate components. The system fails if the cumulative performance of any row or any column cannot meet a predetermined demand. A novel reliability evaluation algorithm is proposed for the considered two-dimensional networked system by extending the universal generating function technique. Furthermore, the proposed model and reliability evaluation algorithm are extended to a two-dimensional networked system with phased missions. The proposed models and algorithms are illustrated by a matrix heating system in a thermoforming machine.     

Revenue maximization in two-station tandem queueing systems

We study optimal pricing for tandem queueing systems with finite buffers. The service provider dynamically quotes prices to incoming price sensitive customers to maximize the long-run average revenue. We present a Markov decision process model for the optimization problem. For systems with two stations, general-sized buffers, and two or more prices, we describe the structure of the optimal dynamic pricing policy and develop tailored policy iteration algorithms to find an optimal pricing policy. For systems with two stations but no intermediate buffer, we characterize conditions under which quoting either a high or a low price to all customers is optimal and provide an easy-to-implement algorithm to solve the problem. Numerical experiments are conducted to compare the developed algorithms with the regular policy iteration algorithm. The work also discusses possible extensions of the obtained results to both three-station systems and two-station systems with price and congestion sensitive customers using numerical analysis.