New results on a stochastic duel game with each force consisting of heterogeneous units

Two forces engage in a duel, with each force initially consisting of several heterogeneous units. Each unit can be assigned to fire at any opposing unit, but the kill rate depends on the assignment. As the duel proceeds, each force—knowing which units are still alive in real time—decides dynamically how to assign its fire, in order to maximize the probability of wiping out the opposing force before getting wiped out. It has been shown in the literature that an optimal pure strategy exists for this two‐person zero‐sum game, but computing the optimal strategy remained cumbersome because of the game's huge payoff matrix. This article gives an iterative algorithm to compute the optimal strategy without having to enumerate the entire payoff matrix, and offers some insights into the special case, where one force has only one unit. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 56–65, 2014     

A sequential dynamic pricing model and its applications

Consider a sequential dynamic pricing model where a seller sells a given stock to a random number of customers. Arriving one at a time, each customer will purchase one item if the product price is lower than her personal reservation price. The seller's objective is to post a potentially different price for each customer in order to maximize the expected total revenue. We formulate the seller's problem as a stochastic dynamic programming model, and develop an algorithm to compute the optimal policy. We then apply the results from this sequential dynamic pricing model to the case where customers arrive according to a continuous‐time point process. In particular, we derive tight bounds for the optimal expected revenue, and develop an asymptotically optimal heuristic policy. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

A fluid queueing model for link travel time moments

We analyze the moments of the random time required for a vehicle to traverse a transportation network link of arbitrary length when its speed is governed by a random environment. The problem is motivated by stochastic transportation network applications in which the estimation of travel time moments is of great importance. We analyze this random time in a transient and asymptotic sense by employing results from the field of fluid queues. The results are demonstrated on two example problems. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

离散型随机BAM神经网络时滞分布依赖全局指数稳定性

研究一类具有随机时滞与随机干扰的离散型BAM神经网络的全局指数稳定性,所建模型同时考虑离散时滞变化区间与分布概率对稳定性的影响．通过构造新的Lyapunov泛函并结合线性矩阵不等式（LMI）方法,得到了均方意义下依赖于时滞分布的全局指数稳定性条件．     

具有leakage时滞的随机马尔科夫跳变神经网络的稳定性

研究一类具有leakage时滞的随机马尔科夫跳变神经网络的稳定性,通过构造一个新的Lyapunov-Kra—sovskii泛函,并应用It6公式、随机不等式技术,得到了基于线性矩阵不等式（LMI）的均方意义下的全局稳定性判定条件．     

Evaluating cost and reliability integrated performance of stochastic logistics systems

The significance of integrating reliability into logistics performance has been established [The Logistics Performance Index and Its Indicators, World Bank International Trade and Transport Departments, (2010)]. Hence, as a response to the work by the World Bank, the present article aims to evaluate the performance index R_b,d of logistics systems as the probability that a specified demand d can be distributed successfully through multistate arc capacities from the source to the destination under the constraint that the total distribution cost should not exceed the cost limitation b. This article provides a pioneering approach for a straightforward computation of the performance index R_b,d. The proposed algorithm is a hybrid between the polynomial time capacity‐scaling algorithm, which was presented by Edmonds and Karp [JACM 19 (1972)], and the decomposition algorithm, which was presented by Jane and Laih [IEEE (2008)]. Currently, the proposed approach is the only algorithm that can directly compute R_b,d. An illustration of the proposed algorithm is presented. The results of the computational experiments indicate that the presented algorithm outperforms existing algorithms. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Robust capacity planning in semiconductor manufacturing

We present a stochastic programming approach to capacity planning under demand uncertainty in semiconductor manufacturing. Given multiple demand scenarios together with associated probabilities, our aim is to identify a set of tools that is a good compromise for all these scenarios. More precisely, we formulate a mixed‐integer program in which expected value of the unmet demand is minimized subject to capacity and budget constraints. This is a difficult two‐stage stochastic mixed‐integer program which cannot be solved to optimality in a reasonable amount of time. We instead propose a heuristic that can produce near‐optimal solutions. Our heuristic strengthens the linear programming relaxation of the formulation with cutting planes and performs limited enumeration. Analyses of the results in some real‐life situations are also presented. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

A robust policy for serial agile production systems

One of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Predictability of operational processes over finite horizon

Operational processes are usually studied in terms of stochastic processes. The main information measure used for predictability of stochastic processes is the entropy rate, which is asymptotic conditional entropy, thus not suitable for application over a finite horizon. We use the conditional entropy to study the predictability of stochastic processes over the finite horizon. It is well‐known that the conditional entropies of stationary processes decrease as the processes evolve, implying that, on average, their pasts become more informative about prediction of their future outcomes. Some important operational processes such as martingale, models for maintenance policies, nonhomogeneous Poisson, and mixed Poisson processes are nonstationary. We show that as a nonstationary process evolves, it may provide more information or less information about the future state of the system. We develop results for comparing the predictability of stochastic processes. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Inventory control in divergent supply chains with time‐based dispatching and shipment consolidation

This article analyses a divergent supply chain consisting of a central warehouse and N nonidentical retailers. The focus is on joint evaluation of inventory replenishment and shipment consolidation effects. A time‐based dispatching and shipment consolidation policy is used at the warehouse in conjunction with real‐time point‐of‐sale data and centralized inventory information. This represents a common situation, for example, in various types of vendor managed inventory systems. The main contribution is the derivation of an exact recursive procedure for determining the expected inventory holding and backorder costs for the system, under the assumption of Poisson demand. Two heuristics for determining near optimal shipment intervals are also presented. The results are applicable both for single‐item and multiitem systems. © 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 59–71, 2011