Inventory control and periodic price discounting campaigns

This paper develops an inventory model that determines replenishment strategies for buyers facing situations in which sellers offer price‐discounting campaigns at random times as a way to drive sales or clear excess inventory. Specifically, the model deals with the inventory of a single item that is maintained to meet a constant demand over time. The item can be purchased at two different prices denoted high and low. We assume that the low price goes into effect at random points in time following an exponential distribution and lasts for a random length of time following another exponential distribution. We highlight a replenishment strategy that will lead to the lowest inventory holding and ordering costs possible. This strategy is to replenish inventory only when current levels are below a certain threshold when the low price is offered and the replenishment is to a higher order‐up‐to level than the one currently in use when inventory depletes to zero and the price is high. Our analysis provides new insight into the behavior of the optimal replenishment strategy in response to changes in the ratio of purchase prices together with changes in the ratio of the duration of a low‐price period to that of a high‐price period. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007.     

Rendez‐vous search on a rectangular lattice

In a rendez‐vous search two or more teams called seekers try to minimize the time needed to find each other. In this paper, we consider s seekers in a rectangular lattice of locations where each knows the configuration of the lattice, the distribution of the seekers at time 0, and its own location, but not the location of any other. We measure time discretely, in turns. A meeting takes place when the two seekers reach the same point or adjacent points. The main result is that for any dimension of lattice, any initial distribution of seekers there are optimal strategies for the seekers that converge (in a way we shall make clear) to a center. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Technical note – operational statistics: Properties and the risk‐averse case

Consider a repeated newsvendor problem for managing the inventory of perishable products. When the parameter of the demand distribution is unknown, it has been shown that the traditional separated estimation and optimization (SEO) approach could lead to suboptimality. To address this issue, an integrated approach called operational statistics (OS) was developed by Chu et al., Oper Res Lett 36 (2008) 110–116. In this note, we first study the properties of this approach and compare its performance with that of the traditional SEO approach. It is shown that OS is consistent and superior to SEO. The benefit of using OS is larger when the demand variability is higher. We then generalize OS to the risk‐averse case under the conditional value‐at‐risk (CVaR) criterion. To model risk from both demand sampling and future demand uncertainty, we introduce a new criterion, called the total CVaR, and find the optimal OS under this new criterion. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 206–214, 2015     

On equivalence between the proportionate flow shop and single‐machine scheduling problems

We derive sufficient conditions which, when satisfied, guarantee that an optimal solution for a single‐machine scheduling problem is also optimal for the corresponding proportionate flow shop scheduling problem. We then utilize these sufficient conditions to show the solvability in polynomial time of numerous proportionate flow shop scheduling problems with fixed job processing times, position‐dependent job processing times, controllable job processing times, and also problems with job rejection. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 595–603, 2015     

Optimal pricing and scheduling control of product shipping

In this article, we seek to understand how a capacity‐constrained seller optimally prices and schedules product shipping to customers who are heterogeneous on willingness to pay (WTP) and willingness to wait (WTW). The capacity‐constrained seller does not observe each customer's WTP and WTW and knows only the aggregate distributions of WTP and WTW. The seller's problem is modeled as an M/M/N_s queueing model with multiclass customers and multidimensional information screening. We contribute to the literature by providing an optimal and efficient algorithm. Furthermore, we numerically find that customers with a larger waiting cost enjoys a higher scheduling priority, but customers with higher valuation do not necessarily get a higher scheduling priority. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 215–227, 2015     

对单兵火箭提前修正量的分析研究

为了实现某型单兵火箭的射击在陆军分队作战模拟仿真系统中的仿真模拟,运用数理统计理论对单兵火箭提前修正量进行分析研究,论证了单兵火箭的射程与提前修正量的一元线性回归分析的统计规律,给出了一元线性回归方程和提前修正量的置信区间,论证了在置信区间中的实际提前修正量的射击的弹着点符合正态分布的射击规律和散布律公式。根据得到的理论结果,指导模拟仿真系统对单兵火箭的射击进行仿真模拟。     

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     

Development programs for one‐shot systems using multiple‐state design reliability models

Design reliability at the beginning of a product development program is typically low, and development costs can account for a large proportion of total product cost. We consider how to conduct development programs (series of tests and redesigns) for one‐shot systems (which are destroyed at first use or during testing). In rough terms, our aim is to both achieve high final design reliability and spend as little of a fixed budget as possible on development. We employ multiple‐state reliability models. Dynamic programming is used to identify a best test‐and‐redesign strategy and is shown to be presently computationally feasible for at least 5‐state models. Our analysis is flexible enough to allow for the accelerated stress testing needed in the case of ultra‐high reliability requirements, where testing otherwise provides little information on design reliability change. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004     

Properties of some stochastic orders: A unified study

The notions of the likelihood ratio order of degree s (s ≥ 0) are introduced for both continuous and discrete integer‐valued random variables. The new orders for s = 0, 1, and 2 correspond to the likelihood ratio, hazard rate, and mean residual life orders. We obtain some basic properties of the new orders and their up shifted stochastic orders, and derive some closure properties of them. Such a study is meaningful because it throws an important light on the understanding of the properties of the likelihood ratio, hazard rate, and mean residual life orders. On the other hand, the properties of the new orders have potential applications. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

基于变结构神经网络的L1自适应控制

针对传统模型参考自适应控制存在的鲁棒性问题和神经网络结构庞大因而计算量膨胀的问题,提出了一种变结构神经网络L1自适应控制方法,其中变结构神经网络用于在线辨识系统存在的未知非线性函数,该网络通过对节点进行唤醒与催眠以动态调节结构,以最少的节点数进行有效的逼近,降低计算复杂度;L1自适应控制用于网络权值学习与系统非线性补偿,反馈回路中设有一个低通滤波器,只要满足L1增益条件,就能确保系统的输入输出信号的瞬态响应和稳态跟踪性能与一个期望的线性时不变系统的响应保持一致。通过对四旋翼飞行器进行仿真,验证了该方法的有效性。