Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

A multi‐stage stochastic programming approach for network capacity expansion with multiple sources of capacity

In networks, there are often more than one sources of capacity. The capacities can be permanently or temporarily owned by the decision maker. Depending on the nature of sources, we identify the permanent capacity, spot market capacity, and contract capacity. We use a scenario tree to model the uncertainty, and build a multi‐stage stochastic integer program that can incorporate multiple sources and multiple types of capacities in a general network. We propose two solution methodologies for the problem. Firstly, we design an asymptotically convergent approximation algorithm. Secondly, we design a cutting plane algorithm based on Benders decomposition to find tight bounds for the problem. The numerical experiments show superb performance of the proposed algorithms compared with commercial software. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 600–614, 2017     

随机共振理论在雷达信号截获中的应用

雷达侦察主要通过无源侦察接收设备对空域中敌方雷达辐射源信号进行检测,若要实现对敌辐射源信号的截获,基本条件就是敌雷达信号能量能够达到雷达信号侦收设备的截获灵敏度。然而现代战场中,电磁环境复杂多变,敌雷达信号往往被干扰信号、噪声等掩盖,导致侦收设备漏警概率提高。针对以上问题,提出基于随机共振原理的雷达信号截获判断的方法,增大了截获信号的输出信噪比,解决了由于噪声过大掩盖的雷达信号的侦收问题。将该方法应用于雷达告警接收机的前端截获部分,大大降低了截获系统的漏警概率,保证了整个截获系统的稳定性。仿真实验验证了该方法的有效性。     

滑动聚束SAR步进扫描影响分析

滑动聚束SAR系统在实际工作中通过步进扫描的方式来实现天线照射波束在方位向的扫描,然而该扫描方式会在滑动聚束SAR的成像结果中引入成对回波。为分析该成对回波的形成物理机制,建立滑动聚束SAR步进扫描的数学模型,通过泰勒展开和傅里叶级数分析具体解释了成对回波的成因,并给出了成对回波幅度及位置与步进脉冲控制数之间的定量关系。理论分析和信号仿真结果表明,该模型能够准确有效地解释这一现象,并可为滑动聚束SAR的波束扫描系统参数设计提供理论依据。     

掠飞末敏弹耦合运动动导数计算

以新型掠飞末敏弹为研究对象,提出了基于欧拉转动定理和滑移网格技术的复杂角运动模拟方法,利用著名的罗德里格斯转换矩阵插值求得弹箭在每个时间步的角速度修正值,并指定给球形滑移网格区。通过对非定常气动参数进行求解辨识,分析了不同马赫数下掠飞末敏弹滚转运动对其俯仰组合动导数和升力系数动导数的影响规律。结果表明:所提角运动模拟方法可有效消除姿态角计算的累积误差,实现对弹箭任意给定角运动的准确模拟;弹箭滚转运动对俯仰组合导数和升力系数动导数的辨识结果均存在显著影响,在进行弹箭动导数计算和稳定性分析时需充分考虑俯仰耦合效应的影响。     

An integer decomposition algorithm for solving a two‐stage facility location problem with second‐stage activation costs

We study a stochastic scenario‐based facility location problem arising in situations when facilities must first be located, then activated in a particular scenario before they can be used to satisfy scenario demands. Unlike typical facility location problems, fixed charges arise in the initial location of the facilities, and then in the activation of located facilities. The first‐stage variables in our problem are the traditional binary facility‐location variables, whereas the second‐stage variables involve a mix of binary facility‐activation variables and continuous flow variables. Benders decomposition is not applicable for these problems due to the presence of the second‐stage integer activation variables. Instead, we derive cutting planes tailored to the problem under investigation from recourse solution data. These cutting planes are derived by solving a series of specialized shortest path problems based on a modified residual graph from the recourse solution, and are tighter than the general cuts established by Laporte and Louveaux for two‐stage binary programming problems. We demonstrate the computational efficacy of our approach on a variety of randomly generated test problems. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于相关性函数的多站微动特征分析与提取

针对多站雷达精度跨度大、难以有效进行融合识别的问题,提出了基于相关性函数的多站加权融合方法。首先建立了弹道目标滑动散射模型,通过时延相乘重构回波,并利用扩展Hough变换提取出距离像的曲线参数,从而建立方程组以求取微动信息。然后利用相关性函数对各雷达的支持度进行分析,最终对支持度高的观测数据进行融合识别。仿真结果表明该方法计算简单,能有效提高微动参数的估计精度,客观地反映各部雷达的可靠度。     

Contracts and coordination: Supply chains with uncertain demand and supply

Considering a supply chain with a supplier subject to yield uncertainty selling to a retailer facing stochastic demand, we find that commonly studied classical coordination contracts fail to coordinate both the supplier's production and the retailer's procurement decisions and achieve efficient performance. First, we study the vendor managed inventory (VMI) partnership. We find that a consignment VMI partnership coupled with a production cost subsidy achieves perfect coordination and a win‐win outcome; it is simple to implement and arbitrarily allocates total channel profit. The production cost subsidy optimally chosen through Nash bargaining analysis depends on the bargaining power of the supplier and the retailer. Further, motivated by the practice that sometimes the retailer and the supplier can arrange a “late order,” we also analyze the behavior of an advance‐purchase discount (APD) contract. We find that an APD with a revenue sharing contract can efficiently coordinate the supply chain as well as achieve flexible profit allocation. Finally, we explore which coordination contract works better for the supplier vs. the retailer. It is interesting to observe that Nash bargaining solutions for the two coordination contracts are equivalent. We further provide recommendations on the applications of these contracts. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 305–319, 2016     

基于多目标的雷达组网传感器资源管理算法

在雷达组网系统的多目标跟踪过程中,当目标数量过多时,由于传感器资源不足,无法使用传统传感器的管理方法进行资源分配,且运算时间过长,不满足工程实际需求。针对以上问题,提出了一种新的多传感器多目标跟踪任务快速分配算法,该算法将跟踪目标个数和跟踪目标精度作为优化目标,首先按照设定的分配准则对传感器进行一次分配,最大化跟踪目标个数;然后利用一种基于传感器排序的启发式传感器分配方法进行二次分配,通过控制跟踪目标的协方差水平,使目标的跟踪精度尽量接近期望值。仿真结果表明,该算法能够在较短的时间内对多传感器进行有效快速地分配,既跟踪了更多的目标,又达到了期望目标的跟踪精度,并且在一定程度上控制资源消耗,减少系统的总耗能。