Technical note: A computationally efficient algorithm for undiscounted Markov decision processes with restricted observations

We present a computationally efficient procedure to determine control policies for an infinite horizon Markov Decision process with restricted observations. The optimal policy for the system with restricted observations is a function of the observation process and not the unobservable states of the system. Thus, the policy is stationary with respect to the partitioned state space. The algorithm we propose addresses the undiscounted average cost case. The algorithm combines a local search with a modified version of Howard's (Dynamic programming and Markov processes, MIT Press, Cambridge, MA, 1960) policy iteration method. We demonstrate empirically that the algorithm finds the optimal deterministic policy for over 96% of the problem instances generated. For large scale problem instances, we demonstrate that the average cost associated with the local optimal policy is lower than the average cost associated with an integer rounded policy produced by the algorithm of Serin and Kulkarni Math Methods Oper Res 61 (2005) 311–328. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

一类多对二随机格斗中的最优射击策略

射击策略的选择在随机格斗中是一重要战术问题,当一方武器面临多个武器目标时,如何确定射击目标顺序的研究,显然是具有实际意义的。依据发射间隔服从负指数分布的多对一随机格斗中最优策略应满足的条件,推出求解此类多对一格斗最优策略的方法。进而研究了射击间隔服从此类分布的多对二随机格斗中处于劣势一方的射击策略选择问题,得出寻求最优射击策略的一般方法。     

有源、无源联合探测系统综合性能分析

根据无源探测系统与有源雷达组成的联合探测系统,给出了一种有源、无源联合探测系统的探测模型,定性、定量的仿真分析了不同布站方法时,系统的探测精度、探测模糊区分布问题,得出了联合探测系统的最优布站方法;与无源探测系统相比较,联合探测系统提高了系统探测精度,改善了探测模糊区.仿真结果可为工程实践中雷达组网的优化部署提供理论依据.     

非合作目标视觉/惯导相对导航及敏感器自标定方法

利用视觉/惯导对空间非合作目标进行相对导航时,两敏感器的外参数对导航精度有较大影响。考虑到敏感器间的外参数标定复杂且耗时,提出一种利用视觉/惯导在估计相对状态过程中对其外参数进行标定的方法。该方法将视觉/惯导的外参数作为状态变量,与相对轨道运动学方程、相对姿态方程及惯导模型共同组成系统状态方程。利用该状态方程和单目视觉的观测量设计扩展卡尔曼滤波器对相对位姿、惯导偏差及视觉/惯导外参数进行估计,并通过数学仿真对该方法的有效性进行验证。仿真结果表明,该方法能够在视觉/惯导初始外参有偏差的情况下,有效估计相对位姿及惯导漂移,并对视觉/惯导外参数进行标定。     

Doubly Stochastic Sequential Assignment Problem

This article introduces the Doubly Stochastic Sequential Assignment Problem (DSSAP), an extension of the Sequential Stochastic Assignment Problem (SSAP), where sequentially arriving tasks are assigned to workers with random success rates. A given number of tasks arrive sequentially, each with a random value coming from a known distribution. On a task arrival, it must be assigned to one of the available workers, each with a random success rate coming from a known distribution. Optimal assignment policies are proposed for DSSAP under various assumptions on the random success rates. The optimal assignment algorithm for the general case of DSSAP, where workers have distinct success rate distribution, has an exponential running time. An approximation algorithm that achieves a fraction of the maximum total expected reward in a polynomial time is proposed. The results are illustrated by several numerical experiments. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 124–137, 2016     

Optimal staffing in nonstationary service centers with constraints

This paper considers optimal staffing in service centers. We construct models for profit and cost centers using dynamic rate queues. To allow for practical optimal controls, we approximate the queueing process using a Gaussian random variable with equal mean and variance. We then appeal to the Pontryagin's maximum principle to derive a closed form square root staffing (SRS) rule for optimal staffing. Unlike most traditional SRS formulas, the main parameter in our formula is not the probability of delay but rather a cost‐to‐benefit ratio that depends on the shadow price. We show that the delay experienced by customers can be interpreted in terms of this ratio. Throughout the article, we provide theoretical support of our analysis and conduct extensive numerical experiments to reinforce our findings. To this end, various scenarios are considered to evaluate the change in the staffing levels as the cost‐to‐benefit ratio changes. We also assess the change in the service grade and the effects of a service‐level agreement constraint. Our analysis indicates that the variation in the ratio of customer abandonment over service rate particularly influences staffing levels and can lead to drastically different policies between profit and cost service centers. Our main contribution is the introduction of new analysis and managerial insights into the nonstationary optimal staffing of service centers, especially when the objective is to maximize profitability. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 615–630, 2017     

Capacity expansion and cost efficiency improvement in the warehouse problem

The warehouse problem with deterministic production cost, selling prices, and demand was introduced in the 1950s and there is a renewed interest recently due to its applications in energy storage and arbitrage. In this paper, we consider two extensions of the warehouse problem and develop efficient computational algorithms for finding their optimal solutions. First, we consider a model where the firm can invest in capacity expansion projects for the warehouse while simultaneously making production and sales decisions in each period. We show that this problem can be solved with a computational complexity that is linear in the product of the length of the planning horizon and the number of capacity expansion projects. We then consider a problem in which the firm can invest to improve production cost efficiency while simultaneously making production and sales decisions in each period. The resulting optimization problem is non‐convex with integer decision variables. We show that, under some mild conditions on the cost data, the problem can be solved in linear computational time. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 367–373, 2016     

相控阵雷达LPI搜索方法研究

相控阵雷达可通过合理配置工作参数优化其性能。针对相控阵雷达在搜索目标时易受敌方电子侦察设备威胁的现实,研究了在保持搜索能力的同时,通过合理配置参数降低截获概率的问题。分析了影响相控阵雷达搜索状态LPI(Low Probability of Intercept)性能的主要因素,建立了截获概率模型与搜索能力模型,给出了3种参数调整策略。仿真试验验证了模型的有效性,并比较了3种策略的优劣。     

混合攻击机机群在空战中的最优控制策略

研究了混合攻击机机群在对由截击 -歼击机机群组成的敌国土防空系统进行突防过程中的最优控制方法 ,以攻击机的最小突防损失为战效指标 ,给出了其最优控制策略。     

基于地磁模式组的舰船消磁电流调整器

利用泰勒多项式的建模方法建立了地磁模式组 ,该模式组能够满足消磁电流调整器的应用要求 ,且具有很好的稳定性 ,均方根偏差很小 ,实际应用也比较方便 .在此基础上 ,提出了基于地磁模式组的无探头消磁电流调整器 ,该消磁电流调整器具有结构简单、可靠性高、水上水下通用及免除抗干扰调整等优点