Stochastic call center staffing with uncertain arrival,service and abandonment rates: A Bayesian perspective

In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016     

涡轮盘疲劳寿命可靠性设计仿真及优化策略

涡轮盘是航空发动机主要部件之一,一旦发生破坏性故障将导致严重的后果。在充分考虑影响涡轮盘高低周复合疲劳寿命因素不确定性基础上,以MATLAB为平台,设计了涡轮盘高低周复合疲劳寿命可靠性优化设计的联合仿真平台。利用寿命函数和寿命可靠性分析极限状态函数中的共性需求,提出了在优化迭代的过程中自适应构建寿命函数Kriging模型和寿命可靠性极限状态面Kriging模型时共用训练样本点的策略。同时,提出了一种构建寿命函数Kriging模型的学习函数。使用所搭建的疲劳寿命可靠性优化设计平台,完成了某型涡轮盘盘心、榫槽以及涡轮盘系统高低周复合疲劳寿命的可靠性优化设计。结果表明,最优设计方案的局部最大应力显著降低,均值寿命大幅提高,并满足可靠性约束。     

Optimal replacement of military aircraft: an economic approach

A nonlinear optimization model is developed in this paper to identify the optimal replacement strategy for military aircraft. In the model, the aircraft operating and maintenance (O&M) costs per available year are estimated as a function of age during the aircraft life cycle. After determining the optimal replacement policy, the model is applied to the CF Long-Range Patrol CP-140A Arcturus fleet. A sensitivity analysis is also carried out to assess the impact of some key model parameters on the result.     

Augmented nested sampling for stochastic programs with recourse and endogenous uncertainty

We propose a novel simulation‐based approach for solving two‐stage stochastic programs with recourse and endogenous (decision dependent) uncertainty. The proposed augmented nested sampling approach recasts the stochastic optimization problem as a simulation problem by treating the decision variables as random. The optimal decision is obtained via the mode of the augmented probability model. We illustrate our methodology on a newsvendor problem with stock‐dependent uncertain demand both in single and multi‐item (news‐stand) cases. We provide performance comparisons with Markov chain Monte Carlo and traditional Monte Carlo simulation‐based optimization schemes. Finally, we conclude with directions for future research.     

导弹最优制导律弹道仿真分析

根据导弹仿真数据,绘制可直观显示弹道特性的理想弹道曲线。给出了比例导引法的差分方程,建立了比例导引法的三维弹道仿真模型。在对比例导引法进行三维弹道仿真的基础上,分别对增量比例导引、基于二次型的最优制导律和考虑动态特性的二次型最优制导律进行了三维弹道仿真,绘制出了可直观显示弹道特性的理想弹道,计算了导弹与目标的遭遇时间,并对结果进行了比较分析。最后得出考虑弹体动态特性的二次型最优制导律具有最优性。     

Irreversible demagnetization mechanism of permanent magnets during electromagnetic buffering

The permanent magnets will be irreversibly demagnetized under high temperature and high velocity during the electromagnetic buffering. In this study, the magnetic field induced by eddy currents and the self-demagnetizing field of permanent magnet are taken into consideration together for demagnetiza-tion analyse. The magnetic Reynolds number is used to express the eddy currents demagnetization. The correction coefficient being expressed as the index of the air-gap width, the inner cylinder thickness, iron pole axial length and the permanent magnet demagnetization coefficient is introduced by magnetic path analysis to represent the self-demagnetization effect and the demagnetization extent. The electromag-netic buffer (EMB) prototype is tested under intensive impact loads of different strengths at room temperature. The accuracy of the nonlinear irreversible demagnetization finite element model is verified by demagnetization on damping force, velocity and displacement. Finally, high-velocity demagnetization and high-temperature demagnetization are analysed in order to obtain the distribution law of irre-versible demagnetization.     

不确定失效阈值影响下考虑设备剩余寿命预测信息的最优替换策略

为了进一步提升设备维修决策的科学性,通过建立综合设备剩余寿命预测数据与不确定失效阈值的最优维修决策模型,实现了不可维修设备的最优替换策略.构建基于非线性Wiener过程的设备性能退化模型,并采用极大似然法估计退化模型参数;提出一种基于期望最大(Expectation Maximization,EM)算法的不确定失效阈值...     

Efficient budget allocation strategies for elementary effects method in stochastic simulation

This paper focuses on extending the Morris' elementary effects method (MM) for sensitivity analysis/factor screening originated in the context of deterministic computer experiments to the stochastic simulation setting. Given a fixed simulation budget to expend, the main objective is to provide efficient and accurate estimates of main and interaction (or nonlinear) effects coined by the standard MM for characterizing the importance of each factor, despite the impact of simulation errors. Taking into account both the factor/input sampling uncertainty rooted in MM and the random errors inherent in a stochastic simulation, we develop efficient budget allocation strategies for implementing MM in this new context. Under each strategy proposed, we derive its corresponding optimal budget partition and optimal budget allocation rules. Numerical results corroborate the practical effectiveness of the proposed budget allocation strategies.     

基于PSO算法的脉冲修正弹控制参数优化*

针对脉冲修正弹自身控制离散不连续特征,开展了脉冲修正弹脉冲控制参数优化设计方法研究。考虑到脉冲成本和精度的双重要求,选择以脉冲发动机工作次数和脱靶量最少为双目标函数,并在风干扰的条件下,提出了以脉冲控制时间间隔为离散脉冲控制参数设计变量建立优化模型,以此发展了一种改进型递减惯性权重粒子群优化脉冲控制参数的方法,提高了修正参数优化收敛速度。仿真结果表明,该算法能快速有效地获得最优解,为在干扰条件下寻找最优的脉冲修正参数和脉冲工作方式提供了一种优化设计思路。     

The uncertainty sensitivity index method (USIM) and its extension

This article deals with optimization problems that have some uncertain parameters with unknown probabilities. The article proposes a strategy of transferring the system's uncertainty associated with these optimization problems into a norm or a set of norms that is added to the original objective function(s) within a multiobjective framework. The uncertainty sensitivity index method (USIM) proposed by Haimes and Hall [1977] is extended to several general cases. A robust algorithm is developed to guarantee an ideal solution for cases where the nominal value of the uncertain parameter is itself an uncertain variable. A design problem is also addressed to identify the best-compromise values of the system's parameters by integrating the USIM with the envelope approach.     

作动器最优配置的柔性结构振动主动控制

柔性结构广泛应用于航空航天等领域,为了获得结构的最佳动力学性能,在主动振动控制中作动器或传感器位置优化成为关键。基于结构有限元动力学方程,在状态空间利用系统可控和可观Gramian矩阵考虑结构剩余模态的影响,推导一种新的作动器/传感器优化准则。根据优化准则结合非线性整数规划遗传算法对作动器的位置进行配置。以悬臂板为研究对象,采用基于状态反馈的线性二次型调节器研究悬臂板的振动控制效果。与其他配置方法进行比较,验证了新方法的优越性。     

弹道修正弹系统效能灵敏度分析

灵敏度分析是武器系统效能分析中的一项重要内容,针对正交试验的不足,在分析了弹道修正弹系统效能的影响因素的基础上,建立了基于均匀设计的弹道修正弹系统效能的回归模型。通过对模型求导得到了命中概率对各参数的灵敏度表达式,并进行优化分析,得到了系统效能参数的最优组合以及最优区间,研究结果可作为弹道修正弹参数优化设计的依据。     

基于ModelCenter的顶置武器站稳定精度优化

顶置武器站具有系统组成类型复杂、子系统间存在耦合作用的特点,导致多学科协同仿真的优化模型难以建立。通过Adams、Simulink分别建立了顶置武器站机械系统及控制系统模型,并在多学科优化设计平台Model Center中对该机电联合仿真模型进行系统集成;在此基础上,以顶置武器站稳定精度为目标函数,采用一阶差分模型对炮控系统比例系数及积分系数进行了灵敏度分析,并采用设计探索优化器对该参数进行了优化设计。仿真结果表明,所建立的顶置武器站稳定精度多学科协同优化模型设计周期短、计算效率高,为下一步进行顶置武器站多工况、多结构参数的优化设计提供技术支撑。     

不同导引模式下的末修弹脉冲参数优化研究

在总脉冲量确定的情形下,在启控时间、总脉冲数、最小点火时间间隔及点火阈值等脉冲参数对末修弹落点散布的影响进行详细分析的基础上,利用数值仿真的方法,对比例导引模式、抛物线导引模式、落点预测导引模式、弹道追踪导引模式和zx导引模式等常用导引模式下的脉冲参数优化进行深入分析研究．     

基于最优分离矩阵循环迭代的盲源分离次序调整算法

文章针对盲源分离中输出信号帧与帧之间信号衔接顺序的不确定性问题,提出了最优分离矩阵循环迭代算法,将每帧信号分离时目标函数寻优所得分离矩阵作为下一帧循环的初始化矩阵进行迭代来分离信号。理论分析与计算机仿真表明:该算法能有效解决盲分离中信号次序的不确定性问题,具有较强的实际应用价值。     

信任函数理论在仿真评估中的应用

将信任函数理论应用到了仿真结果评估问题中,给出了总体仿真结果的信任函数和信念区间的计算方法。对仿真结果的真实性评估具有一定意义。这种思想和算法可推广应用到其它各种不确定性推理决策问题中去。     

求解不确定型车辆路径问题的弱鲁棒优化方法

为降低鲁棒优化模型最优解的保守性,以最小化违约车辆数和总惩罚成本为目标,建立针对旅行时间不确定的开放式车辆路径问题的弱鲁棒优化模型。对于不确定数据集的每个取值,该模型的最优解可以使其目标函数值始终不超过某数值,进而改善最优解的保守性。为提高启发式算法发现最优解的概率,提出一种自设计遗传算法对模型进行求解,其主要思想是利用粒子群算法搜索出可使遗传算法预期产生最好解的算法要素,并将其进行组合,从而产生新的遗传算法。采用新产生的遗传算法对模型继续求解,输出最好解。计算结果表明:与以往的鲁棒优化方法相比,弱鲁棒优化方法的最优解的保守性显著降低。     

A model of supply-chain decisions for resource sharing with an application to ventilator allocation to combat COVID-19

We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency are to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse condition. The model is applied to study the allocation of ventilator inventory in the COVID-19 pandemic by FEMA to different U.S. states. Findings suggest that if less than 60% of the ventilator inventory is available for non-COVID-19 patients, FEMA's stockpile of 20 000 ventilators (as of March 23, 2020) would be nearly adequate to meet the projected needs in slightly above average demand scenarios. However, when more than 75% of the available ventilator inventory must be reserved for non-COVID-19 patients, various degrees of shortfall are expected. In a severe case, where the demand is concentrated in the top-most quartile of the forecast confidence interval and states are not willing to share their stockpile of ventilators, the total shortfall over the planning horizon (until May 31, 2020) is about 232 000 ventilator days, with a peak shortfall of 17 200 ventilators on April 19, 2020. Results are also reported for a worst-case where the demand is at the upper limit of the 95% confidence interval. An important finding of this study is that a central agency (FEMA) can act as a coordinator for sharing critical resources that are in short supply over time to add efficiency in the system. Moreover, through properly managing risk-aversion of different entities (states) additional efficiency can be gained. An additional implication is that ramping up production early in the planning cycle allows to reduce shortfall significantly. An optimal timing of this production ramp-up consideration can be based on a cost-benefit analysis.     

基于NSGA-Ⅱ的WTA多目标优化(英文)

将多目标遗传算法NSGA-(改进的非支配排序遗传算法)应用于求解武器-目标分配(WTA)问题。首先,针对以往在建立防空型WTA问题的优化模型上的片面性,把WTA问题看做多目标优化问题,建立了综合考虑作战效能和防御效能的WTA双目标优化模型。然后在此基础上,研究和应用了NSGA-来求解WTA问题。最后由仿真算例验证了NSGA-在WTA问题中的应用可行性,表明了NSGA-可以快速地搜索到WTA多目标优化的Pareto最优解集,从而为求解WTA问题提供了一条有效途径。     

What you should know about simulation and derivatives

Derivatives (or gradients) are important for both sensitivity analysis and optimization, and in simulation models, these can often be estimated efficiently using various methods other than brute‐force finite differences. This article briefly summarizes the main approaches and discusses areas in which the approaches can most fruitfully be applied: queueing, inventory, and finance. In finance, the focus is on derivatives of another sort. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008