The dynamic transshipment problem

We investigate the strategy of transshipments in a dynamic deterministic demand environment over a finite planning horizon. This is the first time that transshipments are examined in a dynamic or deterministic setting. We consider a system of two locations which replenish their stock from a single supplier, and where transshipments between the locations are possible. Our model includes fixed (possibly joint) and variable replenishment costs, fixed and variable transshipment costs, as well as holding costs for each location and transshipment costs between locations. The problem is to determine how much to replenish and how much to transship each period; thus this work can be viewed as a synthesis of transshipment problems in a static stochastic setting and multilocation dynamic deterministic lot sizing problems. We provide interesting structural properties of optimal policies which enhance our understanding of the important issues which motivate transshipments and allow us to develop an efficient polynomial time algorithm for obtaining the optimal strategy. By exploring the reasons for using transshipments, we enable practitioners to envision the sources of savings from using this strategy and therefore motivate them to incorporate it into their replenishment strategies. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:386–408, 2001     

Selecting review periods for a coordinated multi‐item inventory model with staggered deliveries

Consider an N‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. For 1 ≤ j ≤ N, orders for item j can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T_j periods, one reviews the current stock level of item j and decides on deliveries for each of the next T_j periods, thus incurring an item‐by‐item fixed cost k_j. There is also a joint fixed cost whenever any item is reviewed. The problem is to find review periods T₁, T₂, …, T_N and an ordering policy satisfying the average cost criterion. The current article builds on earlier results for the single‐item case. We prove an optimal policy exists, give conditions where it has a simple form, and develop a branch and bound algorithm for its computation. We also provide two heuristic policies with O(N) computational requirements. Computational experiments indicate that the branch and bound algorithm can handle normal demand problems with N ≤ 10 and that both heuristics do well for a wide variety of problems with N ranging from 2 to 200; moreover, the performance of our heuristics seems insensitive to N. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48:430–449, 2001     

导弹对抗离散数学模型

针对现代非接触战争的特点,用数学方法研究导弹对抗模型问题,针对作战的不同目的和要求,建立两个导弹对抗的非线性规划数学模型,对模型求解设计了近似方法,该方法把上述非线性规划模型化为多个线性规划模型进行求解.对一类较简单的特殊情况进行了仔细分析,得到了分析解.最后指出该方法如何应用于动态实时优化决策.本文的方法可用来预测和评估导弹对抗的效果,为作战实时优化决策提供参考.     

Dynamic pricing in a trade-in program with replacement and new customers

Trade-in programs have been widely adopted to enhance repeat purchase from replacement customers. Considering that a market consists of replacement and new segments, we study the joint and dynamic decisions on the selling price of new product (hereafter, “selling price”) and the trade-in price involved in the program. By adopting a vertical product differentiation choice model, we investigate two scenarios in this paper. In the base model, the manufacturer has sufficiently large production capacity to fulfill the customer demand. We characterize the structural properties of the joint pricing decisions and compare them with the optimal pricing policy under regular selling. We further propose a semi-dynamic trade-in program, under which the new product is sold at a fixed price and the trade-in price can be adjusted dynamically. Numerical experiments are conducted to evaluate the performance of the dynamic and semi-dynamic trade-in programs. In an extended model, we consider the scenario in which the manufacturer stocks a batch of new products in the beginning of the selling horizon and the inventory cannot be replenished. Following a revenue management framework, we characterize the structural properties with respect to time period and inventory level of new products.     

Global planning of accelerated degradation tests based on exponential dispersion degradation models

The accelerated degradation test (ADT) is an efficient tool for assessing the lifetime information of highly reliable products. However, conducting an ADT is very expensive. Therefore, how to conduct a cost-constrained ADT plan is a great challenging issue for reliability analysts. By taking the experimental cost into consideration, this paper proposes a semi-analytical procedure to determine the total sample size, testing stress levels, the measurement frequencies, and the number of measurements (within a degradation path) globally under a class of exponential dispersion degradation models. The proposed method is also extended to determine the global planning of a three-level compromise plan. The advantage of the proposed method not only provides better design insights for conducting an ADT plan, but also provides an efficient algorithm to obtain a cost-constrained ADT plan, compared with conventional optimal plans by grid search algorithms.     

考虑禁飞区的高超声速飞行器再入跟踪控制

为确立高超声速飞行器再入精确模型,参考NASA的研究数据对动力学方程中的气动参数进行拟合。基于飞行器结构的相关性质及战略应用背景,加入热流密度、动压、过载和禁飞区等参考约束的限制,融合成强非线性、复杂耦合的最优控制问题。采用改进自适应伪谱法求解模型所构建的微分方程组,通过设置自适应网格细化与配点,使单位时间内状态变量和控制变量波动过大的时间区间被进一步细划,并利用SNOPT求解器解算出符合条件的最优轨迹。设计闭环控制器,实现对最优轨迹的姿态变化的跟踪,测试系统的性能并进行评估。仿真结果表明:整个再入过程中,飞行器速度下降过程偏于平稳,再入轨迹可以满足约束条件,在避开禁飞区的同时取得最大横向航程;三通道角速度收敛可控,对姿态的跟踪较理想,控制器基本可以实现精确调姿。     

空间双体系绳系统展开阶段末端星姿态动力学分析

为了研究空间系绳系统展开过程中末端星的姿态运动,采用第二类拉格朗日方程建立系统展开及末端星角运动的数学模型,分析展开阶段末端星的姿态动力学特性。建模时将系绳末端连接的母星与子星视为尺寸不可忽略的刚体,且母星质量远大于子星质量,系绳视为有质量的刚性杆。利用该数学模型可以分析系绳系统的展开过程,研究影响末端星姿态运动的主要因素,包括姿态角初始扰动以及末端星动/静不对称性。仿真结果表明,系绳展开时末端星姿态角初始扰动及动静不对称性可能会导致姿态角失稳,出现系绳缠绕星体的情况。仿真结果可以为展开阶段末端星姿态控制提供参考。     

Dynamic pricing and matching in ride-hailing platforms

Ride-hailing platforms such as Uber, Lyft, and DiDi have achieved explosive growth and reshaped urban transportation. The theory and technologies behind these platforms have become one of the most active research topics in the fields of economics, operations research, computer science, and transportation engineering. In particular, advanced matching and dynamic pricing (DP) algorithms—the two key levers in ride-hailing—have received tremendous attention from the research community and are continuously being designed and implemented at industrial scales by ride-hailing platforms. We provide a review of matching and DP techniques in ride-hailing, and show that they are critical for providing an experience with low waiting time for both riders and drivers. Then we link the two levers together by studying a pool-matching mechanism called dynamic waiting (DW) that varies rider waiting and walking before dispatch, which is inspired by a recent carpooling product Express Pool from Uber. We show using data from Uber that by jointly optimizing DP and DW, price variability can be mitigated, while increasing capacity utilization, trip throughput, and welfare. We also highlight several key practical challenges and directions of future research from a practitioner's perspective.     

采用扩展有限元法的线式爆炸分离装置裂纹扩展分析

为了提高线式爆炸分离装置的安全性,本研究基于扩展有限元法,通过创建二维和三维动态裂纹扩展模型,探索了线式爆炸分离装置在爆轰波作用过程中的动态裂纹扩展和止裂机理。研究表明,分离壳体的裂纹扩展路径独立于裂纹初始角度;不考虑载荷时序时,二维和三维动态裂纹扩展的主方向分别沿着分离壳体的径向和环向;考虑载荷时序时,受不同区域应力波的联合作用,三维裂纹沿环向扩展的同时会沿着轴向扩展,但裂纹的扩展均不会影响到止裂槽以外的结构。所提方法和相应结论可为线式爆炸分离装置设计提供参考。     

考虑弹体动态特性的非奇异有限时间制导律

为满足导弹拦截机动目标时交会角约束和有限时间收敛的需求,建立了考虑弹体一阶动态特性的制导模型。把目标加速度视为有界外界干扰,同时结合非线性反步设计法中的动态面法,设计一种考虑弹体动态延迟的非奇异滑模制导律,并且证明了基于Lyapunov稳定性理论制导系统状态可渐进收敛到零。在所设计的制导律下,对单侧机动的低空高速目标进行仿真。仿真结果表明所设计的非奇异制导律可以有效降低弹体动态延迟带来的影响,而且具有较低的脱靶量与交会角误差;与考虑弹体动态特性和交会角约束的最优导引律相比,其具有更高的制导精度。