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。     

基于实际飞行数据插值的INS/GNSS组合导航仿真轨迹发生器

针对INS/GNSS组合导航仿真中,捷联惯导系统陀螺、加速度计信号高精度模拟问题,提出了基于实际飞行数据插值的动态轨迹解析生成仿真算法。对转换到地心惯性坐标系中的载体姿态、位置和重力场数据进行关于时间的样条函数插值,得到载体坐标系下陀螺角速率、角增量以及加速度计比力积分增量的高精度分段解析表达式。使生成的陀螺、加速度计信号符合载体运动学和动力学特性,反映杆臂效应影响,同时与经事后处理的实测GNSS伪距、伪距率等数据特征保持一致。提出了四元数约束插值算法,可满足四元数解析插值时范数为1的约束限制条件。基于某实际无人机飞行数据,验证了所提出算法的有效性,完全满足组合导航动态仿真精度要求。该算法也适用于其他高精度高动态导航系统和刚体运动控制仿真中的角运动、线运动传感器信号模拟。     

Dynamic pricing and replenishment: Optimality,bounds, and asymptotics

In many applications, managers face the problem of replenishing and selling products during a finite time horizon. We investigate the problem of making dynamic and joint decisions on product replenishment and selling in order to improve profit. We consider a backlog scenario in which penalty cost (resulting from fulfillment delay) and accommodation cost (resulting from shortage at the end of the selling horizon) are incurred. Based on continuous‐time and discrete‐state dynamic programming, we study the optimal joint decisions and characterize their structural properties. We establish an upper bound for the optimal expected profit and develop a fluid policy by resorting to the deterministic version of the problem (ie, the fluid problem). The fluid policy is shown to be asymptotically optimal for the original stochastic problem when the problem size is sufficiently large. The static nature of the fluid policy and its lack of flexibility in matching supply with demand motivate us to develop a “target‐inventory” heuristic, which is shown, numerically, to be a significant improvement over the fluid policy. Scenarios with discrete feasible sets and lost‐sales are also discussed in this article.     

考虑落角约束与驾驶仪特性的自适应RBF空间末制导律

为使大口径舰炮制导炮弹在打击近岸机动目标的末制导段满足落角约束,现考虑自动驾驶仪动态特性,基于自适应RBF逼近网络与动态面滑模提出一种空间末制导律。构建空间弹目相对运动模型,通过带改进微分跟踪器的扩张状态观测器估计目标加速度。为零化视线角跟踪误差与视线角速率,采用自适应指数趋近律设计非奇异终端滑模动态面,并运用自适应RBF逼近网络削弱控制指令抖振。通过Lyapunov第二法证明了全系统中视线角跟踪误差与视线角速率均最终一致有界。仿真实验表明：该末制导律使制导炮弹在空间中打击具有不同机动形式的近岸目标时,均具备良好的末制导性能。     

北斗RDSS系统新体制信号子载波间干扰产生机理与消除方法

为提高新一代北斗无线电测定卫星服务在有限带宽内的信息服务容量,借鉴了正交频分复用的理念,新体制无线电测定卫星服务信号设计采用多个子载波进行信号调制。以往针对多用户的分析主要考虑多址干扰,对载波频偏损耗和伪码损耗单独考虑,这不能解释新体制调制在相同的同步头的情况下其他子载波上信号在当前观测子载波上形成较大相关峰的问题,该问题对信号接收产生较大干扰。本文对该问题产生机理进行了分析,并提出了两种相关干扰的消除方法。     

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

In urban rail transit systems of large cities, the headway and following distance of successive trains have been compressed as much as possible to enhance the corridor capacity to satisfy extremely high passenger demand during peak hours. To prevent train collisions and ensure the safety of trains, a safe following distance of trains must be maintained. However, this requirement is subject to a series of complex factors, such as the uncertain train braking performance, train communication delay, and driver reaction time. In this paper, we propose a unified mathematical framework to analyze the safety‐oriented reliability of metro train timetables with different corridor capacities, that is, the train traffic density, and determine the most reliable train timetable for metro lines in an uncertain environment. By employing a space‐time network representation in the formulations, the reliability‐based train timetabling problem is formulated as a nonlinear stochastic programming model, in which we use 0‐1 variables to denote the time‐dependent velocity and position of all involved trains. Several reformulation techniques are developed to obtain an equivalent mixed integer programming model with quadratic constraints (MIQCP) that can be solved to optimality by some commercial solvers. To improve the computational efficiency of the MIQCP model, we develop a dual decomposition solution framework that decomposes the primal problem into several sets of subproblems by dualizing the coupling constraints across different samples. An exact dynamic programming combined with search space reduction strategies is also developed to solve the exact optimal solutions of these subproblems. Two sets of numerical experiments, which involve a relatively small‐scale case and a real‐world instance based on the operation data of the Beijing subway Changping Line are implemented to verify the effectiveness of the proposed approaches.     

Revisiting the justification for an all-volunteer force

In 1968, President Nixon established the Commission on an All-Volunteer Armed Force, or the Gates Commission, which served as the impetus and justification for an All-Volunteer Force (AVF). At the end of its deliberations, the commission recommended abolishing the draft and transforming the U.S. military into a force of volunteers beginning in 1973. Interestingly, the debate regarding the merits of both systems appeared to be largely economic – with cost–benefit analysis playing the primary role. Lately, we are beginning to see a new, politically-motivated impetus for returning to a “system of national service.” The ideas spurring this debate are many: the need to reaffirm the nation state, the commitment of citizens to the state, political ownership and oversight of the forces, the need for social equity in serving the nation, limiting the support for armed conflict by burden-sharing among citizens, and equitably spreading the personal cost of war.     

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