Optimal control of a revenue management system with dynamic pricing facing linear demand

This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time‐varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two‐product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two‐product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd.     

腰椎后路非融合固定系统的临床应用

复习腰椎后路非融合固定系统的设计原理、临床应用及治疗效果等相关文献,与传统的脊柱融合术相比,应用非融合系统可获得很好的疗效,并可以减少邻近节段退变的发生率。     

高龄股骨转子间骨折两种治疗方法的临床观察

目的:探讨手术治疗高龄股骨转子间骨折的安全性、合理性。方法:股骨转子间骨折患者65例,其中采用动力髋螺钉(DHS)治疗32例,男14例,女18例;年龄65~79岁,平均(70.6±2.3)岁;EvansⅠ型2例,Ⅱ型7例,Ⅲ型15例,Ⅳ型8例。采用单边外固定支架治疗33例,男14例,女19例;年龄68~90岁,平均(74.2±3.8)岁;EvansⅠ型3例,Ⅱ型15例,Ⅲ型11例,Ⅳ型1例,Ⅴ型3例。临床观察包括术中出血量、手术时间、骨折愈合时间、术后并发症及髋部运动功能等。结果:所有病例均获随访,时间1~34个月,平均19个月。两组手术时间、术中出血量、术后并发症发生率差异有统计学意义(P<0.05)。平均愈合时间DHS组为(13.0±2.7)周,外固定支架组为(12.3±3.0)周,差异无统计学意义。Sanders髋关节功能评价:DHS组优19例,良6例,可3例,差2例;外固定支架组优12例,良8例,可8例,差5例。两组优良率差异有统计学意义(P<0.05)。结论:围手术期外固定支架组较DHS组安全简便,术后疗效DHS组优于外固定支架组。     

应用动力髁螺钉联合骨肽注射液治疗股骨髁上骨不连疗效观察

目的观察应用动力髁螺钉联合骨肽注射液治疗股骨髁上骨不连的疗效。方法53例股骨髁上骨不连患者随机分为两组：对照组（26例）和治疗组（27例）,两组均应用动力髁螺钉治疗,治疗组加用骨肽注射液治疗。随访,进行疗效评价,记录骨愈合时间和测定疼痛指数。结果治疗组疗效优于对照组。结论应用动力髁螺钉联合骨肽注射液治疗股骨髁上骨不连可提高疗效。     

基于双向 S-粗集的动态粗传递模型

根据信息传递中我们需要准确可靠的信息这种实际情况,利用双向S-粗集理论提出了一种动态粗传递模型,即双向S-下近似动态粗传递模型.分析了该模型的特性,得到了信息保持不变、信息发生损失与知识的关系,给出了提高信息传递精确性的方法以及该模型的应用.     

X线透视导航下动力髋(髁)螺钉治疗股骨转子间骨折

目的探讨X线透视导航技术在动力髋(髁)螺钉系统治疗股骨转子间骨折中的临床应用。方法应用连接在标准动力髋(髁)器械上的适配器,X线透视导航辅助完成术中松质骨拉力螺钉在股骨颈通道内的入点选择及拉力螺钉的置入。结果8例股骨转子间骨折的应用结果令人满意。手术时间平均为48.8min,X线图像采集平均3.4次。术中和术后无并发症发生。结论肯定了X线透视导航技术在动力髋(髁)螺钉系统治疗股骨转子间骨折中应用的可行性。术中只需1次X线成像就能做出虚拟的手术环境和路径;导航的瞬时追踪功能使术者能实时监测,减少了X线辐射量,缩短了手术时间,提高了拉力螺钉置入的准确度,减小了手术创伤。     

Dynamics of lipid adsorption at the electrified water∣1,2-dichloroethane interface

A recently introduced setup to measure the dynamic interfacial tension of expanding drops was used to compare the adsorption behaviour of a series of lipids at the electrified water∣dichloroethane interface. Phospholipids with saturated carbon chains of different length (DMPC, DPPC, DSPC, DAPC, DBPC), an unsaturated phospholipid (DOPC) and an ethanolamine (DSPE) were compared. It was found that the adsorption decreases with increasing chain length. Also, the increase of the flow rate reduces the degree of adsorption effectively. On the timescale of the experiments, the DSPE, DAPC and DBPC adsorption showed no potential dependence, whereas the adsorption of DOPC was stronger than that of the saturated lipids. Adsorption was modelled using the Langmuir adsorption isotherm; the potential dependence of adsorption is discussed.     

ITERATIVE DYNAMIC PROGRAMMING FOR MINIMUM ENERGY CONTROL PROBLEMS WITH TIME DELAY

This paper presents the use of iterative dynamic programming employing exact penalty functions for minimum energy control problems. We show that exact continuously non-differentiable penalty functions are superior to continuously differentiable penalty functions in terms of satisfying final state constraints. We also demonstrate that the choice of an appropriate penalty function factor depends on the relative size of the time delay with respect to the final time and on the expected value of the energy consumption. A quadratic approximation (QA) of the delayed variables is much better than a linear approximation (LA) of the same for relatively large time delays. The QA improves the rate of convergence and avoids the formation of ‘kinks‘. A more general way of selecting appropriate penalty function factors is given and the results obtained using four illustrative examples of varying complexity corroborate the efficacy of the method.     

A decomposition approach to suboptimal control of discrete-time systems

A suboptimal controller for a class of discrete-time systems is presented. The controller is derived by first solving ‘off-line’ a simplified optimal control problem obtained by neglecting part of the system state and by considering a larger time step, then by solving ‘on-line’ at each time step an optimization problem based on the results of the previously solved ‘off-line’ problem. A simple numerical example is presented to illustrate the control scheme.     

动力髋螺钉治疗股骨转子间骨折

目的 评价动力髋螺钉(DHS)治疗股骨转子间骨折的临床效果。方法 1996年3月～2002年3月用DHS共治疗患者29例．骨折按Evans分型，本组Evans ⅠA2例，Evans ⅠB 10例，Evans ⅡA 3例，Evanslib12例，Evans Ⅲ2例．结果 29例患者均获随访，随访12～48个月，平均26个月，根据Harris髋关节评分：优16例，良9例，中3例，差1例。结论 如能及时手术良好复位，DHS是治疗股骨转子间骨折的较好选择。