Hierarchical production policies in stochastic two-machine flowshops with finite buffers

This paper concerns production planning in manufacturing systems with two unreliable machines in tandem. The problem is formulated as a stochastic control problem in which the objective is to minimize the expected total cost of production, inventories, and backlogs. Since the sizes of the internal and external buffers are finite, the problem is one with state constraints. As the optimal solutions to this problem are extremely difficult to obtain due to the uncertainty in machine capacities as well as the presence of state constraints, a deterministic limting problem in which the stochastic machine capacities are replaced by their mean capacities is considered instead. The weak Lipschitz property of the value functions for the original and limiting problems is introduced and proved; a constraint domain approximation approach is developed to show that the value function of the original problem converges to that of the limiting problem as the rate of change in machine states approaches infinity. Asymptotic optimal production policies for the orginal problem are constructed explicity from the near-optimal policies of the limiting problem, and the error estimate for the policies constructed is obtained. Algorithms for constructing these policies are presented.This work was partly supported by CUHK Direct Grant 220500660, RGC Earmarked Grant CUHK 249/94E, and RGC Earmarked Grant CUHK 489/95E.     

On inner constraints in plane circular arches

Summary A one-dimensional model of plane circular arches with rigid sections is introduced. Suitable strain measures are defined as deviations from rigid displacements. If the arch is thin, constitutive arguments make the shearing strain negligible. Hence, the shearing indeformability will be assumed as inner constraint. By means of a formal power series expansion of the exact measures of deformation it is shown that the shearing indeformability implies some constraints on the axial strain. In particular, the first-order axial strain must vanish in the case of infinitesimal displacements. The same procedure is applied to pure flexible arches, in order to compare the two sets of results. It is shown that the hypothesis of finite pure flexibility is not compatible with small deformations of the arch. An example is provided to evaluate the effects of the two constraints at the first non-linear step of the perturbation expansions. This work has been supported by the “Progetto giovani ricercatori” grant of the University of Rome “La Sapienza” for the year 2002.     

Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

The nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003     

组装生产企业确定外购元件订货时间的人—机交互式方法

邹斌．组装生产企业确定外购元件订货时间的人—机交互式方法．数理统计与管理，１９９７，１６（４），３７～４０．本文介绍了我们实现的组装生产企业确定外购元件订货时间的人—机交互式方法。该方法考虑了供货时间的随机性，力图在费用和服务水平间寻找平衡。人—机交互式方式的使用为现场管理人员接受运筹学模型提供了有力的工具。本文提供了一个实例。     

Qualitative analysis of a rolling hoop with mass unbalance

The dynamical behavior of a rolling hoop with an unbalanced point mass under the influence of gravity is discussed. The whole process from rolling to hopping of the hoop is analyzed qualitatively. The conditions of slipping, hopping and touching down of the hoop are obtained. It is shown that the hoop cannot maintain a pure rolling before hopping up, and the slippage is unavoidable. The hoop has neither vertical velocity nor vertical acceleration at the moment when the normal constraint force vanishes. The hopping motion of the hoop can occur only when the derivative of the vertical acceleration with respect to time is positive. It requires that the angular velocity of the hoop should be larger than a critical value, and the mass point should be located in the fourth quadrant of the hoop circle at the moment of hopping. The whole process of the pure rolling, rolling with slipping, hopping and falling motions of the hoop is shown in the phase plane, and the physical explanation of the hopping motion is given.     

Edge dislocations generated from a microcrack under initial residual stress of non-uniform distribution

Crystal nucleation gives rise to inhomogeneity in the crystal lattice. The prevailing stresses and strains caused by non-uniform cooling can create microcracks with residual stresses locked-in at the end segments. These stresses can have a non-uniform distribution where the amplitude can increase or decrease from the microcrack tip which is highly strained to generate edge dislocations under in-plane shear. A dual scale microdislocation crack model is considered by focusing attention near the microcrack tip singularity such that more than 10 orders of magnitude in lineal dimension can be covered from the atomic to the microscopic scale. The concept of a scale multiplier is employed to connect the microscopic and atomic scale results. Discontinuity at the cross-scaling location is necessitated by dividing the full range of the non-equilibrium process into two regions within which equilibrium mechanics can be used. When needed, additional mesoregions can be added to reduce the transient discontinuities.Solved in closed form is the solution for the generation of edge dislocations due to non-uniform residual stress distributions at the end segment of the microcrack tip which will henceforth be referred to simply as the “tip”. Three different Cases I, II and III will be considered where the residual stress will possess a peak at the different locations. Case I for the furthest away from the tip, Case II for the peak nearest to the tip and Case III for the peak in the middle of the residual stress segment. Compared are the scale multiplier α whose maximum value being one corresponding to no discontinuity at cross-scaling. Hence, small α corresponds to large discontinuity. For Cases I, II and III, αs are found, respectively as 0.17, 0.43 and 0.28. The largest discontinuity occurred at α = 0.17 when the peak of the residual stress is farthest away from the microcrack tip. The largest number of edge dislocations or imperfections are also generated for Case I. The precise location of the residual stress peak is related to the magnitude and the segment length of the residual stress. These findings are manifestation of the variety of non-homogeneities that can arise in a metal alloy during crystal formation, not to mention the prevailing conditions at the grain boundaries. The idea is not to account for the details per se but to test the sensitivities of the microscopic and atomic parameters involved. To this end, the energy density function for the dual scale model will be determined and discussed in connection with what has been emphasized.     

一种部分约束满足车辆路线问题及其求解算法

描述了一类过度约束车辆路线问题，其中可用车辆数较少而时间窗口等其它约束又不允许放松，因而导致不存在满足所有约束的可行解。此时问题求解可以转化为一类部分约束满足问题来处理，相应的优化目标是最小化未访问顾客的损失和。本给出了求解这类特殊问题的一种禁忌搜索算法设计，并通过规模不同的几个算例与其它常用方法进行了比较。最后分析了模型和算法的实用意义。     

Property testers for dense constraint satisfaction programs on finite domains

Many NP‐hard languages can be “decided” in subexponential time if the definition of “decide” is relaxed only slightly. Rubinfeld and Sudan introduced the notion of property testers, probabilistic algorithms that can decide, with high probability, if a function has a certain property or if it is far from any function having this property. Goldreich, Goldwasser, and Ron constructed property testers with constant query complexity for dense instances of a large class of graph problems. Since many graph problems can be viewed as special cases of the Constraint Satisfaction Problem on Boolean domains, it is natural to try to construct property testers for more general cases of the Constraint Satisfaction Problem. In this paper, we give explicit constructions of property testers using a constant number of queries for dense instances of Constraint Satisfaction Problems where the constraints have constant arity and the variables assume values in some domain of finite size. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 14–32, 2002