考虑三级货损成本的冷链物流配送中心选址优化

为解决冷链物流配送中心的选址优化问题,依据易腐品完好率线性递减理论,提出了易腐品完好率与运输距离之间的分段递减函数关系,通过分析从供应点到配送中心运输过程,配送中心内部操作过程和从配送中心到需求点配送过程中所产生的三级货损实际情况,探究了本级货损对下级货损的叠加影响,以货物完好量作为客户的最终需求,构建了考虑三级货损成本的冷链物流配送中心选址优化模型,算例验证了所建模型的适用性和可行性.     

Likelihood-based confidence bands for fault lines in response surfaces

 We consider the problem of constructing asymptotic confidence bands, both pointwise and simultaneous, for a smooth fault line in a response surface when the design is represented by a point process, either deterministic or stochastic, with intensity n diverging to infinity. The estimator of the fault line is defined as the ridge line on the likelihood surface which arises from locally fitting a model that employs a linear approximation to the fault line, to a kernel smooth of the data. The construction is based on analysis of the limiting behaviour of perpendicular distance from a point on the true fault line to the nearest point on the ridge. We derive asymptotic properties of bias, and the limiting distribution of stochastic error. This distribution is given by the location of the maximum of a Gaussian process with quadratic drift. Although the majority of attention is focused on the regression problem, the limiting distribution is shown to have wider relevance to local-likelihood approaches to fault line estimation for density or intensity surfaces. Received: 20 August 2000 / Revised version: 27 September 2001 / Published online: 22 August 2002     

A centering by the monte-carlo method

The maximization of Gaussian probability of the multidimensional set is considered, when expectations of Gaussian distribution are varying and the co-variance matrix is fixed. It is shown that the necessary condition of maximum is a centering, i.e. the optimal point coincides with the weight center of the set. Iterative methods for solving this problem are developed: the analytical centering procedure and the stochastic one by series of Monte-Carlo samples of fixed or regulated size. The convergence of these procedures is considered and the properties of their application in the computer-aided design of systems are discussed     

Nonself-similar flow with a shock wave reflected from the center of symmetry and new self-similar solutions with two reflected shocks

In some problems concerning cylindrically and spherically symmetric unsteady ideal (inviscid and nonheat-conducting) gas flows at the axis and center of symmetry (hereafter, at the center of symmetry), the gas density vanishes and the speed of sound becomes infinite starting at some time. This situation occurs in the problem of a shock wave reflecting from the center of symmetry. For an ideal gas with constant heat capacities and their ratio γ (adiabatic exponent), the solution of this problem near the reflection point is self-similar with a self-similarity exponent determined in the course of the solution construction. Assuming that γ on the reflected shock wave decreases, if this decrease exceeds a threshold value, the flow changes substantially. Assuming that the type of the solution remains unchanged for such γ, self-similarity is preserved if a piston starts expanding from the center of symmetry at the reflection time preceded by a finite-intensity reflected shock wave propagating at the speed of sound. To answer some questions arising in this formulation, specifically, to find the solution in the absence of the piston, the evolution of a close-to-self-similar solution calculated by the method of characteristics is traced. The required modification of the method of characteristics and the results obtained with it are described. The numerical results reveal a number of unexpected features. As a result, new self-similar solutions are constructed in which two (rather than one) shock waves reflect from the center of symmetry in the absence of the piston.     

Location of a distribution center for a perishable product

A model that combines an inventory and location decision is presented, analyzed and solved. In particular, we consider a single distribution center location that serves a finite number of sales outlets for a perishable product. The total cost to be minimized, consists of the transportation costs from the distribution center to the sales outlets as well as the inventory related costs at the sales outlets. The location of the distribution center affects the inventory policy. Very efficient solution approaches for the location problem in a planar environment are developed. Computational experiments demonstrate the efficiency of the proposed solution approaches.     

Asymptotic behavior of the Weber location problem on the plane

The asymptotic behavior of the Weber location problem is investigated. We consider problems wheren demand points are randomly generated in a unit disk by a uniform distribution and all weights are equal to one. The main result of the paper is that the probability that the optimal solution be on a demand point is approximately 1/n. Additional results for a largen: the optimal solution converges almost surely to the center of the disk; the difference between the optimal value of the objective function and the minimal value of the objective function on a demand point converges to 1/2.     

基于人工蜂群算法的配送中心选址问题求解

采用人工蜂群算法对配送中心选址问题进行求解,给出食物源的编码方法,通过整数规范化,使算法能在整数空间内对问题进行求解.应用算法进行了仿真实验,并将结果与其它一些启发式算法进行了比较和分析.计算结果表明人工蜂群算法可以有效求解配送中心选址问题,同时也为算法求解其它一些组合优化问题提供了有益思路.     

A polynomial algorithm for the multicriteria cent-dian location problem

Given a network with several weights per node and several lengths per edge, we address the problem of locating a facility on the network such that the convex combinations of the center and median objective functions are minimized. Since we consider several weights and several lengths, various objective functions should be minimized, and hence we have to solve a multicriteria cent-dian location problem. A polynomial algorithm to characterize the efficient location point set on the network is developed. Furthermore, this model can generalize other problems such as the multicriteria center problem and the multicriteria median problem. Computing time results on random planar networks considering different combinations of weights and lengths are reported, which strengthen the polynomial complexity of the procedure.     

On the characterization of fisher information and stability of the least favorable lattice distributions

The paper is concerned with the stability properties of the least favorable distributions minimizing the Fisher information in a given class of distributions. The derivation of a least favorable distribution (the solution of a variational problem) is a necessary stage of the Huber minimax approach in robust estimation of a location parameter. Generally, the solutions of variational problems essentially depend on the regularity restrictions of a functional class. The stability of these optimal solutions to violations of the smoothness restrictions is studied under the lattice distribution classes. The discrete analogues of Fisher information are obtained in these cases. They have the form of the Hellinger metrics with the estimation of a real continuous location parameter and the form of the X² metrics with the estimation of an integer discrete location parameter. The analytical expressions for the corresponding least favorable discrete distributions are derived in some classes of lattice distributions by means of generating functions and Bellman's recursive functional equations of dynamic programming. These classes include the class of nondegenerate distributions with a restriction on the value of the density in the center of symmetry, the class of finite distributions, and the class of contaminated distributions. The obtained least favorable lattice distributions preserve the structure of their prototypes in the continuous case. These results show the stability of robust minimax solutions under different types of transitions from the continuous distribution to the discrete one. Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajduszoboszló, Hungary, 1997, Part II.     

二阶随机控制变点的Kolmogrov型检验和估计

基于Kolmogrov型统计量和Kiefer过程,对一样本情形,我们讨论了二阶随机控制变点的检验和估计到了检验统计量的渐近分布且用模拟方法给出了其有限样本的分位数,并证明了变点的估计为强相合的。     

Stochastic center of systems of stochastic differential equations on the plane

We study a stochastic analogy of the famous center problem of Dulac for quadratic differential equations in the plane. We introduce the concept of center for systems of stochastic differential equations of It\^o''s type on the plane, called stochastic center. We derive a criterion for the existence of such a center. We apply it to obtain necessary and sufficient conditions for quadratic stochastic differential equations in dimension 2.     

Explore Stochastic Instabilities of Periodic Points by Transition Path Theory

We consider the noise-induced transitions from a linearly stable periodic orbit consisting of T periodic points in randomly perturbed discrete logistic map. Traditional large deviation theory and asymptotic analysis at small noise limit cannot distinguish the quantitative difference in noise-induced stochastic instabilities among the T periodic points. To attack this problem, we generalize the transition path theory to the discrete-time continuous-space stochastic process. In our first criterion to quantify the relative instability among T periodic points, we use the distribution of the last passage location related to the transitions from the whole periodic orbit to a prescribed disjoint set. This distribution is related to individual contributions to the transition rate from each periodic points. The second criterion is based on the competency of the transition paths associated with each periodic point. Both criteria utilize the reactive probability current in the transition path theory. Our numerical results for the logistic map reveal the transition mechanism of escaping from the stable periodic orbit and identify which periodic point is more prone to lose stability so as to make successful transitions under random perturbations.     

基于两阶段启发式算法的物流配送选址-路径问题研究

为了解决配送中心选址与带时间窗的多中心车辆路径优化组合决策问题,利用双层规划法建立了配送中心选址与车辆路径安排的多目标整数规划模型,针对该模型的特点,采用两阶段启发式算法进行了求解。首先,通过基于聚集度的启发式算法对客户进行分类,确定了备选配送中心的服务范围;然后,基于双层规划法,以配送中心选址成本最小作为上层规划目标,以车辆配送成本最小作为下层规划目标,建立了多目标整数规划模型;最后,利用改进的蚁群算法进行了求解。通过分析实例数据和Barreto Benchmark算例的实验结果,验证了该模型的有效性和可行性。     

基于网络分析方法的物流配送中心选址的研究

经济全球化。信息技术和电子商务的发展对物流产生了深刻的影响。使之呈现出新的特点。这些特点对配送中心选址的研究提出了更高，更新的要求。本在对GIS网络分析方法的阐述和P中心选址模型的分析的基础上，建立了配送中心选址优化模型。该模型通过引入商品保管费用、处理费用、配送中心建造费用对P中心选址模型进行了拓展，并通过总费用最小化确定配送中心的数量、位置以及资源点与配送中心、配送中心与用户之间的供需关系。     

Symmetry analysis of a model of stochastic volatility with time-dependent parameters

We provide the solutions for the Heston model of stochastic volatility when the parameters of the model are constant and when they are functions of time. In the former case, the solution follows immediately from the determination of the Lie point symmetries of the governing 1+1 evolution partial differential equation. This is not the situation in the latter case, but we are able to infer the essential structure of the required nonlocal symmetry from that of the autonomous problem and hence can present the solution to the nonautonomous problem. As in the case of the standard Black-Scholes problem the presence of time-dependent parameters is not a hindrance to the demonstration of a solution.     

Designing a two-echelon distribution network under demand uncertainty

This paper proposes a comprehensive methodology for the stochastic multi-period two-echelon distribution network design problem (2E-DDP) where product flows to ship-to-points are directed from an upper layer of primary warehouses to distribution platforms (DPs) before being transported to the ship-to-points. A temporal hierarchy characterizes the design level dealing with DP location and capacity decisions, as well as the operational level involving transportation decisions as origin-destination flows. These design decisions must be calibrated to minimize the expected distribution cost associated with the two-echelon transportation schema on this network under stochastic demand. We consider a multi-period planning horizon where demand varies dynamically from one planning period to the next. Thus, the design of the two-echelon distribution network under uncertain customer demand gives rise to a complex multi-stage decisional problem. Given the strategic structure of the problem, we introduce alternative modeling approaches based on two-stage stochastic programming with recourse. We solve the resulting models using a Benders decomposition approach. The size of the scenario set is tuned using the sample average approximation (SAA) approach. Then, a scenario-based evaluation procedure is introduced to post-evaluate the design solutions obtained. We conduct extensive computational experiments based on several types of instances to validate the proposed models and assess the efficiency of the solution approaches. The evaluation of the quality of the stochastic solution underlines the impact of uncertainty in the two-echelon distribution network design problem (2E-DDP).     

A BSDE-based approach for the optimal reinsurance problem under partial information

We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival intensity and claim sizes distribution affected by an unobservable environmental stochastic factor. By filtering techniques (with marked point process observations), we reduce the original problem to an equivalent stochastic control problem under full information. Since the classical Hamilton–Jacobi–Bellman approach does not apply, due to the infinite dimensionality of the filter, we choose an alternative approach based on Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize the value process and the optimal reinsurance strategy in terms of the unique solution to a BSDE driven by a marked point process.     

A Study of the Motions of an Autonomous Hamiltonian System at a 1:1 Resonance

We examine the motions of an autonomous Hamiltonian system with two degrees of freedom in a neighborhood of an equilibrium point at a 1:1 resonance. It is assumed that the matrix of linearized equations of perturbed motion is reduced to diagonal form and the equilibrium is linearly stable. As an illustration, we consider the problem of the motion of a dynamically symmetric rigid body (satellite) relative to its center of mass in a central Newtonian gravitational field on a circular orbit in a neighborhood of cylindrical precession. The abovementioned resonance case takes place for parameter values corresponding to the spherical symmetry of the body, for which the angular velocity of proper rotation has the same value and direction as the angular velocity of orbital motion of the radius vector of the center of mass. For parameter values close to the resonance point, the problem of the existence, bifurcations and orbital stability of periodic rigid body motions arising from a corresponding relative equilibrium of the reduced system is solved and issues concerning the existence of conditionally periodic motions are discussed.     

A multi-objective chance-constrained network optimal model with random fuzzy coefficients and its application to logistics distribution center location problem

The problem of the distribution center is concerned with how to select distribution centers from a potential set in order to minimize the total relevant cost comprising of fixed costs of the distribution center and transport costs, and minimize the transportation time. In this paper, we propose a multi-objective network optimal model with random fuzzy coefficients for the logistics distribution center location problem. Furthermore, we convert the uncertain model into a deterministic one by the probability and possibility measure. Then the spanning tree-based genetic algorithm (st-GA) by the Prüfer number representation is introduced to solve the crisp multiobjective programming. At last, the proposed model and algorithm are applied to the Xinxi Dairy Holdings Limited Company to show the efficiency.     

基于加权绝对值距离Steiner最优树的选址问题

提出基于加权绝对值距离Steiner最优树思想的选址模型,给出了该模型的蚂蚁算法实现策略.在此基础上,分析了电子商务环境下企业配送中心选址问题,并用算例验证了该选址方案的可行性.