基于数量折扣合同和缺货损失的EOQ模型的改进

经济订购批量模型假定需求率、单位持有成本、订货成本为常数下得到总成本最低的订购批量,这些参数常数化的假设在现实中通常难以满足.假定需求和订货费为不确定的、库存成本包括年固定成本(与订货量无关)和年可变成本(与订货量有关),用三角模糊数表示年需求和订货费,通过引入数量折扣合同来量化单位产品进价,分别在不允许缺货和考虑缺货损失两种情况下得到最佳订货量.最后的算例表明了模型的合理性.     

基于设备状态监控的单级备件库存系统补货策略研究

本文研究一个周期性订货的多设备同备件库存系统,将备件库存策略与设备状态监控相结合,讨论了存在设备状态监控情形下的备件库存策略。针对设备状态自然腐蚀过程和人 为修复过程的复合过程,运用一个新的马尔科夫概率转移矩阵对设备需求概率进行刻画,并在此基础上给出静态订货模型和状态监控下的动态订货模型的最优订货策略。通过对比以上两种订货策略优缺点,本文提出一种新的启发式订货策略: 基于关键状态的订货策略模型。该策略可以有效降低对全部设备实行动态监控的信息成本,且成本节省优于静态订货策略,对于企业的现实问题有着较好的指导意义。     

预付款融资下基于熵成本的零售商最优订货策略

在预付款策略中,引入熵成本来构建零售商的库存模型,并结合数值分析探讨零售商的最优订货策略.研究发现,考虑熵成本的预付款模型中,随着供应商要求的预付期的增加,零售商的最优订货周期和最优订货批量下降,单位产品流动产生的熵成本上升,单位时间总成本下降.随着利息率的增加,最优订货周期和最优订货批量下降,单位产品流动产生的熵成本在上升,单位时间总成本上升.订货批量越大,单位产品流动产生的熵成本越小.含有熵成本的模型中的最优订货量稳健性,高于不考虑熵成本的库存模型中的,并且受利息收益率和预付款提前期的影响较小.     

基于供应商视角的提前订货协调研究

本文针对一个供应商和零售商组成的供应链系统,主要研究零售商如何设计提前订货折扣来吸引顾客提前订货;而供应商如何根据市场需求的不确定性,设计零售商提前订货资金的付款时间等问题。在供应商-Stackelberg框架下,以期望利润为目标,建立了相应的决策模型。通过对模型的分析求解,给出了不同市场环境下供应商要求零售商支付提前订货资金的策略。最后,用算例验证了模型和理论分析的可行性。     

考虑需求率变化与延期支付的临时订货模型

供应商给予临时价格折扣、并针对采购商的临时订货给予优惠的延期支付条件;同时考虑到采购商的自身需求即为终端需求并对价格敏感,由于考虑需求量变化的同时考虑到时间因素,因此需求率实际上发生了改变。在这样的背景下,采购商在价格变化时刻面临两种选择:以低价购进大量货物或者放弃这个机会。本文以EOQ模型单位产品成本为参考,从成本节约最大的角度出发,分析了采购商临时订货量的确定过程,并用数例分析了参数变化对最优订货以及成本节约情况的影响。     

需求不确定的供应链两阶段订货模型

销售商如何在不确定需求的市场环境下根据制造商提供的订货条件进行合理订货是供应链管理的一个核心问题。本文利用信号博弈的原理从销售商的角度研究在不确定需求且传统需求预测方法失效的情况下，允许调整订货量的短生命周期产品两阶段订货模型，得到了在两次订货条件下销售商应该采取的最优订货量与调整策略以及制造商对契约灵活性限制的成本函数。     

基于时变需求的集成多级供应链生产订货策略研究

考虑一个时变需求环境下集成多级供应链问题,在有限的规划时间内销售商以固定周期订货,而生产商以不同的周期生产,目的是寻找销售商最优的订货周期和生产商最佳的生产策略,从而使供应链系统的总运营成本最少.建立了该问题的混合整数非线性规划模型,求解该模型分为两步：先求对应一个订货周期的最佳生产策略,再求最优的订货周期,第一步用到了图论里求最短路方法.给出了两个步骤的算法和程序,实验证明它们是有效的.通过算例对模型进行了分析,研究了各参数对最优解及最小费用的影响.     

碳限额与碳交易约束下制造商生产-库存控制策略

针对制造商订货、储存、生产过程中的碳排放问题,探讨了碳限额与碳交易约束下制造商生产-库存控制策略,在对碳限额与碳交易进行数学度量的基础上构建了碳限额与碳交易约束下制造商生产-库存成本模型,并通过模型分析得出有碳约束且成本最优生产量及原材料最大订货倍数以及碳限额与碳交易约束下制造商最优生产-库存策略。计算实验与算例分析表明:相比于无碳约束情形,碳限额与碳交易约束下制造商订货数量更高,而订货频率及生产批量更低,并得出三种交易价格之下,决策变量的变化趋势。     

允许延期付款条件下的经济订货批量

本文给出了在允许延期付款条件下的经济订货批量模型.该条件假设:供方允许需方在接到订货后先支付B倍的订货货款(0≤B≤1),剩下的(1-B)倍的贷款可延迟T_c时间付款.最后给出了应用的例子.本文的结论包括了文献[1]和[2]的结果,且更具有一般性和通用性.     

带有随机订货点的两阶段报童模型

销售商可通过二次订货以达到降低风险、增加利润的目的,然而在实际中由于生厂商供货能力不足等不可控因素,销售商往往无法确定何时能进行第二次订货。针对这种现象,本文研究二次订货时间不确定的报童问题,假设随机订货时间点和需求率均服从均匀分布,建立了带有随机订货点的两阶段报童模型,给出了两阶段最优期望总订货量,使得零售商在整个销售期内的期望利润达到最大值。最后通过数值算例,对比分析了本文的二次订购模型与传统一次订购模型,研究结果指出在整个销售期内二次订货可以提高零售商的期望利润。     

Sur l'estimation des modèles autorégressifs d'ordre multiple de séries temporelles

In this Note, we determine the minimum Hellinger distance estimate of a multiple order autoregressive time series model. Under some assumptions which ensure some probabilistic properties, and under other mild conditions, we establish the asymptotic properties of this estimate. As an example, we consider the exponential autoregressive models.     

Biased Online Parameter Inference for State-Space Models

We consider Bayesian online static parameter estimation for state-space models. This is a very important problem, but is very computationally challenging as the state-of-the art methods that are exact, often have a computational cost that grows with the time parameter; perhaps the most successful algorithm is that of SM C² (Chopin et al., J R Stat Soc B 75: 397–426 2013). We present a version of the SM C² algorithm which has computational cost that does not grow with the time parameter. In addition, under assumptions, the algorithm is shown to provide consistent estimates of expectations w.r.t. the posterior. However, the cost to achieve this consistency can be exponential in the dimension of the parameter space; if this exponential cost is avoided, typically the algorithm is biased. The bias is investigated from a theoretical perspective and, under assumptions, we find that the bias does not accumulate as the time parameter grows. The algorithm is implemented on several Bayesian statistical models.     

时滞Hopfield神经网络模型的全局吸引性和全局指数稳定性

对具有时滞的Hopfield神经网络模型,在非线性神经元激励函数是Lipschitz连续(而非已有的大部分文献中假设是Sigmoid函数)的条件下,通过构造适当的泛函,给出了这类模型全局吸引和平衡点全局指数稳定的易于验证的充分条件。     

Energy decay of variable-coefficient wave equation with acoustic boundary conditions and delay

In this paper, we consider a variable-coefficient wave equation with memory type acoustic boundary conditions and a constant time delay in the boundary feedback. Using the Riemannian geometry method, we prove the exponential decay of the system with memory type acoustic boundary conditions and a constant time delay under some suitable assumptions.     

Power utility maximization in exponential Lévy models: convergence of discrete-time to continuous-time maximizers

We consider power utility maximization of terminal wealth in a 1-dimensional continuous-time exponential Lévy model with finite time horizon. We discretize the model by restricting portfolio adjustments to an equidistant discrete time grid. Under minimal assumptions we prove convergence of the optimal discrete-time strategies to the continuous-time counterpart. In addition, we provide and compare qualitative properties of the discrete-time and continuous-time optimizers.     

Pullback attractors for a two-dimensional Navier-Stokes model in an infinite delay case

We prove the existence of solutions for a Navier-Stokes model in two dimensions with an external force containing infinite delay effects in the weighted space C_γ(H). Then, under additional suitable assumptions, we prove the existence and uniqueness of a stationary solution and the exponential decay of the solutions of the evolutionary problem to this stationary solution. Finally, we study the existence of pullback attractors for the dynamical system associated to the problem under more general assumptions.     

一类非自治发展方程一致吸引子的存在性

本文主要讨论一类非线性发展方程整体强解的长时间行为,利用文献[3]的方法,我们获得了整体强解对应的解过程族的一致耗散性,然后,通过验证一致(关于σ∈Σ)ω-极限紧,得到了系统的一致吸引子的存在性,其中非线性项满足临界指数增长条件.     

Optimal control policies for ambulance diversion

Ambulance diversion (AD) is used by emergency departments (EDs) to relieve congestion by requesting ambulances to bypass the ED and transport patients to another facility. We study optimal AD control policies using a Markov Decision Process (MDP) formulation that minimizes the average time that patients wait beyond their recommended safety time threshold. The model assumes that patients can be treated in one of two treatment areas and that the distribution of the time to start treatment at the neighboring facility is known. Assuming Poisson arrivals and exponential times for the length of stay in the ED, we show that the optimal AD policy follows a threshold structure, and explore the behavior of optimal policies under different scenarios. We analyze the value of information on the time to start treatment in the neighboring hospital, and show that optimal policies depend strongly on the congestion experienced by the other facility. Simulation is used to compare the performance of the proposed MDP model to that of simple heuristics under more realistic assumptions. Results indicate that the MDP model performs significantly better than the tested heuristics under most cases. Finally, we discuss practical issues related to the implementation of the policies prescribed by the MDP.     

On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions

Failures of machines have a significant effect on the behavior of manufacturing systems. As a result it is important to model this phenomenon. Many queueing models of manufacturing systems do incorporate the unreliability of the machines. Most models assume that the times to failure and the times to repair of each machine are exponentially distributed (or geometrically distributed in the case of discrete-time models). However, exponential distributions do not always accurately represent actual distributions encountered in real manufacturing systems. In this paper, we propose to model failure and repair time distributions bygeneralized exponential (GE) distributions (orgeneralized geometric distributions in the case of a discretetime model). The GE distribution can be used to approximate distributions with any coefficient of variation greater than one. The main contribution of the paper is to show that queueing models in which failure and repair times are represented by GE distributions can be analyzed with the same complexity as if these distributions were exponential. Indeed, we show that failures and repair times represented by GE distributions can (under certain assumptions) be equivalently represented by exponential distributions.This work was performed while the author was visiting the Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.     

Global well-posedness and exponential stability of solutions for the viscous radiative and reactive gas

This paper is concerned with the global well-posedness and exponential stability of solutions to a one-dimensional model for the viscous radiative and reactive gas with higher-order kinetics. We prove that under rather general assumptions on the heat conductivity κ, for any large smooth initial data, the problem admits a unique global classical solution. Moreover, the solution will exponentially decay to the unique steady state as time goes to infinity.