Efficient Scheduling Rules in a Combined Make-to-Stock and Make-to-Order Manufacturing System

In this paper, we consider a mixed MTS/MTO policy to manage a single manufacturing facility producing two classes of end-products. A few end-products have high volume demands, whereas a fairly large number of end-products have low volume demands. In this situation, it is appealing to try to produce the high volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the choice of the scheduling policy on the overall performance of the system. We consider two policies: the classical FIFO policy and a priority policy (PR). The PR policy gives priority to production orders corresponding to low volume products over production orders corresponding to high volume products. Under some simple stochastic modeling assumptions, we develop analytical/numerical solutions to optimise each system. We then provide insights regarding this issue with the help of numerical examples. It appears that for some range of parameters, the PR rule can outperform the FIFO rule in the sense that, to achieve the same service level constraint, the corresponding cost under the PR rule is much lower. This situation is encountered when the low volume products can be managed with an MTO policy under the PR scheduling rule, while they have to be managed according to an MTS policy under the FIFO scheduling rule. We also derive some theoretical properties that support our empirical findings.     

汽车企业集团的准时化集中生产配送系统研究

汽车企业集团的准时化集中生产配送是供应链物流一体化的重要环节。实现汽车企业集团的准时化集中生产配送,要明确其目标,做好供应商关系、配送物流的统一运作、基础数据、信息网络、配送中心仓库作业设备的现代化和领导支持六个方面的基础工作;针对我国汽车企业集团的实际,构建准时化集中配送系统的框架及流程;在准时化集中配送系统运作上探讨了包括配送资源的整合、配送中心库区的划分、配送中心库位管理、配送中心库存管理、不同物料配送流程(、6)配送中心信息系统、物料索取系统等七个方面问题。     

IPA Derivatives for Make-to-Stock Production-Inventory Systems with Backorders

A single-stage Make-to-Stock (MTS) production-inventory system consists of a production facility coupled to an inventory facility, and is subject to a policy that aims to maintain a prescribed inventory level (called base stock) by modulating production capacity. This paper considers a class of single-stage, single-product MTS systems with backorders, driven by random demand and production capacity, and subject to a continuous-review base-stock policy. A model from this class is formulated as a stochastic fluid model (SFM), where all flows are described by stochastic rate processes with piecewise constant sample paths, subject to very mild regularity assumptions that merely preclude accumulation points of jumps with probability 1. Other than that, the MTS model in SFM setting is nonparametric in that it assumes no specific form for the underlying probability law, and as such is quite general. The paper proceeds to derive formulas for the (stochastic) IPA (Infinitesimal Perturbation Analysis) derivatives of the sample-path time averages of the inventory level and backorders level with respect to the base-stock level and a parameter of the production rate. These formulas are comprehensive in that they are exhibited for any initial condition of the system, and include right and left derivatives (when they do not coincide). The derivatives derived are then shown to be unbiased and their formulas are seen to be amenable to fast computation. The generality of the model and comprehensiveness of the IPA derivative formulas hold out the promise of gradient-based applications. More specifically, since the base-stock level and production rate are the key control parameters of MTS systems, the results provide the theoretical underpinnings for optimizing the design of MTS systems and for devising prospective on-line adaptive control algorithms that employ IPA derivatives. The paper concludes with a discussion of those issues.     

Global Optimality Conditions for Nonconvex Optimization

In this paper we give an analytical equivalent for the inclusion of a set to the Lebesque set of a convex function. Using this results, we obtain global optimality conditions (GOC) related to classical optimization theory for convex maximization and reverse-convex optimization. Several examples illustrate the effectiveness of these optimality conditions allowing to escape from stationary points and local extremums.     

模糊环境下批量制造业提前/拖期交货的生产计划

描述了基于客户需求为模糊量的批量生产提前/拖期交货的生产计划,并建立了模糊环境下的三个模型.为了有效求解优化模型,我们将模糊模拟和遗传算法相结合给出了混合智能算法.最后通过数值例子说明算法的有效性.     

Multiple Solutions for a Differential Inclusion Problem with Nonhomogeneous Boundary Conditions

In this paper, we use a mountain pass theorem with Cerami type conditions for locally Lipschitz functions to investigate the existence of at least one nontrivial solution for a differential inclusion problem involving the p-Laplacian and with nonlinear and nonsmooth boundary conditions. Moreover, by a symmetric version of the mountain pass theorem, we prove the existence of infinitely many solutions.     

一类双k次B样条曲面的G1连续性条件

本文针对两个k×k次B样条曲面的节点向量为端点插值、内部是单节点的情形 ,给出它们之间的G1光滑拼接条件 ,同时得到它们的公共边界曲线的控制顶点所要满足的本征方程 .其中本征方程是B样条曲面片所独有的现象 .     

Determination of Optimum Production Quantity for a Two-Stage Production System

In this paper, a method is given for determining the optimum production quantity for a two-stage production system. The method assumes that a lot size is manufactured through two production stages with only one set-up at each stage. A production lot is manufactured in a number of sub-batches of sizes which reduce the total manufacturing cycle time of a production lot. The production quantity is considered 'optimum' when the sum of all the costs is minimized.     

Analysis of a single-server queue interacting with a fluid reservoir

We consider a single-server queueing system with Poisson arrivals in which the speed of the server depends on whether an associated fluid reservoir is empty or not. Conversely, the rate of change of the content of the reservoir is determined by the state of the queueing system, since the reservoir fills during idle periods and depletes during busy periods of the server. Our interest focuses on the stationary joint distribution of the number of customers in the system and the content of the fluid reservoir, from which various performance measures such as the steady-state sojourn time distribution of a customer may be obtained. We study two variants of the system. For the first, in which the fluid reservoir is infinitely large, we present an exact analysis. The variant in which the fluid reservoir is finite is analysed approximatively through a discretization technique. The system may serve as a mathematical model for a traffic regulation mechanism - a two-level traffic shaper - at the edge of an ATM network, regulating a very bursty source. We present some numerical results showing the effect of the mechanism. This revised version was published online in June 2006 with corrections to the Cover Date.     

成批到达的有特殊服务时间的多重休假排队系统分析

本文利用嵌入马尔可夫链方法研究了多重休假M^X／Gn／1排队系统。首先，利用概率分析法得到了排队系统的嵌入马尔可夫链的一步转移概率矩阵，以此为依据得到系统的稳态队长和同批第一个接受服务顾客的稳态等待时间。     

多工作点加速度计组合件高精度鲁棒温度控制

将存在多个工作环境的加速度计组合件温度控制受控对象描述为存在有界时变参数摄动和有界干扰的非线性时变不确定系统,提出了一种基于信号补偿的鲁棒温度控制方法,该方法设计的控制器由标称控制器和鲁棒补偿器组成.证明了闭环系统的鲁棒控制特性,实验结果显示所设计的控制系统能够在多个工作环境下实现高精度的鲁棒温度控制.     

An efficient computation algorithm for a multiserver feedback retrial queue with a large queueing capacity

Kumar et al. consider the M/M/c/N+c feedback queue with constant retrial rate [1]. They provide a solution for the steady state probabilities based on the matrix-geometric method. We show that there exists a more efficient computation method to calculate the steady state probabilities when N+c$N+c$ is large. We prove that the number of zero-eigenvalues of the characteristic matrix polynomial associated with the balance equation is ⌊(N+c+2)/2⌋$\lfloor (N+c+2)/2\rfloor$. As consequence, the remaining eigenvalues inside the unit circle can be computed in a quick manner based on the Sturm sequences. Therefore, the steady state probabilities can be determined in an efficient way.     

一类平面系统的定性分析

利用平面系统的定性理论 ,提供系统的全局分析 ,讨论了一类平面系统奇点的稳定性和极限环问题 ,给出奇点稳定和极限环唯一的充分条件     

Necessary Optimality Conditions for Problems with Equality and Inequality Constraints: Abnormal Case

This article concerns second-order necessary conditions for an abnormal local minimizer of a nonlinear optimization problem with equality and inequality constraints. The obtained optimality conditions improve the ones available in the literature in that the associated set of Lagrange multipliers is the smallest possible. The first and the second authors were supported by Russian Foundation of Basic Research, Projects 08-01-90267, 08-01-90001. The second and third authors were supported by FCT (Portugal), Research Projects SFRH/BPD/26231/2006, PTDC/EEA-ACR/75242/2006.     

Further results for the M/M(a, ∞)/N batch-service system

A multi-server Markovian queueing system is considered such that an idle server will take the entire batch of waiting customers into service as soon as their number is as large as some control limit. Some new results are derived. These include the distribution of the time interval between two consecutive commencements of service (including itsrth moment) and the actual service batch size distribution. In addition, the average customer waiting time in the queue is derived by a simple combinatorial approach. This is an expanded version of “Combinatorial analysis of batch-service queues” which was presented at the ORSA/TIMS meeting, Orlando, Florida, November 1983.     

Optimal Batch Sizes for a Two-Stage Production System

A 2-stage production model is considered in which items are processed in batches at both stages. Items processed at Stage 1 are stored until needed at Stage 2 and new batches are processed at Stage 1 only when necessary to meet second stage demand. It is shown that in an optimal policy the batch size at the first stage must be an integer multiple of second stage batch size. This can be used in an analytical derivation of the optimum batch sizes.     

A fluid queue driven by a Markovian queue

We consider an infinite buffer fluid queue receiving its input from the output of a Markovian queue with finite or infinite waiting room. The input is characterized by a Markov modulated rate process. We derive a new approach for the computation of the stationary buffer content. This approach leads to a numerically stable algorithm for which the precision of the result can be given in advance. This revised version was published online in June 2006 with corrections to the Cover Date.     

具有位相型修理的离散时间可修排队系统

本文研究了具有一般独立输入，位相型修理的离散时间可修排队系统，假定服务台对顾客的服务时间和服务台寿命服从几何分布，运用矩阵解析方法我们给出系统嵌入在到达时刻的稳态队长分布和等待时间分布，并证明这些分布均为离散位相型分布．我们也得到在广义服务时间内服务台发生故障次数的分布，证明它服从一个修正的几何分布．我们对离散时间可修排队与连续时间可修排队进行了比较，说明这两种排队系统在一些性能指标方面的区别之处．最后我们通过一些数值例子说明在这类系统中顾客的到达过程、服务时间和服务台的故障率之间的关系．     

对一类等待空间有限的抢占优先权排队的分析

讨论M/M/1抢占优先权排队模型, 且假设低优先权顾客的等待空间有限. 该模型可以用有限位相拟生灭过程来描述. 由矩阵解析方法, 对该拟生灭过程进行了分析, 并得到排队模型平稳队长的计算公式, 最后还用数值 结果说明了方法的有效性.     

Efficient Hedging and Pricing of Life Insurance Policies in a Jump-Diffusion Model

Abstract

This paper is devoted to the problem of hedging contingent claims in the framework of a two factors jump-diffusion model under initial budget constraint. We give explicit formulas for the so called efficient hedging. These results are applied for the pricing of equity linked-life insurance contracts.