On the safety stock problem for random delivery processes

Inventory models are considered in which the delivery of an order occurs not on one occasion but at random moments of a period in random parts. We give two extensions of the reliability type inventory model of A. Prékopa. In this model a known constant demand rate is assumed and a simple approximate formula is given for the initial stock of the order period which serves as safety stock and ensures a continuous supply during the whole order period on a prescribed probability level. This formula is widely used in practice for safety stock planning in the case when deliveries in random parts occur.We formulate a generalized version of the random delivery process and derive the exact solution of the safety stock which can be applied also for the previous model. In the second model a random demand rate is considered together with a random delivery process. An exact solution method and a simple approximate formula for the safety stock will be discussed. We have experiences in the application of these models both in a steel works and a textile factory in Hungary.     

Several methods usable in production systems prediction

In this paper, we describe three methods based on the use of a dynamical system, the use of neural networks with rough sets, and the use of a fuzzy-logic method in order to predict the behavior of data processing extracted from a highly automated factory.The work presented here is a preliminary study done in order to develop a decision aid system for a highly automated factory in southern France (Merlin-Gérin). This factory produces low cost electrical circuit breakers in high volumes with short order delays. The aim is to predict the occurrence of ruptures in the production system where a rupture corresponds to a missed delivery date.The aim of our research is to model the global behavior of manufacturing systems, and then to correlate production tactical choices with their effects. We would like then to clarify the existing relations between some sectors of the enterprise. More precisely, the work carried out at Merlin-Gérin consists in a prediction of their nondelivery ratio, which is evaluated according to an analysis of historical data provided by production processing.     

集团分布式制造模式下生产调配优化模型研究及算法设计

基于分布式概念的集团分布式制造生产管理模式在市场中占据着越来越重要的地位,此种运营模式由制造型企业向服务型企业蔓延的趋势也越来越明显,然而针对这一具有自身特点的集团分布式概念下的生产管理模型的调度研究却很少。研究针对此生产管理模式下集团级的生产调配问题建立数学模型,综合考虑客户订单的分散情况、各分厂日生产能力限制和产品品种多样性的特点,采用改进的遗传算法求解该模型,提出一种基于订单和工厂的两段式非负整数染色体编码方法,保证了生产能力约束和订单约束,采用PMX交叉算法避免不合法染色体的出现。选取W集团一定计划期内的客户订单数据进行实例分析,验证了该生产调配模型和算法的有效性。     

Simulation of capacity expansion and sequencing alternatives for a sheet metal producer

We present a simulation case study carried out for a make-to-order aluminium sheet producer located in Istanbul, Turkey. We are concerned with a subsystem of the factory consisting of continuous casting, cold rolling, and annealing processes. Two simulation models are developed: (1) a combined model for studying the casting process only; (2) a discrete event model for comparing capacity expansion alternatives and order sequencing rules in the subsystem. Operational characteristics of the real system and past data are extensively analysed for modelling and validation purposes. Capacity expansion and sequencing alternatives are evaluated in an experimental design setting with the objectives of satisfying the demand, balancing the process loads, and keeping the work-in-process inventory under control.     

Mathematical modeling of the argon oxygen decarburization converter exhaust gas system at the reduction stage

For metallurgical processes, many problems relate to the combination of very large computing domain, chemical reaction, and radiation, high turbulent and multiphase flow, which causes difficulties in the implementation of mathematical modeling. This paper describes the CFD simulation of the complex turbulent exhaust gas flow in an argon oxygen decarburization (AOD) converter in the metallurgical industry combining with species transfer, combustion, and radiation. Some details are explained in order to obtain a fast and good convergence to solve this sort of high non-linear problem. The influence on the simulation result of selecting different species as the last species in the species transfer model is discussed in this paper. The influence of argon blowing rate from bottom tuyeres on the gas flow pattern in the system is also investigated. Although it is very difficult to fully verify the simulated results in the industry at this moment, some of measured data in the factory agree well with the calculation.     

基于排队理论的最优生产线设计

本研究了在工厂生产线的设计过程中,如何安排生产线上的机器、工人、甚至物料运输设备,以提高生产率的水平,降低生产过程中的原料和半成品存量的最优化问题,用排队论方法建立了该问题的数学模型,并解出了结果和进行经济评价。     

多工厂环境下考虑个体利益的多目标协同生产计划模型及算法

针对由多个工厂组成的分布式系统,考虑不同工厂的个体利益诉求,构建了多目标协同生产计划模型。在该模型中,以最大化整体收益作为第一个优化目标;同时,基于亚当斯的公平理论,利用偏离系数法,以最小化个体收益平衡偏差作为第二个优化目标。结合模型结构特点,基于快速非支配排序遗传算法,设计了相应的求解过程。最后,通过一个算例验证表明,本文设计的计划模型和求解方法,不仅可以从网络集成角度协调各个工厂的生产、库存和运输活动,而且能够实现整体利益和个体利益非一致性的最小化。     

Goal Programming Approach to a Type of Quality Control Problem

Fixing the levels of inputs and process variables in order to meet a required specification of output is a common quality control problem. However difficulties can arise when the output has a number of characteristics and when each of these characteristics has to satisfy a specification. Such a problem was met in a paper manufacturing factory and the problem was solved using Goal Programming (GP). The method can be applied to other process control problems and this paper gives the GP formulation of the general process control problem. The paper also gives details of the case study from which the method was developed.     

Modeling the process of human body iron homeostasis using a variant of timed Petri nets

The body iron homeostasis is one of the most important processes in the human body. This complex process is not fully understood and until recently only some parts of it have been described in the literature. In our recent papers the main part of the process has been described and a model based on Petri net theory has been proposed. However, in this model any time dependencies occurring in the biochemical process have not been taken into account. In the present paper the model is enriched in the way that durations of biochemical reactions composing this process have been included into the model. A variant of Petri net where with each place a time interval is associated has been used in order to describe these dependencies. The time interval associated with a place corresponds to a time lag of biochemical conditions which must be fulfilled in order to enable a biochemical reaction to start.     

An Interactive Planning Model for the New Zealand Dairy Industry

A long-term planning model for a large New Zealand dairy company is described. The model presents an integrated view of the company's operation, including transportation and processing. The model used is based on a network formulation, NETPLAN, developed by the authors to carry out the optimisation. NETPLAN is highly flexible, interactive and provides graphical output of the results. The optimisation maximises net revenue based on product prices, variable process costs and variable transport costs subject to factory capacity, product demand and raw material supply constraints.     

Evaluating focused factory benefits with queuing theory

In this paper, we study the benefits of a focused factory using lead-time as a performance measure. Specifically, we model a production process, using multi-class (multiple product types), general interarrival and processing time distributions with multiple machines (GI/G/c) queuing models for deriving each product’s mean lead-time. We also perform simulations for estimating the standard deviation of lead times. There are two product types: a standard and a customized product. The customized product has a more variable demand pattern than the standard product, and also requires additional processing time (setup and run time) in its production process. We assume that management is willing to sacrifice the lead-time performance of the customized product in favor of improved performance for the standard product. The paper shows that focusing the factory is more attractive for plants operating at higher utilization, and manufacturing products that have higher processing time and demand variability differentials between product types.     

Linear Programming Applied to Production Planning—A Case Study

This paper describes the installation of a planning system in a food factory, based on the use of linear programming. Owing to the seasonal nature of many of the parameters, it is essential to use a multi-period model.The formulation of the L.P. model is discussed in some detail. This includes a considerable number of restrictions of a commercial rather than a physical nature.A particular aspect of the application is the way in which the model is used, in slightly different forms, at the three distinct stages of the planning process.Some of the practical difficulties encountered in implementing the solution are discussed.     

地球科学中的一类耦合抛物方程组的数值模拟

地质流体的性质和动力学行为是当前地球科学研究的前沿领域.铜陵冬瓜山层控夕卡岩型铜矿床成矿作用中矿质输运-化学反应耦合过程的数学模型是一个非局部的耦合抛物方程组初边值问题.本文考虑这一数学模型的数值模拟,用降阶法对此耦合方程组建立了一个具有二阶精度的差分格式.用能量方法给出了差分方程问题解的先验估计式,并证明了差分格式的可解性、稳定性和收敛性,其收敛阶在L2范数下关于时间步长和空间步长均是二阶的.最后给出了数值例子,数值结果和理论分析结果是吻合的.     

食用豆腐生产经营过程中区间决策问题的研究

研究了豆腐作坊生产经营豆腐的最优决策问题.深入的实际调研表明:随着自然环境的改变、生产条件和市场资源的变化,豆腐作坊的净收益表现出不确定性.于是豆腐作坊的最优净收益就呈现出区间的特性.以豆腐作坊最优净收益为目标,首先建立了两大区间决策模型-改变生产规模的区间决策模型和不改变生产规模的区间决策模型.其次给出了有关区间决策的基本定理及求解方法.最后对实际问题进行了求解,从而为豆腐作坊提供了最优净收益的范围—区间,并对求得的结果进行了分析,说明所给的求解方法及所得结论是正确的.     

A fourth‐order compact algorithm for nonlinear reaction‐diffusion equations with Neumann boundary conditions

In this article, we discuss a scheme for dealing with Neumann and mixed boundary conditions using a compact stencil. The resulting compact algorithm for solving systems of nonlinear reaction‐diffusion equations is fourth‐order accurate in both the temporal and spatial dimensions. We also prove that the standard second‐order approximation to zero Neumann boundary conditions provides fourth‐order accuracy when the nonlinear reaction term is independent of the spatial variables. Numerical examples, including an application of this algorithm to a mathematical model describing frontal polymerization process, are presented in the article to demonstrate the accuracy and efficiency of the scheme. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005     

随机环境下再制造产品的定价策略研究

再制造产品的定价是逆向供应链中重要的决策问题之一。依据目前我国废旧品回收和再制造的运作机制,在随机环境下建立了以传统生产厂为主导、再制造工厂为从属的Stackelberg博弈模型,分析了新产品与再制造产品的差异定价策略,结合数值算例给出了最优的定价结果。并进一步将模型进行扩展,考虑了二者形成垂直纳什均衡以及存在集成厂商时的情形。研究表明:集成厂商对两种产品的定价最高,系统收益也最大,Stack-elberg情形次之,纳什均衡时最低。     

Modelling lumped-parameter sorption kinetics and diffusion dynamics of odour-causing VOCs to dust particles

An analytical algorithm is presented for fast simulation of the adsorption kinetics and diffusion dynamics of odour-causing volatile organic compounds (VOC-odour) which originate in the stored swine manure to airborne dust particles in a ventilated airspace. The model is an extension to the well-known lumped-parameter model (LPM) that incorporates a Langmuir–Hinshelwood (LH) kinetic concept dependent on VOC-odour concentration with diffusion limitation. The basic idea behind the model implementation is to couple the calculations of the two major processes in the VOC-odour/dust particle system: VOC-odour diffusion based on the homogeneous surface diffusion model (HSDM) and surface reaction based on the LH kinetics in an LPM scheme. The LPM employs Laplace transforms and gamma distributions of the rate coefficient to produce a lumped-parameter gamma model (LPGM) for kinetic equation of VOC-odour adsorption to airborne dust particles, whereas the HSDM incorporates the age and size distributions of airborne dust for evaluating the dust-borne VOC-odour dynamics. The integrate assessment of VOC-odour sorption kinetics and diffusion dynamics allows to relate the adsorption rate coefficient, reaction order, and surface effective diffusivity in a complex VOC-odour/dust particle system. The LPGM fitted well with the data obtained numerically from HSDM and successfully determined the adsorption rate coefficient and reaction order for each sorption process.     

堆积颗粒系统中颗粒级配的优化

堆积颗粒系统中的颗粒级配在许多产品的生产中起着重要的作用,它不仅对产品的最终性质有很大影响,而且对许多工艺性质起决定作用.此文首先以不定型耐火材料生产中如何选取合理颗粒级配为背景,把紧密堆积理论与实际生产条件及工艺要求相结合,建立了堆积颗粒系统中颗粒级配的优化模型.然后证明了模型的合理性,并结合模型的特征、针对实际情况构造出了求解该优化模型的算法.计算结果表明所给的优化模型及算法对于堆积颗粒系统中颗粒级配的优化是可行的.     

专业零售商与厂家直售商的多渠道供应价格博弈的混沌动力学研究

在零售市场,专业零售商与厂家直售商的价格竞争日益突起,再次背景下构建了专业零售商和厂家直售商组成的多渠道供应链价格博弈模型。利用管理学、经济学以及混沌动力学有关理论,对多渠道供应链中各渠道间长期价格博弈的动态演化过程进行理论验证和数据仿真,研究了专业零售商和厂家直售商的价格决策变量的变化给市场带来的影响。研究表明,双方价格决策变量的不断增加,市场从稳定进入混沌无序状态。采用调整参数可以对混沌进行有效的控制,研究结果具有较好的理论和实际应用价值。     

Adaptive Control Model and Algorithms for the Dynamic Flowshop Scheduling Problem

1.IntroductionProductionschedulingcanbedefinedgenerallyastheallocationoftheresourcesinaproductionsystemovertimetoperformtheoperationsneededtotransformrawmaterialsilltoproducts.Aneffectiveandefficientschedulingsystemisnecessarytowellachievethepotentialsofaproductionfacility.Productionschedulingproblemsareextremelycomplex.Thecomplexityismainlyduetothefollowingtwofeaturesoftheproblem(Liu,1995).InterconnectedDecisions:Thecomponentsofaproductionsystem,e.g.,machines,ma-tenalhandlingdevicesandstora…