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1、外文出处：Wu, Y., & Dong, M. (2008). Combining multi-class queueing networks and inventory models for performance analysis of multi-product manufacturing logistics chains.The International Journal of Advanced Manufacturing Technology,37, 5-6, 564-575.Combining multi-class queueing networks and inventory
2、models for performance analysis of multi-product manufacturing logistics chainsYifan Wu & Ming DongReceived: 15 October 2006 /Accepted: 6 March 2007 /Published online: 31 March 2007# Springer-Verlag London Limited 2007Abstract Manufacturing logistics chains consist of complex interconnections among
3、several suppliers, manufacturing facilities, warehouses, retailers and logistics providers. Performance modeling and analysis become increasingly more important and difficult in the management of such complex manufacturing logistics networks. Many research studies have developed different methods to
4、 solve such problems. However, most of the research focuses on logistics systems with either a single stage or single type of product. In the real world, industries always involve multiple stages and produce multiple types of products at one stage. This paper is geared toward developing a new method
5、ology by combining multi-class queueing networks and inventory models for the performance analysis of multi-product manufacturing logistic chains. A network ofmulti-class inventory queue models is presented for the performance analysis of a serial multi-stage manufacturing logistics chain in which m
6、ultiple types of products are produced at each stage. A job queue decomposition strategy is employed to analyze the major performance measures and an approach for aggregating input streams and separating output streams is proposed to link all the sites or nodes in the logistics chain together. Numer
7、ical results show that the proposed method is effective for the application examples.Keywords Multi-class queueing networks .Inventory models .Multi-stage manufacturing logistic chains . Aggregation . Separation1 IntroductionA manufacturing logistic chain can be viewed as a network of suppliers, man
8、ufacturing sites, distribution centers, and customer locations, through which components and products flow. A node in a network can be a physical location, a sub-network, or just an operation process, while links represent material (components or products) flow. These networks find significant appli
9、cations in manufacturing and logistics in many industries, such as the electronic and automobile industries 10. Throughout these networks, there are different sources of uncertainties, including supply (availability and quality), process (machine breakdown, operator variation), and demand (arrival t
10、ime and volume). Moreover, these variations will propagate from upstream stages to downstream stages. These uncertainties degrade the performances of a network such as longer cycle time and lower fill-rates. Inventories at different stages of a network can be used to buffer the uncertainties, but th
11、ey also have varying costs and different impacts on the end-item service level. Their effective allocation and control becomes a great challenge to the managers of logistics chains. Performance modeling and analysis become increasingly more important and difficult in the management of such complex m
12、anufacturing logistics chains. Inventory including raw materials, components and finished goods usually represents from 2060% of the total assets of manufacturing firms 2. Therefore, a good inventory management system has always been important in the workings of an effective manufacturing logistic c
13、hain. Motivated by this challenge, many researchers have devoted much work to this issue. However, most of the literature is focused on systems with single products only and literature on multi-stage logistics chains with multi-products is limited. The assumption that every stage or node of the netw
14、ork produces a single class of product does not characterize the real world very well since nearly all firms produce more than one kind of product with limited service capacity. In this paper, a model is developed to characterize the dynamics of complex manufacturing logistics chains with multi-prod
15、uct and finite capacity. An analytical method is proposed to obtain performance measures of such models. Numerical results show that the proposed method works well. Simulation techniques may generally be used to analyze the performance of a system, but to identify an optimal configuration of a logis
16、tics chain, many different system variants have to be evaluated. Simulation-based evaluation is usually very time-consuming. Analytical evaluation methods are therefore needed that can determine the key performance measures quickly, even if these methods only approximate the true performance of the
17、logistics chain. In order to evaluate the performance of a serial manufacturing logistics chain, a parametric decomposition approach is adopted, which has been widely used to analyze multi-stage systems or networks. The basic idea is to approximately analyze the individual queues separately after ap
18、proximately characterizing the arrival processes to each queue by a few parameters (usually two, one to represent the rate and another to represent the variability). The goal is to approximately represent the network dependence through these arrival-process parameters. Once the congestion in each qu
19、eue has been described, the total network performance can be approximated by acting as if all the queues are mutually independent, i.e., the rest of the approximation is performed as if the steady-state distribution of the numbers of customers at hte queues had a product form 18. In the proposed app
20、roach, the whole chain is decomposed into multiple single-stage multi-class inventory queues (an inventory-queue is a queueing model that incorporates certain inventory replenishment policies such as base stock). The inputs (raw materials or components arrival processes) of each single-stage multi-c
21、lass inventory queue are used to capture the characteristics of input flows of the original chain. The rest of the paper is organized as follows. Section 2 provides a review of the relevant literature. In Sect. 3, the operations and the principal characteristics of the developed model are described.
22、 A decomposition method that divides the whole logistics chain into multiple single-stage queuing networks is proposed and the performance measures by analyzing the single-stage queueing network are obtained in Sect. 4. Section 5 presents some numerical results. Section 6 summarizes this research an
23、d gives some future research directions. 2 Literature reviewSignificant literature exists on inventory management in logistics chains. In the following, some prior studies devoted to the issues which are similar to the above described problems are reviewed. Some important work on single-product mult
24、i-stage systems is reviewed. Lee and Zipkin 11, 12 and Duri et al. 9 used the decomposition method to analyze the tandem queues and processing networks. They transformed the production system into a multi-echelon model with limited production capacities. Azaron et al. 3 developed an open queueing ne
25、twork for multi-stage assemblies in which each service station represents a manufacturing or assembly operation. In the proposed model, not only the manufacturing and assembly processing times are considered as the functions of the arrival and service rates of the various stages of the manufacturing
26、 process, but also the role of transport times between the service stations in the manufacturing lead time is considered. An assumption is that the arrival processes of the individual parts of the product are independent Poisson processes with equal rates. In each service station, there is a server
27、with exponential distribution of processing time. The transport times between the service stations are assumed to be independent random variables with exponential distributions. By applying the longest path analysis in queueing networks, the distribution function of time spent by a product in the sy
28、stem or the manufacturing lead time can be obtained. The study in this paper is more similar to Liu et al. 13. They developed a multi-stage inventory queue model and a job-queue decomposition approach that evaluates the performance of serial manufacturing and supply chain systems with inventory cont
29、rol at every stage. In this paper, the proposed method decomposes a queue at each stage into two components, a backlog queue and a material queue. Instead of the single type product queues in their model 13, the queues contain a multi-class of items in the proposed model. The purpose of this paper i
30、s threefold: (1) To provide an integrated modeling framework for manufacturing logistics chains in which the interdependencies between model components are captured; (2) To develop a network of inventory-queue models for performance analysis of an integrated logistics chain with inventory control at
31、 all sites; and (3) To extend the previous work developed for a supply network model with base-stock control and service requirements. Instead of a single type product produced at each stage with infinite capacity, the problem of multiple types of products produced at each stage with finite capacity
32、 is considered.3 An integrated modeling framework for logistics chainsLogistics chains may differ in the network structure (serial, parallel, assembly and arborescent distribution), product structure (levels of bill-of-materials), transportation modes, and degree of uncertainty that they face. Howev
33、er, they have some basic elements in common 8. 3.1 Sites and stores A logistics chain can be viewed as a network of functional sites connected by different material flow paths. Generally, there are four types of sites: (1) Supplier sites which procure raw materials from outside suppliers; (2) Fabric
34、ation sites which transform raw materials into components; (3) Assembly sites which assemble the components into semi-finished products or finished goods; and (4) Distribution sites which deliver the finished products to warehouses or customers. All sites in the network are capable of building parts
35、, subassemblies or finished goods in either make-to- stock or make-to-order mode. The sites can be treated as the building blocks for modeling the whole logistics chain. Figure 1 shows a physical model of a logistics chain. Typically, there are two types of operations performed at a site in a logist
36、ics chain: material receiving and production. A material receiving operation is one that receives input materials from upstream sites and stocks them as a stockpile to be used for production. A production operation is one in which fabrication or assembly activities occur, transforming or assembling
37、input materials into output materials. Correspondingly, each site in the logistics chain has two kinds of stores: input stores and output stores. Each store stocks a single SKU. The input stores model the stocking of different types of components received from upstream sites, and output stores model
38、 the stocking of finished-products at the site (in Fig. 2, a site is represented by the dashed box containing input and output stores).3.2 LinksAll stores in the logistics chains are connected together by links that represent supply and demand processes. Two types of links are defined: internal link
39、 and external link. Internal links are used to connect the stores within a site, i.e., they represent the material flow paths from input stores to output stores within a site. A link connecting an output store of one site to an input store of another site is called an external link. This kind of lin
40、k represents that the output store provides replenishments to the specified downstream input store. 结合多级排队网络和库存模型用于多产品生产物流链的性能分析Ming Dong（马萨诸塞州立大学）收稿日期：2006年10月15日/接受日期：2007年3月6日/发表时间：二零零七年三月施普林格出版社伦敦有限公司2007摘要：生产物流链包含着几个供应商、生产设备、仓库、零售商和物流提供者之间错综复杂的联系。管理如此复杂的生产物流网时，性能建模与分析就变得越来越重要，也变得越来越困难。许多调研研究已开发
41、了集中方法来解决这种问题。然而，大多数的研究都集中在物流体系上的单一阶段或单一产品。现实情况中，行业常涉及多个阶段，并在某一阶段生产多种产品。本文旨在通过将多级排队网络与库存模型结合起来，开发一种新的方法，以用于多产品生产物流链的性能分析。多级库存排队模型网络是用来分析一系列多阶段生产物流链的性能分析，并且每一阶段都生产多种类型的产品。采用任务队列分解策略来分析改进性能得主要措施和方法，用于输入流的聚合。本文也提出输出流的分离以将物流链中的所有厂址及节点联系在一起。计算结果表明，所提出的方法对应用实例是有效的。关键词：多级排队网络 库存模式 多阶段生产物流链 聚合 分离1. 简介生产物流链可被
42、视作是一系列供应商、生产厂址、配送中心与顾客所在地之间的网络，通过这一网络，各个组件和产品可以自由流通。一个网络中的节点可以是一个物理位置、子网络，或只是一个操作过程，而联系代表物料流通。这些网络在许多行业的生产和物流中都有很多重要的应用，例如电子和汽车行业。在这些网络中，有各种来源的不确定性，包括电源（可用性和质量）、过程（机器故障、操作变化）、需求（到达时间和数量）。此外，这些变化会从上游阶段传播到下游阶段。这些不确定性降低了该网络的性能表现，如更长的周期时间，更低的填充速率。在该网络的不同阶段，库存可用于缓冲不确定性，但他们也有不同的成本，并且会对最终产品服务产生不同程度的影响。因此，他
43、们的有效配置和控制就成为物流链管理者的一大挑战。在这种复杂生产物流链的管理中，性能建模与分析就变得越来越重要，也越来越困难。库存包括原材料、组件和成品，经常占生产型企业总资产的20%到60%。因此，良好的库存管理系统对生产物流链的有效运作是很重要的。受这一挑战激励，许多研究者对这一问题已做了许多研究。然而，大多数的文献都集中于单一产品的系统，关于多产品的多阶段物流链的文献少之又少。该网络中的每一阶段或每一节点都只生产单一产品的假设，并不与现实世界的情形一致，因为几乎所有公司在有限的服务能力内，都生产了好几种产品。在本文中，我们研究了一个模式，来描述多产品与有限能力内的复杂生产物流链的动态。提出
44、的分析方法是为了提高这些模型的性能。计算结果分析表明提出的模型效果显著。仿真技术也可用于分析该系统的性能表现，但要想找到物流链的一个优化配置，许多不同的系统变量都应进行评估。仿真评估经常消耗大量的时间。因此需要分析评估方法，以快速确定关键的性能措施，即使这些方法只是物流链真实表现的一个大概。为评估串行生产物流链的性能，我们采用了参数分解法，这一方法经常被广泛用于分析多阶段系统或网络。基本理念是在几个参数（通常是两个，一个代表速率，另一个代表可变性）近似地描述到达每一队的过程后，再近似地分析单个列队。目标是通过这些到达过程参数表明网络依赖度。即使某个队列中出现堵塞，整个网络性能也不会受到影响，因
45、为所有这些队列都是相互独立的，即，其余部分评估过程的执行的前提是，所有的稳态分布的客户数量都有一个产品表格。在提出的模型中，整个物流链被分解成多个单一阶段多级库存队列（库存队列是一种排队模型，它采用一定的存库补充政策，如基料）。每个单一阶段多级库存队列的输入（原材料或组件到达过程）都用于捕捉原始链中的输入流的特点。本文其他部分的组织结构如下。第二部分为文献综述。第三部分描述了开发模型的操作与主要特点。第四部分提出了一种分解方法，将整个物流链分解成多个单一阶段的排队网络，并通过分析单一阶段的排队网络，提供了几项提高物流性能得措施。第五部分呈现了一些计算结果。第六部分总结了该项研究，并未未来的研究
46、指明了一些方向。2. 文献综述关于物流链中的库存管理，存在着很多有重大意义的文献。接下来，我们将回顾一些先前的致力于解决以上描述的类似问题的文献。关于单一产品多个阶段系统的一些文献也是我们回顾的重点。Lee and Zipkin 11, 12 and Duri et al. 9 使用分解方法分析了串联队列和处理网络问题。他们将生产系统转变成为一个有限产能的多级模式。Azaron 等人3为多级组装开发一个开放的排队网络,在其中每个服务组件在多级站代表一个生产或装配操作。在该模型中, 在不同的生产阶段不仅制造和组装加工时间被视为到达率和服务率的函数,而且制造之前在服务站点之前的传送时间也被考虑在其
47、中。假设产品单个部件到达过程是相互独立的等速率泊松过程。在每个服务站中，存在处理时间为指数分布的服务。服务站之间的传送时间假设为具有指数分布的相互独立的随机变量。通过在排队网络中使用最长路径分析法，可以的到一个产品在系统中的时间或制造所需时间的分布函数。本文研究内容与Liu等人13的研究更为相似。他们开发了一个多阶段库存排队模式和任务队列分解方法，用于评估串行生产和供应链系统在每个阶段的库存管理性能表现。本文中，提出的模型将每个阶段的队列分解成两个部分，一个积压队列和一个材料队列。未讨论单一产品队列，提出的模型中包含了多级产品。本文的目的有三个：（1）为生产物流链提供一个综合的建模框架，可用于
48、发现模型组件中的相互依存关系；（2）开发一个库存排队模型网络，用于所有场址综合物流链库存管理的性能分析；和（3）延伸先前开展的工作，开发一个用于基库控制和服务需求的供应网络模型。未讨论单一阶段无限能力内的单一产品生产，我们考虑了单一阶段有限能力内的多产品生产。3. 一个物流链的综合建模框架物流链可能会因网络结构（串行、并行、装配和树状分布）、产品结构（材料清单的水平）、运输模式、和他们面临的不确定性程度而异。然而，他们有一些共同的基本元素。3.1厂址与商铺物流链可看作由不同材料流通路径所建立的厂址之间的联系。通常说来，有四种类型的物流链：（1）供应商厂址：从外部供应商处生产原材料；（2）制造厂
49、址：将原材料转换成组件；（3）装配厂址：将组件装配成半成品或成品；和（4）配送厂址：将成品运至仓库或客户。该网络中的所有厂址都能够构建零件、组件或成品，无论是按库存生产模式还是按订单生产模式。这些厂址都可视作整个物流链建模过程中的构建模块。图1显示了一个物流链的物理模型。通常，物流链的一个厂址会实行两种操作模式：材料接收和生产。材料接收操作是从上游厂址接收输入材料，然后将他们作为储备储藏起来，以便用于生产。生产操作是指制造或组装活动，将输入材料改造或装配成输出材料的过程。相应地，物流链中的每个厂址也对应两种商铺：输入商铺与输出商铺。每种商铺都储存单个SKU。输入商铺接收并储存来自上游厂址的不同种类的部件，输出商铺则储存该厂址的成品（在图2中，一个厂址由一个虚线框表示，包含输入商铺和输出商铺）。3.2 联系物流链上的所有商铺都通过代表供应与需求过程的联系而彼此关联。本文定义了两种联系：内部联系和外部联系。内部联系