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1、Combining multi-class queueing networks and inventory models for performance analysis of multi-product manufacturing logistics chains Yifan Wu & Ming Dong Received: 15 October 2006 /Accepted: 6 March 2007 /Published online: 31 March 2007 # Springer-Verlag London Limited 2007 Abstract Manufacturing l

2、ogistics chains consist of complex interconnections among 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.

3、 Many research studies have developed different methods to 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

4、stage. This paper is geared toward developing a new methodology by combining multi-class queueing networks and inventory models for the performance analysis of multi-product manufacturing logistic chains. A network of multi-class inventory queue models is presented for the performance analysis of a

5、serial multi-stage manufacturing logistics chain in which multiple 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 al

6、l the sites or nodes in the logistics chain together. Numerical 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 . Separation 1 Introduction A manufacturi

7、ng logistic chain can be viewed as a network of suppliers, manufacturing 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 (compo

8、nents or products) flow. These networks find significant applications 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

9、(machine breakdown, operator variation), and demand (arrival time 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 stage

10、s of a network can be used to buffer the uncertainties, but they 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 mo

11、re important and difficult in the management of such complex manufacturing 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 impo

12、rtant in the workings of an effective manufacturing logistic chain. 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 i

13、s limited. The assumption that every stage or node of the network 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 dyna

14、mics of complex manufacturing logistics chains with multi-product 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

15、 a system, but to identify an optimal configuration of a logistics 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

16、if these methods only approximate the true performance of the 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 a

17、pproximately analyze the individual queues separately after approximately 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 th

18、ese arrival-process parameters. Once the congestion in each queue 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 cust

19、omers at hte queues had a product form 18. In the proposed approach, 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

20、 or components arrival processes) of each single-stage multi-class 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 p

21、rincipal characteristics of the developed model are described. 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

22、 some numerical results. Section 6 summarizes this research and gives some future research directions. 2 Literature review Significant 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 pr

23、oblems are reviewed. Some important work on single-product multi-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 produ

24、ction capacities. Azaron et al. 3 developed an open queueing network 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 arriv

25、al and service rates of the various stages of the manufacturing 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 processe

26、s with equal rates. In each service station, there is a server 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,

27、 the distribution function of time spent by a product in the system 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 se

28、rial manufacturing and supply chain systems with inventory control 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-cl

29、ass of items in the proposed model. The purpose of this paper is 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 anal

30、ysis of an integrated logistics chain with inventory control at 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 multipl

31、e types of products produced at each stage with finite capacity is considered. 3 An integrated modeling framework for logistics chains Logistics chains may differ in the network structure (serial, parallel, assembly and arborescent distribution), product structure (levels of bill-of-materials), tran

32、sportation modes, and degree of uncertainty that they face. However, 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 sit

33、es which procure raw materials from outside suppliers； (2) Fabrication 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

34、customers. All sites in the network are capable of building parts, 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,

35、there are two types of operations performed at a site in a logistics 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 input materials