【正文】 at every stage. In this paper, the proposed method deposes a queue at each stage into two ponents, a backlog queue and a material queue. Instead of the single type product queues in their model [13], the queues contain a multiclass 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 ponents are captured。 (2) To develop a work of inventoryqueue models for performance analysis of an integrated logistics chain with inventory control at all sites。 and (4) Distribution sites which deliver the finished products to warehouses or customers. All sites in the work are capable of building parts, subassemblies or finished goods in either maketo stock or maketoorder 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 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 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 ponents received from upstream sites, and output stores model the stocking of finishedproducts at the site (in Fig. 2, a site is represented by the dashed box containing input and output stores). Links All stores in the logistics chains are connected together by links that represent supply and demand processes. Two types of links are defined: internal link and external link. Internal links are used to connect the stores within a site, ., 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 link represents that the output store provides replenishments to the specified downstream input store. 結(jié)合多級排隊網(wǎng)絡(luò)和庫存模型用于多產(chǎn)品生產(chǎn)物流鏈的性能分析 Ming Dong（馬薩諸塞州立大學(xué)） 收稿日期： 2021年 10 月 15日 /接受日期： 2021年 3月 6日 /發(fā)表時間：二零零七年三月 ＃施普林格出版社倫敦有限公司 2021 摘要： 生產(chǎn)物流鏈包含著幾個供應(yīng)商、生產(chǎn)設(shè)備、倉庫、零售商和物流提供者之間錯綜復(fù)雜的聯(lián)系?，F(xiàn)實情況中，行業(yè) 常涉及多個階段，并在某一階段生產(chǎn)多種產(chǎn)品。本文也提出輸出流的分離以將物流鏈中的所有廠址及節(jié)點聯(lián)系在一起。這些網(wǎng)絡(luò)在許多行業(yè)的生產(chǎn)和物流中都有很多重要的應(yīng)用，例如電子和汽車行業(yè)。在該網(wǎng)絡(luò)的不同階 段，庫存可用于緩沖不確定性，但他們也有不同的成本，并且會對最終產(chǎn)品服務(wù)產(chǎn)生不同程度的影響。因此，良好的庫存管理系統(tǒng)對生產(chǎn)物流鏈的有效運(yùn)作是很重要的。在本文中，我們研究了一個模式，來描述多產(chǎn)品與有限能力內(nèi)的復(fù)雜生產(chǎn)物流鏈的動態(tài)。仿真評估經(jīng)常消耗大量的時間。目標(biāo)是通過這些到達(dá)過程參數(shù)表明網(wǎng)絡(luò)依賴度。 本文其他部分的組織結(jié)構(gòu)如下。第五部分呈現(xiàn)了一些計算結(jié)果。關(guān)于單一產(chǎn)品多個階段系統(tǒng)的一些文獻(xiàn)也是我們回顧的重點。在該模型中 , 在不同的生產(chǎn)階段不僅制造和組裝加工時間被視為 到達(dá)率和服務(wù)率的函數(shù) ,而且制造之前在服務(wù)站點之前的傳送時間也被考慮在其中。通過在排隊網(wǎng)絡(luò)中使用最長路徑分析法，可以的到一個產(chǎn)品在系統(tǒng)中的時間或制