Networks of items

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Russian: Структура многопродуктовых систем с несколькими складами

1 Items: Product-Location Pairs

Multiproduct systems and multilocation systems are fundamentally identical[1]. The same models and analytical techniques can be applied just as well to one as the other. Indeed, a system with multiple products and locations can be approached in the same way. The differences, such as they are, are mainly differences in wording. This parallel should not be too surprising. Demand for one product cannot be met by supply of another, just as demand in one place cannot be met by supply elsewhere. To meet the demand, it is necessary to transform the available goods, either by moving them or by processing them into something else. Production and transportation are both physical transformations; both require time and money. Instead of products or locations, consider generic entities called items. Items can indicate locations, or products, or product-location pairs. A multi-item model can represent either geographically separated points, or physically distinct products, or both. There are a few apparent exceptions, models designed originally to capture specific production- or transportation-oriented features. Even then, the specificity is more a matter of interpretation than intrinsic structure. Virtually every production-specific feature has some analogue in the context of transportation, and vice versa. Many innovations in distribution management have been adapted from the production sphere, and the other way around. The item approach allows to conceptualize, model, and manage production and transportation activities in a unified manner.

2 Structural Complexity: Networks of Items

There are important and interesting things to learn about multiple items, even when each item is entirely independent of the others. Paragraph 3 examines such systems. Now consider items that are intrinsically linked, either through supply-demand relationships or through a shared supply process. Consider supply-demand relationships first. For example, a large retailer may purchase goods centrally, stock them in a central warehouse, and supply its several stores from the warehouse. Or a manufacturer may acquire raw materials, fabricate them into various components, and assemble the components into finished products. In such situations the items and the relationships between them form a network, specifically a directed graph. The nodes represent the items, and the arcs depict the supply-demand relationships. It is important to distinguish several broad network structures: The simplest structure is a series system, figure 1:


Fig.1. Series systems

Here, the items represent the outputs of successive production stages or stocking points along a supply chain. Each product is used as input to make the next one; or each location supplies the next one. Only the first item receives supplies from outside the system, and only the last one meets exogenous customer demands. (The figure omits the exogenous supply and demand processes as well as all internal processing steps. Only the items' inventories and their links are shown.) The next simplest structure is an assembly system, figure 2:


Fig.2. Assembly systems

This usually represents production activities. As in a series system, there is only one finished product. There may be several raw materials, however, all supplied exogenously. These are processed and/or combined ("assembled") into components, which in turn are assembled further, ultimately forming the final product. Some arcs in the network may represent transportation, moving materials, components, or the final product from one location to another. A distribution system looks like a backwards assembly system, figure 3:


Fig.3. Distribution systems

In production terms, there is one raw material and several final products. The raw material is successively specialized or refined as it moves through the production stages. In transportation terms, the first node represents a central warehouse, and the ending nodes are retail outlets; the nodes in the middle are intermediate stocking points, such as regional warehouses. Of course, a series system is a special case of both an assembly and a distribution system. A tree system, figure 4, combines the features of an assembly system and a distribution system, roughly in that order:


Fig.4. Tree systems

A fully general system, figure 5, represents still more complex relationships:


Fig.5. General systems

Compare Figures 4 and 5: The general system includes distributionlike activities whose outputs are later combined in assembly operations, while the tree system does not. This distinction is important. General systems are fundamentally more complex than tree systems. The main objective is to construct a good policy and an accurate cost estimate for a given system. One can think of purely independent items as forming a network, though a trivial one with no arcs. In light of the classification above we might call this a parallel system. This notion is useful conceptually: For instance, a distribution system combines the features of the series and parallel structures.


  1. Zipkin P. (2000) Foundations of inventory management; The McGraw-Hill Companies, Inc.
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