Abstract
This chapter deals with the modeling of product substitution and flexible BOMs. In Sect. 3.1, we describe several real-world applications where product substitution occurs. Section 3.2 presents four approaches for modeling substitution: Blending models, substitution graphs, substitution hypergraphs, and task-oriented modeling. Complementary classification criteria for product substitution models are developed in Sect. 3.3. Finally, Sect. 3.4 focusses on conditions where substitution can be beneficial, requirements for organizationally implementing substitutions, and potential pitfalls that should be kept in mind.
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Notes
- 1.
http://www.tesco.com/.
- 2.
The content of this section is partly presented in Lang and Domschke (2008).
- 3.
Wedekind and Müller (1981) developed an approach for modeling variant BOMs that is similar to AND-XOR-graph representations of substitution hypergraphs.
- 4.
STN are related to the Production Process Model (PPM) concept described, e.g., by Stadtler (2005, p. 202f.) and Richter and Stockrahm (2005, p. 443f.): A PPM consists of one or more operations (manufacturing stages), each of which consists of several activities and is associated with a primary resource. Each of the activities may use one or more secondary resources, consume certain input materials, and produce certain output materials. Precedence relations are defined for activities belonging to the same operation, and visualized as arcs between activity nodes. Also, minimal and maximal lead times between activities can be specified. In contrast to STN, in which task nodes are always connected by a state node in between, there are direct arcs between activities in PPM. Operations are connected by pegging arcs from an output material of one operation to an input material of another operation. PPMs seem suitable to model flexible production sequences similarly to STN by defining alternative routings (Stadtler, 2005, p. 205).
- 5.
There are certain analogies between STN, RTN and the graphical modeling language of Oracle® Strategic Network Optimization (SNO) (formerly: PeopleSoft SNO). The entities in an SNO model are time periods, commodities, nodes, and arcs (Wagner and Meyr, 2005, p. 377f.). “Commodity” either refers to a (physical) good or consumed time. Thus, an SNO commodity representing a physical good corresponds to an STN state node or an RTN resource node that stands for a product/state. Considering the various types of nodes in SNO, SNO process nodes roughly correspond to STN/RTN tasks, and SNO machine nodes to RTN resource nodes that represent processing equipment items. Interestingly, SNO automatically transforms models developed with its graphical language into LP/MILP models.
- 6.
This differs from the approach chosen in the Oracle® SNO modeling framework: Here, the usage of a machine/reactor would be modeled as a commodity flow (of the “commodity machine time”) from an SNO machine node to an SNO process node. Thus, there would only be one arc – from the resource to the task, not reversely – in the corresponding graph.
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Lang, J.C. (2010). Graphical Modeling of Substitutions and Flexible Bills-of-Materials. In: Production and Inventory Management with Substitutions. Lecture Notes in Economics and Mathematical Systems, vol 636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04247-8_3
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