Virtual Nodes and Completeness Constraints

In the next section two important tests are introduced: is a node in the BOM unique and complete?

Definition 4.4| Uniqueness and Completeness of Nodes Given a BOM b, a structure

node n ∈ NS(b)and its material nodes NM(n) = {n1, . . . ,nm}. The node n is

unique if for each valid vehicle of each covered product type at most one usage

constraint constraint(ni)with i ∈ {1, . . . , m} evaluates to true. I.e. there is no constructible vehicle in which more than one part of this structural node can be used at the same time. The node n is complete if for each valid vehicle of each covered product type at least one usage constraint must evaluate to true. I.e there is no constructible vehicle in which no part of this structural node is used. If a node is both unique and complete, we refer to it as a consistent node. In this case exactly one part of this node is used in every vehicle.

4.3 Analyzing the BOM

The idea behind these tests is that one wants to assure that certain parts are used exactly once in a vehicle. E.g. there should be only one steering wheel or exactly one front-left door in each vehicle. In a typical BOM for a middle-sized product line there are e.g. more than one hundred variants of steering wheels—each with usage constraints with tens or hundreds of options. Therefore it is impossible for the maintainers to guarantee that really each single possible vehicle gets exactly one steering wheel. The tests for completeness and uniqueness which will be introduced in the next section can automate this step and prove the consistency of nodes.

Vehicle Entertainment System Head Units GPS System Head Units … … 123451 Head Unit 1 123452 Head Unit 2 123453 HU Cable 1 123454 Head Unit 4 123455 Head Unit 5 Structure Nodes Material Nodes 123456 HU Cable 2 n1 n2

Figure 4.2 |A small excerpt of a BOM with non-complete nodes

However, there is a big problem in the real-life BOM of car manufacturers. Not every manufacturer has already a hierarchy of structural nodes which allow these tests. This means some manufacturers do not divide their physical parts into structural nodes which guarantee consistency. Consider e.g. the excerpt of a BOM as presented in Figure 4.2. Clearly each vehicle should have exactly one head unit but the head unit material nodes are split across two structural nodes n1and n2—none of which is intended to be complete. Also in both nodes n1and n2there are both head units and cables. So in this case it could be intended that more than one material node of n1or n2is used in a vehicle. Therefore the nodes are not intended to be unique. If a manufacturer structures its BOM in such a way, the automated tests cannot work, since we do not know which parts should be used exactly once in a vehicle.

To circumvent this problem it is necessary to introduce virtual nodes. A virtual node groups material nodes over different structural nodes and is intended to be consistent, i.e. unique and complete. But that is usually not enough. Imagine e.g. a coupling device. Clearly, in a vehicle there should be at most one coupling device. Therefore all coupling devices should be in one virtual node n to guarantee uniqueness. However, not every vehicle must have a coupling device—it should only be used if the customer has specified so in her order. Therefore n does not necessarily have to be complete. In this case it is necessary to introduce a completeness constraint—a propositional formula which states the condition under which a part should be used in this virtual node. In the example of the coupling device the completeness constraint should state that there has to be only a physical coupling device if the customer selected the equipment option for the coupling device.

Definition 4.5| Virtual Node and Completeness Constraint A virtual node n is a set of

material nodes N = NM(n). A virtual node can have a completeness constraint constraint(n).

Definition 4.6| Uniqueness and Completeness of Virtual Nodes A virtual node n =

{n1, . . . ,nm}of a BOM b is unique if for each valid vehicle of each covered product type at most one usage constraint constraint(ni)with i ∈ {1, . . . , m} evaluates to true. The virtual node n is complete if for each valid vehicle of each covered product type which satisfies constraint(n) at least one usage constraint evaluates to true. Vehicle Entertainment System Head Units GPS System Head Units … … 123451 Head Unit 1 123452 Head Unit 2 123453 HU Cable 1 123454 Head Unit 3 123455 Head Unit 4 Structure Nodes Material Nodes 123456 HU Cable 2 n1 n2

Virtual Node 1 Virtual Node 2

Figure 4.3 |A small excerpt of a BOM with virtual nodes

Figure 4.3 presents a partition of the BOM of Figure 4.2 in virtual nodes. Virtual node 1 groups all head units, whereas virtual node 2 groups all head unit cables. Both nodes are intended to be consistent and therefore can be automatically tested by the algorithms of the next section.

The introduction of virtual nodes and completeness constraints must be performed by documentation experts. However, Section 4.3.6 introduces an algorithm which automatically generates a proposal for a completeness constraint, given the material nodes of a virtual node.

Remark There are some manufacturers which already have a BOM where each structural

node is intended to be unique and complete. These manufacturers introduce empty parts which are used if no real physical part is used at a node. In this case the original nodes can be used as virtual nodes and each completeness constraint is simply >.