K- and V-matrix Method

Bongulielmi et al. (2001) have developed a matrix-based method to control external and internal variety of the product. The main purpose has been to establish a well-defined de- scription language for variant products to satisfy the needs of the configurator. The knowl- edge developed during the product realization process is gathered to be used in subsequent phases of the product’s life cycle (Bongulielmi et al. 2001). The aim of Bongulielmi et al.

Matrix-based product modeling methods Element-level matrices

Intra-domain matrices Inter-domain matrices

Product-level matrices

Matrix methodologies

• Same element types in rows and columns

• Relations between elements of the same type in the cells

• Relations can hold multiple attributes

• Different element types in rows and columns

• Relations between elements of different type in the cells

• Entire product/system in col- umns

• Product aspect in rows

• Relations between aspects and entire products in cells

• A set of element-level and product-level matrices are used in a coherent fashion

(2001) is to manage and analyze the variants of the product and also to reflect the logic of the product structure in a systematic way to marketing and sales. The main driver is the us- ability of the description language to the industrial cases, i.e. the description language needs to support the variant generation, description and management during the product realiza- tion process and later during the sales process (Bongulielmi et al. 2001).

The method presented by Bongulielmi et al. (2001) consists of two types of matrices. The first type of matrix is called the K-Matrix which is used for mapping two correlated product views. This matrix has two different views as shown in Figure 18. The number of views is unlimited and the company specific views can be established (Bongulielmi et al. 2001).

According to Bongulielmi et al. (2001), the K-Matrix can be used to manage the product variety, both internal and external. The idea is that the customer view is translated into the technical view (Figure 18) and the effect of customer variants can be reflected on the tech- nical side.

Figure 18. The K- and V-Matrix method (Bongulielmi 2002)

The V-Matrix concentrates on one view and the rows and columns have the same data in the same order, i.e. the data of the rows have been transposed into the columns. The matrix

is a square matrix showing the dependencies between the selected elements. Because the type of matrix is a square one, there is no need to present the dependencies at the lower tri- angular of the matrix as shown in Figure 18. According to Bongulielmi et al. (2001), the V- Matrix can be used to compare all the variants of every module with each other to define all the combinations in the product family. If the module level is shown in the V-Matrix, the compatibilities between the modules are shown in the cell. Considering the three matrices needed there is only need to construct two and the third can be derived from the first two (Bongulielmi et al. 2001). According to Bongulielmi et al. (2001), the V-Matrix for cus- tomer view can be established by the knowledge provided by the K-Matrix and the V- Matrix for the technical view.

Considering there is a total of three matrices, two of which show the compatibility of the elements and one integrates the two views together, a well-defined software tool for inter- preting the matrices is needed. The manual configuration of the product can be confusing in the case of multiple matrices. Bongulielmi et al. (2001) have also developed software sys- tem that is used to edit, maintain and query the data from the databases serving the method- ology. This enables the effective use of the K- and V-Matrix method to be used in industrial environments.

Bongulielmi et al. (2002) discuss the relationship between the K- and V-Matrix method and other matrix presentations found in literature and also the position of the methods during the product design process. Their idea is that the configuration knowledge should be gener- ated during the detail design as part of the product design process. At this point the aspect of configurability is considered and the product structure finalized. The methods compared were QFD (Bongulielmi et al. 2002), MFD (Erixon 1998), MPA (Dahmus et al. 2001), DSM (Steward 1981) and DfV (Martin and Ishii 2000). Bongulielmi et al. (2002) use the classification presented by Malmqvist (2002) and locate the methods as follows (Table 3):

Table 3. The classification of matrix presentations (Bongulielmi et al. 2002)

Inter-domain matrices Intra-domain matrices

QFD QFD-roof MFD DSM MPA DfV K-Matrix V-Matrix According to Bongulielmi et al. (2002), the main difference between the methods presented (Table 3) and the K- and V-Matrix method is that the values of the cells in the K- and V- Matrix presentation are either “0” or “1”, which means that there exists a relationship or there is no relationship between the two elements. The second difference is that the K- and V-Matrices are set up during the late phases of the product design process (Bongulielmi et al. 2002). Bongulielmi et al. (2002) consider all the other methods to support the design teams in issues related to solving product architecture problems like commonality and modularization. The K- and V-Matrix method is not used for the above mentioned product structure issues, but is used to solve problems related to product configuration related is- sues. According to Bongulielmi et al. (2002), the K- and V-Matrices can be set up after the

product structure has been established and the general design of the modules is done. The main point that Bongulielmi et al. (2002) present is the fact that the variant modules (the technical view) are defined during the design of the product structure and the functional view (customer view) related options are defined during the planning phases of the innova- tion process (see the general process for product design, Ulrich and Eppinger 2000, section 2.2.4). This way the customer needs have been considered. The product structure estab- lished can be described as matrix presentation to be used during the subsequent phases of the product design process and also during the configuration process. The benefits and tools for analyses that the K- and V-Matrix method provides for the design team are as follows (Bongulielmi et al. 2002):

• The overview of the degree of fulfilling the customer requirements (K-matrix)

• The overview of the knowledge volume (number of rules and constraints) due to exceptions and sub-optimal product family structure (V-matrix)

The role of the K- and V-Matrix method is to provide the tools for handling the configura- tion knowledge and to be a complementary tool for other matrix methods. The combination of the K- and V-Matrix method with other matrix methods supports (Bongulielmi et al.

2002):

• The design of modular product architecture

• The consideration of aspects concerning the configuration during the design process

• A systematic description of a major part of the configuration knowledge

• A communicative bridge between the engineering and the sales department

Next to Bongulielmi (2002), Aldanondo et al. (2000) use matrices as a basis for their expert configurator. This type of configurator is used for highly customized products and the need for expressing the configuration knowledge is even more important since usually the rout- ings and related cost estimations are also influenced. Aldanondo et al. (2000) use a graphic model next to the matrices, but as the dependencies get more complex, the matrices are used as the primary tools for presenting dependencies. They use matrices for presenting the dependencies between (Aldanondo et al. 2000):

• Two attributes

• An attribute and a component characteristic

• An attribute and a quotation characteristic

• An attribute and an operation characteristic

As the above list is considered, Aldanondo et al. (2000) cover the function model, the bill of material domain, the quotation domain and the routing domain with matrices.