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family a product that exactly matches the demanded service levels. But the interest of the producer remains to satisfy this demand at the lowest cost and thus as close as possible to the demanded service levels. Consequently, the demand will be ful?lled by the smallest variant (in the sense of the partial relation of order)that oversatis?es all the demanded service levels. Another consequence is that a product family must at least contain one variant that exactly matches all the functional requirements at the maximal service level so that any demand can be oversatis?ed by this variant. This means that it is not necessary to manufacture all the possible variants: one can select the variants to manufacture in order to satisfy all the functional diversity at the lowest global cost (or at the maximal pro?t). Fig. 2 depicts the design challenge in a case with 2 requirements and 3 service levels. There can be 9 variants (Variant x 198。 y satis?es Requirement 1 at the Service Levels 1/x and Requirement 2 at the Service Levels2/y). In practice, it is not possible to manufacture all the variants because of the binatory size(V requirements with W service levels lead WV variants). But the Variant is necessary because it enables to oversatisfy any demand. So the design challenge is to select some of these variants and design their design diversity is therefore the diversity of choices in order to de?ne the set of variants, their associated service levels, and their billofmaterials. The systematic approach de?ned by Pahl and Beitz is usually adopted for designing a product. The ?rst step consists in choosing design principles. These design principles are technical and technological choices and the de?nition of a product family architecture. The architecture de?nes the types of subassemblies, their technology, and their relations. In order to design the architecture of a product family two main strategies are identi?ed which we call‘‘marketsegment oriented’’ strategy and ‘‘modular’’ strategy. Next subsections detail how to describe the result of such design strategies. Market segment design strategy The market segment strategy works on a restricted list of market segments usually de?ned by a marketing department. A market segment is characterized by ?xing a speci?c service level for each of the functional requirements. Then a variant is designed in order to ful?ll a speci?ed market segment. As several design principles can be applied to the same market segment, several admissible variants can be obtained per market segment. Moreover, as market segments are de?ned as a set of service levels of the requirements,a partial order relation between the market segments also exists. In the case of the example with 2 requirements and 3 service levels, Fig. 3 depicts the result of a design process in which only 4 market segments have been selected among the 9 possible ones. Several design principles have been applied to the market segments MS1 (3 principles) and MS4 (2 principles), and corresponding variants are obtained (notation : Variant Vi denotes the design principle number ‘‘i’’ for the variant ‘‘V’’). The bold arrows depict the order relations on the market segments. Therefore a variant designed for the market segment MS2 can also oversatisfy the needs of MS1. Demand will always be expressed on the four market segments (MS1, . . . , MS4). But the design choices that remain ?nally are: whether to oversatisfy a market segment with a variant designed for an upper market segment。 to select a variant among the designed ones for the not oversatis?ed market segments. in the example, an extreme decision can be to only manufacture either Variant or Variant in order to satisfy all the market segments. Modular design strategy The second strategy aims at adopting modular principles. This strategy appears to be es