Fractional factorial design for model based evaluation of customer preferences

In this article, we explore the connection between Conjoint Analysis (CA) and a recent theory for minimum size orthogonal fractional factorial design generation (Fontana, 2013). We show how searching for a minimum size OFFD that satisfies a set of constraints, expressed in terms of orthogonality between simple and interaction effects, is equivalent to solving an integer linear programming problem. It is worth noting that the methodology puts no restriction either on the number of levels of each factor or on the orthogonality constraints and so it can be applied to a very wide range of designs, including mixed orthogonal arrays. An algorithm, that has been implemented in SAS/IML, is briefly described. The use of this