GEOMETRY APPLICATION EVOLUTION - FROM RESEARCH TO INDUSTRIAL APPLICATIONS OVER TWO DECADES

Digitalisation is making significant inroads into society at the same time as the general commercial trend is to able to personalise the product one acquires. The field of digital product representation, and the techniques for adopting a particular product in accordance with the customer's expectations, have become very important corporate assets. From a company's perspective these assets can be leveraged both for internal efficiency and also for different types of external customer interactions. In this article, the standpoint is that product geometry forms the foundation for digital product representation. It is from this perspective that the geometrical ecosystem comes into focus. Geometry creation and geometry consumption, in combination with geometrical configuration management, are high-value areas that must be mastered. A research-based 20-year industrial perspective building up such capabilities serves as an example. The article concludes with a forward-looking perspective on potential areas for continued exploration on this journey.

Implications of Competitor Representation for Profit-Maximizing Design

Design optimization studies that model competition with other products in the market often use a small set of products to represent all competitors. We investigate the effect of competitor product representation on profit-maximizing design solutions. Specifically, we study the implications of replacing a large set of disaggregated elemental competitor products with a subset of competitor products or composite products. We derive first-order optimality conditions and show that optimal design (but not price) is independent of competitors when using logit and nested logit models (where preferences are homogeneous). However, this relationship differs in the case of random-coefficients logit models (where preferences are heterogeneous), and we demonstrate that profit-maximizing design solutions using latent-class or mixed-logit models can (but need not always) depend on the representation of competing products. We discuss factors that affect the magnitude of the difference between models with elemental and composite representations of competitors, including preference heterogeneity, cost function curvature, and competitor set specification. We present correction factors that ensure models using subsets or composite representation of competitors have optimal design solutions that match those of disaggregated elemental models. While optimal designs using logit and nested logit models are not affected by ad-hoc modeling decisions of competitor representation, the independence of optimal designs from competitors when using these models raises questions of when these models are appropriate to use.

Multilinear Common Component Analysis via Kronecker Product Representation

We consider the problem of extracting a common structure from multiple tensor data sets. For this purpose, we propose multilinear common component analysis (MCCA) based on Kronecker products of mode-wise covariance matrices. MCCA constructs a common basis represented by linear combinations of the original variables that lose little information of the multiple tensor data sets. We also develop an estimation algorithm for MCCA that guarantees mode-wise global convergence. Numerical studies are conducted to show the effectiveness of MCCA.