Joint optimization of product family configuration and scaling design by Stackelberg game

• Currently module configuration and scaling design are treated as two separate decisions.
• A significant finding that these two problems are coupled in nature, leading to joint optimization.
• A novel application of Stackelberg game models to the product family design field.
• Synthesis of unique context of product families within a coherent equilibrium decision framework.
• Comparative study reveals that our bilevel model is advantageous over the existing practice.

Product family design is generally characterized by two types of approaches: module-based and scale-based. While the former aims to enable product variety based on module configuration, the latter is to variegate product design by scaling up or down certain design parameters. The prevailing practice is to treat module configuration and scaling design as separate decisions or aggregate two design problems as a single-level, all-in-one optimization problem. In practice, optimization of scaling variables is always enacted within a specific modular platform; and meanwhile an optimal module configuration depends on how design parameters are to be scaled. The key challenge is how to deal with explicitly the coupling of these two design optimization problems.This paper formulates a Stackelberg game theoretic model for joint optimization of product family configuration and scaling design, in which a bilevel decision structure reveals coupled decision making between module configuration and parameter scaling. A bilevel mixed 0–1 non-linear programming model is developed and solved, comprising an upper-level optimization problem and a lower-level optimization problem. The upper level seeks for an optimal configuration of modules and module attributes by maximizing the shared surplus of an entire product family. The lower level entails parametric optimization of attribute values for optimal technical performance of each individual module. A case study of electric motors demonstrates that the bilevel joint optimization model excels in leveraging optimal scaling in conjunction with optimal module configuration, which is advantageous over the existing paradigm of product family scaling design that cannot change the product family configuration.