A Single-Stage Gradient-Based Approach for Solving the Joint Product Family Platform Selection and Design Problem Using Decomposition

Abstract

A core challenge in product family optimization is to develop a single-stage approach that can optimally select the set of variables to be shared in the platform(s) while simultaneously designing the platform(s) and variants within an algorithm that is efficient and scalable. However, solving the joint product family platform selection and design problem involves significant complexity and computational cost, so most prior methods have narrowed the scope by treating the platform as fixed or have relied on stochastic algorithms or heuristic two-stage approaches that may sacrifice optimality. In this paper, we propose a single-stage approach for optimizing the joint problem using gradient-based methods. The combinatorial platform-selection variables are relaxed to the continuous space by applying the commonality index and consistency relaxation function introduced in a companion paper. In order to improve scalability properties, we exploit the structure of the product family problem and decompose the joint product family optimization problem into a two-level optimization problem using analytical target cascading so that the system-level problem determines the optimal platform configuration while each subsystem optimizes a single product in the family. Finally, we demonstrate the approach through optimization of a family of ten bathroom scales; Results indicate encouraging success with scalability and computational expense.

Product Family Commonality Selection Through Interactive Visualization

“…Handling continuous and categorical variables simultaneously poses computational challenges for any optimization environment. Either mixed-integer nonlinear programming (MINLP) or non-gradient based methods can potentially be used to solve such an optimization problem, and MINLP formulations for product family design are being investigated [15]. Success of MINLP approaches in finding optimal solutions typically depends on a number of factors, such as: starting point, convexity of design space, and continuity and infeasibility associated with the design space.…”