Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game

Abstract

Product family design by module configuration is conducive to accommodating product variety while maintaining mass production efficiency. Effective fulfillment of product families necessitates joint decision making of product family configuration (PFC) and downstream supply chain configuration (SCC), due to nowadays manufacturers’ moving towards assembly-to-order production throughout a distributed supply chain network. Existing decision models for joint optimization of product family and supply chain configuration are originated from an “all-in-one” approach that assumes both PFC and SCC decisions can be integrated into one optimization problem by aggregating two different types of objectives into a single objective function. Such an assumption neglects the complex tradeoffs underlying two different decision making problems and fails to reveal the inherent coupling of PFC and SCC.This paper formulates joint configuration of a product family and its supply chain as a leader-follower Stackelberg game that is enacted through a bi-level hierarchical optimization mechanism to model the coordination between two self-interested decision makers for PFC and SCC. The PFC decisions are modeled as an upper-level optimization problem (called leader) for optimal selection of modules, module instances, and product variants. The SCC decisions are modeled as a lower-level optimization problem (called follower), which responds to decisions of the upper level in order to determine an optimal supply chain configuration and inventory policies. A nonlinear, mixed integer programming model is formulated for the bi-level joint decision in the leader-follower game. To solve the nonlinear optimization model, a bi-level, nested genetic algorithm with constraint reasoning is developed and implemented. A case study of a power transformer product family and supply chain configuration is reported to demonstrate the feasibility and potential of the proposed leader-follower game-theoretic method.