A review of leader-follower joint optimization problems and mathematical models for product design and development

Product design and development (PDD) involves various types of tradeoffs, for which multi-objective optimization has been a prevailing approach. Complex PDD optimization problems are associated with multidisciplinary decision makers and may encompass different levels of the design decision hierarchy. A practical concern is that many conflicting goals with diverse decision variables have to compete to arrive at equilibrium solutions, entailing a paradigm of leader-follower joint optimization (LFJO). In line with a typical decision chain of engineering optimization, comprising such consecutive stages as problem formation, optimization modeling, model solution, and optimization evaluation, this paper provides a state-of-the-art review of the LFJO problems that are widely observed in the PDD literature, along with a survey of LFJO mathematical modeling methods. Also reviewed is the status quo of bilevel programming (BLP) models for LFJO problems with focus on their engineering implications for PDD. The paper also reviews the prevailing algorithms for solving BLP mathematical models, as well as common practice of LFJO model evaluation in the PDD literature. Finally, the critical issues of LFJO problems and outlook for further research are discussed.