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

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Abstract

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.

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Funding

This research was partially supported by the National Natural Science Foundation of China under Project No. 71371132.

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Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Gang Du, Yingying Zhang & Yi Xia

  2. Center for Management Innovation and Evaluation, Tianjin University of Commerce, Tianjin, 300134, China

    Xiaojie Liu

  3. School of Management, Tianjin University of Commerce, Tianjin, 300134, China

    Xiaojie Liu

  4. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0405, USA

    Roger J. Jiao

  5. School of Economics and Management, Shihezi University, Xinjiang, 832003, Uygur Autonomous Region, China

    Yan Li

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  1. Gang Du
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  2. Yingying Zhang
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  3. Xiaojie Liu
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  4. Roger J. Jiao
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  5. Yi Xia
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  6. Yan Li
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Correspondence to Gang Du or Roger J. Jiao.

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Du, G., Zhang, Y., Liu, X. et al. A review of leader-follower joint optimization problems and mathematical models for product design and development. Int J Adv Manuf Technol 103, 3405–3424 (2019). https://doi.org/10.1007/s00170-019-03612-6

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  • DOI: https://doi.org/10.1007/s00170-019-03612-6

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