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Leader-follower joint optimization problems in product family design

Author

Listed:
  • Gang Du

    (Tianjin University)

  • Yi Xia

    (Tianjin University)

  • Roger J. Jiao

    (Georgia Institute of Technology)

  • Xiaojie Liu

    (Tianjin University)

Abstract

Product family design (PFD) has been traditionally tackled as a single-level multi-objective optimization problem. This paper reveals a complex type of leader-follower joint optimization (LFJO) problems that are widely observed for PFD. Leader-follower decision making is inherent in product family optimization that involves multiple decision makers and encompasses different levels of decision hierarchy, in which many conflicting goals compete to arrive at equilibrium solutions. It is important for PFD to explicitly model such leader-follower decisions in line with a Stackelberg game. Consistent with multiple decision makers across different stages of the PFD process and multiple levels of the PFD decision hierarchy, this paper classifies the leader-follower decisions of PFD using a quartet grid, which serves as a reference model for conceptualization of diverse types of LFJO problems associated with PFD. Coinciding with the bilevel decision structure of game theoretic optimization, each LFJO problem formulation defined from the quartet grid can be quantitatively mapped to a bilevel programming mathematical model to be solved effectively by nested genetic algorithms. A case study of gear reducer PFD is presented to demonstrate the rational and potential of the LFJO quartet grid for dealing with game-theoretic optimization problems underpinning PFD decisions.

Suggested Citation

  • Gang Du & Yi Xia & Roger J. Jiao & Xiaojie Liu, 2019. "Leader-follower joint optimization problems in product family design," Journal of Intelligent Manufacturing, Springer, vol. 30(3), pages 1387-1405, March.
    • Handle: RePEc:spr:joinma:v:30:y:2019:i:3:d:10.1007_s10845-017-1332-4
    DOI: 10.1007/s10845-017-1332-4
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    References listed on IDEAS

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    Cited by:

    1. Helene Krieg & Tobias Seidel & Jan Schwientek & Karl-Heinz Küfer, 2022. "Solving continuous set covering problems by means of semi-infinite optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 39-82, August.
    2. Jia Hao & Mengying Zhou & Guoxin Wang & Liangyue Jia & Yan Yan, 2020. "Design optimization by integrating limited simulation data and shape engineering knowledge with Bayesian optimization (BO-DK4DO)," Journal of Intelligent Manufacturing, Springer, vol. 31(8), pages 2049-2067, December.

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