Journal of Intelligent Manufacturing

, Volume 30, Issue 3, pp 1387–1405 | Cite as

Leader-follower joint optimization problems in product family design

  • Gang Du
  • Yi XiaEmail author
  • Roger J. Jiao
  • Xiaojie Liu


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.


Product family design Leader-follower joint optimization Quartet grid Game theoretic decision making Bilevel programming 


  1. Adelson, B. (1999). Developing strategic alliances: A framework for collaborative negotiation in design. Research in Engineering Design, 11(3), 133–144.CrossRefGoogle Scholar
  2. Anandalingam, G., & White, D. J. (1990). A solution method for the linear static Stackelberg problem using penalty functions. IEEE Transactions on Automatic Control, 35(10), 1170–1173.CrossRefGoogle Scholar
  3. Bahler, D., Dupont, C., & Bowen, J. (1995). Mixed quantitative/qualitative method for evaluating compromise solutions to conflicts in collaborative design. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 9, 325–33.CrossRefGoogle Scholar
  4. Balesdent, M., Bérend, N., Dépincé, P., et al. (2012). A survey of multidisciplinary design optimization methods in launch vehicle design. Structural and Multidisciplinary Optimization, 45(5), 619–642.CrossRefGoogle Scholar
  5. Bard, J. F. (1998). Practical bilevel optimization: Algorithms and applications. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle Scholar
  6. Bialas, W. F., & Karwan, M. H. (1982). On two-level optimization. IEEE Transactions on Automatic Control, 27(1), 211–214.CrossRefGoogle Scholar
  7. Blackenfelt, M. (2000). Design of robust interfaces in modular products. In ASME design engineering technical conferences, Baltimore, MD, DETC00/DAC-14486.Google Scholar
  8. Bracken, J., & McGill, J. (1973). The equivalence of two mathematical programs with optimization problems in the constraints. Operations Research, 21, 37–44.CrossRefGoogle Scholar
  9. Chu, C., Li, W., Jiao, R. J., et al. (2013). Design chain management: Bridging the gap between engineering and management. Journal of Intelligent Manufacturing, 24, 541–544.CrossRefGoogle Scholar
  10. Coello, C. A. C., & Christiansen, A. D. (1999). Moses: A multiobjective optimization tool for engineering design. Engineering Optimization, 31, 337–368.CrossRefGoogle Scholar
  11. Colson, B., Marcotte, P., & Savard, G. (2007). An overview of bilevel optimization. Annals of Operations Research, 153, 235–256.CrossRefGoogle Scholar
  12. Cooper, S., & Taleb-Bendiab, A. (1998). Consensus: Multi-party negotiation support for conflict resolution in concurrent engineering design. Journal of Intelligent Manufacturing, 9, 155–159.CrossRefGoogle Scholar
  13. Dai, Z., & Scott, M. J. (2007). Product platform design through sensitivity analysis and cluster analysis. Journal of Intelligent Manufacturing, 18(1), 97–113.CrossRefGoogle Scholar
  14. Deciu, E. R., Ostrosi, E., Ferney, M., et al. (2005). Configurable product design using multiple fuzzy models. Journal of Engineering Design, 16(2), 209–233.CrossRefGoogle Scholar
  15. Dempe, S. (2003). Annotated bibliography on bilevel programming and mathematical programs with equilibrium constraints. Optimization, 52, 333–359.CrossRefGoogle Scholar
  16. de Weck, O. L., Suh, E. S., & Chang, D. (2003). Product family and platform portfolio optimization. In ASME design engineering technical conferences, DETC03/DAC-48721, Chicago, IL.Google Scholar
  17. D’souza, B., & Simpson, T. W. (2003). A genetic algorithm based method for product family design optimization. Engineering Optimization, 35(1), 1–18.CrossRefGoogle Scholar
  18. Du, G., Jiao, R. J., & Chen, M. (2014). Joint optimization of product family configuration and scaling design by Stackelberg game. European Journal of Operational Research, 232, 330–341.CrossRefGoogle Scholar
  19. Du, G., Yu, J., Sun, L., et al. (2013). Leader-followers joint optimization of product family configuration and supply chain design. International Journal of Knowledge, Innovation and Entrepreneurship, 1(1), 6–23.Google Scholar
  20. Erens, F., & Verhulst, K. (1997). Architectures for product families. Computer in Industry, 33, 165–178.CrossRefGoogle Scholar
  21. Erlandsson, A., Erixon, G., & Ostgren, B. (1992). Product modules the link between QFD and DFA. Newport, RI: The International Forum on Product Design for Manufacture and Assembly.Google Scholar
  22. Fellini, R., Kokkolaras, M., & Papalambros, P. Y. (2006). Quantitative platform selection in optimal design of product families, with application to automotive engine design. Journal of Engineering Design, 17(5), 429–446.CrossRefGoogle Scholar
  23. Fine, C. H. (2005). Are you modular or integral? Be sure your supply chain knows. Strategy + Business, 2005(39), 1–8.Google Scholar
  24. Fortuny-Amat, J., & McCarl, B. (1981). A representation and economic interpretation of a two-level programming problem. Journal of the Operational Research Society, 32(9), 783–792.CrossRefGoogle Scholar
  25. Fujita, K., & Yoshida, H. (2004). Product variety optimization simultaneously designing module combination and module attributes. Concurrent Engineering: Research and Application, 12(2), 105–118.CrossRefGoogle Scholar
  26. Gu, X., Renaud, J., Ashe, L., et al. (2002). Decision-based collaborative optimization. Journal of Mechanical Design, 124, 1–13.CrossRefGoogle Scholar
  27. Hernandez, G., Seepersad, C. C., & Mistree, F. (2002). Designing for maintenance: A game theoretic approach. Engineering Optimization, 34, 561–577.CrossRefGoogle Scholar
  28. Huang, G. Q., Li, L., & Schulze, L. (2008). Genetic algorithm-based optimisation method for product family design with multi-level commonality. Journal of Engineering Design, 19(5), 401–416.CrossRefGoogle Scholar
  29. Jeroslow, R. G. (1985). The polynomial hierarchy and a simple model for competitive analysis. Mathematical Programming, 32(2), 146–164.CrossRefGoogle Scholar
  30. Ji, Y., Jiao, R. J., & Chen, L. (2013). Green modular design for material efficiency: A leader follower joint optimization model. Journal of Cleaner Production, 41, 187–201.CrossRefGoogle Scholar
  31. Jiao, R. J., Tseng, M. M., Duffy, V. G., et al. (1998). Product family modeling for mass customization. Computers and Industrial Engineering, 35(3–4), 495–498.CrossRefGoogle Scholar
  32. Jiao, R. J., & Zhang, Y. (2005). Product portfolio planning with customer-engineering interaction. IIE Transactions, 37(9), 801–814.CrossRefGoogle Scholar
  33. Jiao, R. J., Simpson, T. W., & Siddique, Z. (2007). Product family design and platform-based product development: A state-of-the-art review. Journal of Intelligent Manufacturing, 18, 5–29.CrossRefGoogle Scholar
  34. Jiao, R. J., & Zhang, Y. (2007). A generic genetic algorithm for product family design. Journal of Intelligent Manufacturing, 18, 233–247.CrossRefGoogle Scholar
  35. Jiao, J., & Tseng, M. M. (2000). Fundamentals of product family architecture. Integrated Manufacturing Systems, 11(7), 469–483.CrossRefGoogle Scholar
  36. Jiao, R. J., & Tseng, M. M. (2013). On equilibrium solutions to joint optimization problems in engineering design. CIRP Annals—Manufacturing Technology, 62, 155–158.CrossRefGoogle Scholar
  37. Jin, M., & Chen, R. (2008). The platform configuration for product family production. In: 4 th international conference on wireless communications, networking and mobile computing, Dalian (pp. 19–21).Google Scholar
  38. Kalashnikov, V. V., Dempe, S., Perez-Valdes, G. A., et al. (2015). Bilevel programming and applications. Mathematical Problems in Engineering, 310301, 1–16.Google Scholar
  39. Kim, H. M. (2001). Target cascading in optimal system design. Ph.D. Diss., University of Michigan.Google Scholar
  40. Kim, H. M., Michelena, N. F., Papalambros, P. Y., et al. (2003). Target cascading in optimal system design. ASME Journal of Mechanical Design, 125(3), 474–480.CrossRefGoogle Scholar
  41. Kodiyalam, S., & Sobieszczanski-Sobieski, J. (2001). Multidisciplinary design optimization-some formal methods, framework requirements, and application to vehicle design. International Journal of Vehicle Design, 25, 3–22.CrossRefGoogle Scholar
  42. Kristianto, Y., Helo, P., & Jiao, R. J. (2013). Mass customization design of engineer-to-order products using Benders’ decomposition and bi-level stochastic programming. Journal of Intelligent Manufacturing, 24, 961–975.CrossRefGoogle Scholar
  43. Kumar, D., Chen, W., & Simpson, T. W. (2009). A Market-driven approach to product family design. International Journal of Production Research, 47(1), 71–104.CrossRefGoogle Scholar
  44. Li, X., Zhou, X., & Ruan, X. (2002). Conflict management in closely coupled collaborative design system. International Journal of Computer Integrated Manufacturing, 15(4), 345–352.CrossRefGoogle Scholar
  45. Lynwander, P. (1983). Gear Drive Systems: Design and Application. New York, NY: Marcel Dekker. ISBN-13: 978–0824718961.Google Scholar
  46. Marinelli, F., de Weck, O., et al. (2009). A general framework for combined module- and scale-based product platform design. In Second international symposium on engineering systems.Google Scholar
  47. Martins, J. R., & Lambe, A. B. (2013). Multidisciplinary design optimization: A survey of architectures. AIAA Journal, 51(9), 2049–2075.CrossRefGoogle Scholar
  48. McAllister, C. D., & Simpson, T. W. (2003). Multidisciplinary robust design optimization of an internal combustion engine. Journal of Mechanical Design, 125(1), 124–130.CrossRefGoogle Scholar
  49. Messac, A., Martinez, M. P., & Simpson, T. W. (2002a). Effective product family design using physical programming and the product platform concept exploration method. Engineering Optimization, 3(3), 245–261.CrossRefGoogle Scholar
  50. Messac, A., Martinez, M. P., & Simpson, T. W. (2002b). A penalty function for product family design using physical programming. ASME Journal of Mechanical Design, 124(2), 164–172.CrossRefGoogle Scholar
  51. Mistree, F., Hughes, O. F., & Bras, B. (1993). The compromise decision support problem and the adaptive linear programming algorithm. In M. P. Kamat (Ed.), Structural optimization: Status and promise (pp. 247–289). Washington, DC: AIAA.Google Scholar
  52. Nayak, R. U., Chen, W., & Simpson, T. W. (2002). A variation-based method for product family design. Journal of Engineering Optimization, 34(1), 65–81.CrossRefGoogle Scholar
  53. Newcomb, P. J., Bras, B., & Rosen, D. W. (1996). Implications of modularity on product design for the life cycle. In ASME design engineering technical conferences, DETC96/DTM-1516, Irvine, CA.Google Scholar
  54. Nomaguchi, Y., Nakashima, K., & Fujita, K. (2009). Proposal of management framework of engineering analysis modeling knowledge for design validation. In Proceedings of the 9th Japan-Korea Design Engineering Workshop (pp. 67–72), Yomitan, Okinawa, Japan.Google Scholar
  55. Papalambros, P. Y., & Chirehdast, M. (1990). An integrated environment for structural configuration design. Journal of Engineering Design, 1(1), 73–96.CrossRefGoogle Scholar
  56. Roy, R., Hinduja, S., & Teti, R. (2008). Recent advances in engineering design optimization: Challenges and future trends. Manufacturing Technology, 57(2), 697–715.Google Scholar
  57. Sakawa, M., Katagiri, H., & Matsui, T. (2011). Interactive fuzzy random two-level linear programming through fractile criterion optimization. Mathematical and Computer Modelling, 54(11–12), 3153–63.CrossRefGoogle Scholar
  58. Simpson, T. W. (2004). Product platform design and customization: status and promise. Artificial Intelligence for Engineering Design, Analysis and Manufacturing, 18(1), 3–20.CrossRefGoogle Scholar
  59. Simpson, T. W., Chen, W., Allen, J. K., et al. (1996). Conceptual design of a family of products through the use of the robust concept exploration method. In 6th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization (pp. 1535–1545).Google Scholar
  60. Simpson, T. W., Jiao, R. J., Siddique, Z., & Hölttä-Otto, K. (2014). Advances in product family and product platform design: Methods and applications. Springer. ISBN: 978-1-4614-7936-9.Google Scholar
  61. Simpson, T. W., Maier, J. R. A., & Mistree, F. (2001). Product platform design: Method and application. Research in Engineering Design, 13(1), 2–22.CrossRefGoogle Scholar
  62. Swaminathan, J. M., & Lee, H. L. (2003). Design for postponement. In S. Graves & T. de Kok (Eds.), Supply Chain Management—Handbook in OR/MS (Vol. 11, pp. 199–226). Amsterdam: North-Holland.Google Scholar
  63. Talbi, E. G. (2013). A taxonomy of metaheuristics for bi-level optimization. In E. G. Talbi (Ed.), Metaheuristics for bi-level optimization (pp. 1–39). Berlin, Heidelberg: Springer.Google Scholar
  64. Tao, J., & Yu, S. (2012). Incorporating reuse and remanufacturing in product family planning. In M. Matsumoto, Y. Umeda, K. Masui, & S. Fukushige (Eds.), Design for innovative value towards a sustainable society (pp. 795–800). Heidelberg: Springer.CrossRefGoogle Scholar
  65. Tappeta, R. V., & Renaud, J. E. (2001). Interactive multiobjective optimization design strategy for decision based design. Journal of Mechanical Design, 123, 205–215.CrossRefGoogle Scholar
  66. Ulrich, K., & Eppinger, S. (2011). Product design and development, 5e. New York: McGraw-Hill Higher Education.Google Scholar
  67. von Stackelberg, H. (2011). Market structure and equilibrium, English translation of Stackelberg (1934). Heidelberg: Springer.Google Scholar
  68. Wang, D., Du, G., Jiao, R. J., et al. (2016). A Stackelberg game theoretic model for optimizing product family architecting with supply chain consideration. International Journal of Production Economics, 172, 1–18.CrossRefGoogle Scholar
  69. Wikipedia. (2015). Volkswagen Group A platform.
  70. Yang, D., Jiao, J. R., Ji, Y., et al. (2015). Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game. European Journal of Operational Research, 246(1), 263–280.CrossRefGoogle Scholar
  71. Ye, J. J., & Zhu, D. (2010). New necessary optimality conditions for bilevel programs by combining MPEC and the Value Function Approach. SIAM Journal on Optimization, 20(4), 1885–1905.Google Scholar
  72. Yokota, T., Gen, M., & Li, Y. X. (1996). Genetic algorithm for non-linear mixed-integer programming and its applications. Computers & Industrial Engineering, 30(4), 905–917.CrossRefGoogle Scholar
  73. Yu, T. L., Yassine, A. A., & Goldberg, D. E. (2003). A genetic algorithm for developing modular product architectures. ASME design engineering technical conferences (pp. 515–524). Chicago: Illinois.Google Scholar
  74. Yu, Y., & Huang, G. Q. (2010). Nash game model for optimizing market strategies, configuration of platform products in a Vendor Managed Inventory (VMI) supply chain for a product family. European Journal of Operational Research, 206(2), 361–373.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.College of Management and EconomicsTianjin UniversityTianjinChina
  2. 2.School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

Personalised recommendations