IDEAS home Printed from https://ideas.repec.org/a/inm/orijoc/v34y2022i5p2828-2844.html
   My bibliography  Save this article

Managing Product Transitions: A Bilevel Programming Approach

Author

Listed:
  • Rahman Khorramfar

    (MIT Energy Initiative, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142)

  • Osman Y. Özaltın

    (Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina 27695)

  • Karl G. Kempf

    (Intel Corporation, Chandler, Arizona 85226)

  • Reha Uzsoy

    (Edward P. Fitts Department of Industrial and Systems Engineering, North Carolina State University, Raleigh, North Carolina 27695)

Abstract

We model the hierarchical and decentralized nature of product transitions using a mixed-integer bilevel program with two followers, a manufacturing unit and an engineering unit. The leader, corporate management, seeks to maximize revenue over a finite planning horizon. The manufacturing unit uses factory capacity to satisfy the demand for current products. The demand for new products, however, cannot be fulfilled until the engineering unit completes their development, which, in turn, requires factory capacity for prototype fabrication. We model this interdependency between the engineering and manufacturing units as a generalized Nash equilibrium game at the lower level of the proposed bilevel model. We present a reformulation where the interdependency between the followers is resolved through the leader’s coordination, and we derive a solution method based on constraint and column generation. Our computational experiments show that the proposed approach can solve realistic instances to optimality in a reasonable time. We provide managerial insights into how the allocation of decision authority between corporate leadership and functional units affects the objective function performance. This paper presents the first exact solution algorithm to mixed-integer bilevel programs with interdependent followers, providing a flexible framework to study decentralized, hierarchical decision-making problems.

Suggested Citation

  • Rahman Khorramfar & Osman Y. Özaltın & Karl G. Kempf & Reha Uzsoy, 2022. "Managing Product Transitions: A Bilevel Programming Approach," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2828-2844, September.
  • Handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2828-2844
    DOI: 10.1287/ijoc.2022.1210
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/ijoc.2022.1210
    Download Restriction: no

    File URL: https://libkey.io/10.1287/ijoc.2022.1210?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Martine Labbé & Patrice Marcotte & Gilles Savard, 1998. "A Bilevel Model of Taxation and Its Application to Optimal Highway Pricing," Management Science, INFORMS, vol. 44(12-Part-1), pages 1608-1622, December.
    2. C. Audet & G. Savard & W. Zghal, 2007. "New Branch-and-Cut Algorithm for Bilevel Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(2), pages 353-370, August.
    3. Matteo Fischetti & Ivana Ljubić & Michele Monaci & Markus Sinnl, 2017. "A New General-Purpose Algorithm for Mixed-Integer Bilevel Linear Programs," Operations Research, INFORMS, vol. 65(6), pages 1615-1637, December.
    4. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    5. Lim, Wei Shi & Tang, Christopher S., 2006. "Optimal product rollover strategies," European Journal of Operational Research, Elsevier, vol. 174(2), pages 905-922, October.
    6. Liao, Shuangqing & Seifert, Ralf W., 2015. "On the optimal frequency of multiple generation product introductions," European Journal of Operational Research, Elsevier, vol. 245(3), pages 805-814.
    7. Stein, Oliver & Sudermann-Merx, Nathan, 2018. "The noncooperative transportation problem and linear generalized Nash games," European Journal of Operational Research, Elsevier, vol. 266(2), pages 543-553.
    8. Evan Rash & Karl Kempf, 2012. "Product Line Design and Scheduling at Intel," Interfaces, INFORMS, vol. 42(5), pages 425-436, October.
    9. Chao Liang & Metin Çakanyıldırım & Suresh P. Sethi, 2014. "Analysis of Product Rollover Strategies in the Presence of Strategic Customers," Management Science, INFORMS, vol. 60(4), pages 1033-1056, April.
    10. Simone Sagratella, 2017. "Algorithms for generalized potential games with mixed-integer variables," Computational Optimization and Applications, Springer, vol. 68(3), pages 689-717, December.
    11. Geraldo Ferrer & Jayashankar M. Swaminathan, 2006. "Managing New and Remanufactured Products," Management Science, INFORMS, vol. 52(1), pages 15-26, January.
    12. M. Köppe & M. Queyranne & C. T. Ryan, 2010. "Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs," Journal of Optimization Theory and Applications, Springer, vol. 146(1), pages 137-150, July.
    13. Jonathan F. Bard & James T. Moore, 1992. "An algorithm for the discrete bilevel programming problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(3), pages 419-435, April.
    14. Huppmann, Daniel & Siddiqui, Sauleh, 2018. "An exact solution method for binary equilibrium problems with compensation and the power market uplift problem," European Journal of Operational Research, Elsevier, vol. 266(2), pages 622-638.
    15. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    16. Ankit Bansal & Reha Uzsoy & Karl Kempf, 2020. "Iterative combinatorial auctions for managing product transitions in semiconductor manufacturing," IISE Transactions, Taylor & Francis Journals, vol. 52(4), pages 413-431, April.
    17. Le Cadre, Hélène & Jacquot, Paulin & Wan, Cheng & Alasseur, Clémence, 2020. "Peer-to-peer electricity market analysis: From variational to Generalized Nash Equilibrium," European Journal of Operational Research, Elsevier, vol. 282(2), pages 753-771.
    18. Francisco Facchinei & Christian Kanzow, 2010. "Generalized Nash Equilibrium Problems," Annals of Operations Research, Springer, vol. 175(1), pages 177-211, March.
    19. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
    20. Lavigne, Denis & Loulou, Richard & Savard, Gilles, 2000. "Pure competition, regulated and Stackelberg equilibria: Application to the energy system of Quebec," European Journal of Operational Research, Elsevier, vol. 125(1), pages 1-17, August.
    21. Suleyman Karabuk & S. David Wu, 2003. "Coordinating Strategic Capacity Planning in the Semiconductor Industry," Operations Research, INFORMS, vol. 51(6), pages 839-849, December.
    22. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    23. Onur Tavaslıoğlu & Oleg A. Prokopyev & Andrew J. Schaefer, 2019. "Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function," Operations Research, INFORMS, vol. 67(6), pages 1659-1677, November.
    24. Dajun Yue & Jiyao Gao & Bo Zeng & Fengqi You, 2019. "A projection-based reformulation and decomposition algorithm for global optimization of a class of mixed integer bilevel linear programs," Journal of Global Optimization, Springer, vol. 73(1), pages 27-57, January.
    25. Osman Y. Özaltın & Oleg A. Prokopyev & Andrew J. Schaefer, 2018. "Optimal Design of the Seasonal Influenza Vaccine with Manufacturing Autonomy," INFORMS Journal on Computing, INFORMS, vol. 30(2), pages 371-387, May.
    26. Druehl, Cheryl T. & Schmidt, Glen M. & Souza, Gilvan C., 2009. "The optimal pace of product updates," European Journal of Operational Research, Elsevier, vol. 192(2), pages 621-633, January.
    27. Didier Aussel & Simone Sagratella, 2017. "Sufficient conditions to compute any solution of a quasivariational inequality via a variational inequality," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(1), pages 3-18, February.
    28. Ted Klastorin & Weiyu Tsai, 2004. "New Product Introduction: Timing, Design, and Pricing," Manufacturing & Service Operations Management, INFORMS, vol. 6(4), pages 302-320, August.
    29. Xufei Liu & Changhyun Kwon, 2020. "Exact robust solutions for the combined facility location and network design problem in hazardous materials transportation," IISE Transactions, Taylor & Francis Journals, vol. 52(10), pages 1156-1172, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Rahman Khorramfar & Osman Ozaltin & Reha Uzsoy & Karl Kempf, 2024. "Coordinating Resource Allocation during Product Transitions Using a Multifollower Bilevel Programming Model," Papers 2401.17402, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rahman Khorramfar & Osman Ozaltin & Reha Uzsoy & Karl Kempf, 2024. "Coordinating Resource Allocation during Product Transitions Using a Multifollower Bilevel Programming Model," Papers 2401.17402, arXiv.org.
    2. Junlong Zhang & Osman Y. Özaltın, 2021. "Bilevel Integer Programs with Stochastic Right-Hand Sides," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1644-1660, October.
    3. Sagratella, Simone & Schmidt, Marcel & Sudermann-Merx, Nathan, 2020. "The noncooperative fixed charge transportation problem," European Journal of Operational Research, Elsevier, vol. 284(1), pages 373-382.
    4. George Kozanidis & Eftychia Kostarelou, 2023. "An Exact Solution Algorithm for Integer Bilevel Programming with Application in Energy Market Optimization," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 573-607, May.
    5. Claudio Contardo & Jorge A. Sefair, 2022. "A Progressive Approximation Approach for the Exact Solution of Sparse Large-Scale Binary Interdiction Games," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 890-908, March.
    6. Liu, Shaonan & Wang, Mingzheng & Kong, Nan & Hu, Xiangpei, 2021. "An enhanced branch-and-bound algorithm for bilevel integer linear programming," European Journal of Operational Research, Elsevier, vol. 291(2), pages 661-679.
    7. Maximilian Merkert & Galina Orlinskaya & Dieter Weninger, 2022. "An exact projection-based algorithm for bilevel mixed-integer problems with nonlinearities," Journal of Global Optimization, Springer, vol. 84(3), pages 607-650, November.
    8. Lorenzo Lampariello & Simone Sagratella, 2020. "Numerically tractable optimistic bilevel problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 277-303, June.
    9. Beck, Yasmine & Ljubić, Ivana & Schmidt, Martin, 2023. "A survey on bilevel optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 311(2), pages 401-426.
    10. Michelle M.H. Şeref & Janice E. Carrillo & Arda Yenipazarli, 2016. "Multi-generation pricing and timing decisions in new product development," International Journal of Production Research, Taylor & Francis Journals, vol. 54(7), pages 1919-1937, April.
    11. Joaquim Dias Garcia & Guilherme Bodin & Alexandre Street, 2024. "BilevelJuMP.jl: Modeling and Solving Bilevel Optimization Problems in Julia," INFORMS Journal on Computing, INFORMS, vol. 36(2), pages 327-335, March.
    12. Schwarz, Justus Arne & Tan, Barış, 2021. "Optimal sales and production rollover strategies under capacity constraints," European Journal of Operational Research, Elsevier, vol. 294(2), pages 507-524.
    13. Liao, Shuangqing & Seifert, Ralf W., 2015. "On the optimal frequency of multiple generation product introductions," European Journal of Operational Research, Elsevier, vol. 245(3), pages 805-814.
    14. Wu, Cheng-Han & Lai, Jing-Yi, 2019. "Dynamic pricing and competitive time-to-market strategy of new product launch under a multistage duopoly," European Journal of Operational Research, Elsevier, vol. 277(1), pages 138-152.
    15. Liu, Jingchen & Zhai, Xin & Chen, Lihua, 2018. "The interaction between product rollover strategy and pricing scheme," International Journal of Production Economics, Elsevier, vol. 201(C), pages 116-135.
    16. Leonardo Lozano & J. Cole Smith, 2017. "A Value-Function-Based Exact Approach for the Bilevel Mixed-Integer Programming Problem," Operations Research, INFORMS, vol. 65(3), pages 768-786, June.
    17. Liu, Jingchen & Zhai, Xin & Chen, Lihua, 2019. "Optimal pricing strategy under trade-in program in the presence of strategic consumers," Omega, Elsevier, vol. 84(C), pages 1-17.
    18. Tanınmış, Kübra & Aras, Necati & Altınel, İ. Kuban, 2022. "Improved x-space algorithm for min-max bilevel problems with an application to misinformation spread in social networks," European Journal of Operational Research, Elsevier, vol. 297(1), pages 40-52.
    19. Yohan Shim & Marte Fodstad & Steven Gabriel & Asgeir Tomasgard, 2013. "A branch-and-bound method for discretely-constrained mathematical programs with equilibrium constraints," Annals of Operations Research, Springer, vol. 210(1), pages 5-31, November.
    20. Jiawang Nie & Xindong Tang & Lingling Xu, 2021. "The Gauss–Seidel method for generalized Nash equilibrium problems of polynomials," Computational Optimization and Applications, Springer, vol. 78(2), pages 529-557, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:orijoc:v:34:y:2022:i:5:p:2828-2844. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.