IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v203y2025ics0167947324001610.html
   My bibliography  Save this article

Analysis of order-of-addition experiments

Author

Listed:
  • Zhang, Xueru
  • Lin, Dennis K.J.
  • Liu, Min-Qian
  • Chen, Jianbin

Abstract

The order-of-addition (OofA) experiment involves arranging components in a specific order to optimize a certain objective, which is attracting a great deal of attention in many disciplines, especially in the areas of biochemistry, scheduling, and engineering. Recent studies have highlighted its significance, and notable works have aimed to address NP-hard OofA problems from a statistical perspective. However, solving OofA problems presents challenges due to their complex nature and the presence of uncertainty, such as scheduling problems with uncertain processing times. These uncertainties affect processing times, which are not known with certainty in advance. They introduce heteroscedasticity into OofA experiments, where different orders result in varying dispersions. To address these challenges, a unified framework is proposed to analyze scheduling problems without making specific assumptions about the distribution of these certainties. It encompasses model development and optimization, encapsulating existing homoscedastic studies (where different orders produce the same dispersion value) as a specific instance. For heteroscedastic cases, a dual response optimization within an uncertainty set is proposed, aiming to minimize the dispersion of response while keeping the location of response with a predefined target value. However, solving the proposed non-linear minimax optimization is rather challenging. An equivalent optimization formulation with low computational cost is proposed for solving such a challenging problem. Theoretical supports are established to ensure the tractability of the proposed method. Simulation studies are conducted to demonstrate the effectiveness of the proposed approach. With its solid theoretical support, ease of implementation, and ability to find an optimal order, the proposed approach offers a practical and competitive solution to solving general order-of-addition problems.

Suggested Citation

  • Zhang, Xueru & Lin, Dennis K.J. & Liu, Min-Qian & Chen, Jianbin, 2025. "Analysis of order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:csdana:v:203:y:2025:i:c:s0167947324001610
    DOI: 10.1016/j.csda.2024.108077
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947324001610
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2024.108077?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Yuna Zhao & Dennis K. J. Lin & Min-Qian Liu, 2021. "Designs for order-of-addition experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(8), pages 1475-1495, June.
    2. Aharon Ben-Tal & Dick den Hertog & Anja De Waegenaere & Bertrand Melenberg & Gijs Rennen, 2013. "Robust Solutions of Optimization Problems Affected by Uncertain Probabilities," Management Science, INFORMS, vol. 59(2), pages 341-357, April.
    3. İhsan Yanıkoğlu & Dick den Hertog & Jack P. C. Kleijnen, 2016. "Robust dual-response optimization," IISE Transactions, Taylor & Francis Journals, vol. 48(3), pages 298-312, March.
    4. Chen, Jianbin & Mukerjee, Rahul & Lin, Dennis K.J., 2020. "Construction of optimal fractional Order-of-Addition designs via block designs," Statistics & Probability Letters, Elsevier, vol. 161(C).
    5. Kai Hu & Xingfang Zhang & Mitsuo Gen & Jungbok Jo, 2017. "A new model for single machine scheduling with uncertain processing time," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 717-725, March.
    6. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    7. Zhao, Yuna & Lin, Dennis K.J. & Liu, Min-Qian, 2022. "Optimal designs for order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    8. Richard L. Daniels & Panagiotis Kouvelis, 1995. "Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production," Management Science, INFORMS, vol. 41(2), pages 363-376, February.
    9. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    Full references (including those not matched with items on IDEAS)

    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. Shengli Zhao & Zehui Dong & Yuna Zhao, 2022. "Order-of-Addition Orthogonal Arrays with High Strength," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    2. Zhao, Yuna & Lin, Dennis K.J. & Liu, Min-Qian, 2022. "Optimal designs for order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    3. Shunichi Ohmori, 2021. "A Predictive Prescription Using Minimum Volume k -Nearest Neighbor Enclosing Ellipsoid and Robust Optimization," Mathematics, MDPI, vol. 9(2), pages 1-16, January.
    4. L. Jeff Hong & Zhiyuan Huang & Henry Lam, 2021. "Learning-Based Robust Optimization: Procedures and Statistical Guarantees," Management Science, INFORMS, vol. 67(6), pages 3447-3467, June.
    5. Guo, Bing & Chen, Xueping & Wang, Xiaodi, 2024. "Component projection balanced designs for order of addition experiments," Statistics & Probability Letters, Elsevier, vol. 211(C).
    6. Antonio J. Conejo & Nicholas G. Hall & Daniel Zhuoyu Long & Runhao Zhang, 2021. "Robust Capacity Planning for Project Management," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1533-1550, October.
    7. Wang, Fan & Zhang, Chao & Zhang, Hui & Xu, Liang, 2021. "Short-term physician rescheduling model with feature-driven demand for mental disorders outpatients," Omega, Elsevier, vol. 105(C).
    8. Zhi Chen & Melvyn Sim & Peng Xiong, 2020. "Robust Stochastic Optimization Made Easy with RSOME," Management Science, INFORMS, vol. 66(8), pages 3329-3339, August.
    9. Meysam Cheramin & Jianqiang Cheng & Ruiwei Jiang & Kai Pan, 2022. "Computationally Efficient Approximations for Distributionally Robust Optimization Under Moment and Wasserstein Ambiguity," INFORMS Journal on Computing, INFORMS, vol. 34(3), pages 1768-1794, May.
    10. Wolfram Wiesemann & Daniel Kuhn & Melvyn Sim, 2014. "Distributionally Robust Convex Optimization," Operations Research, INFORMS, vol. 62(6), pages 1358-1376, December.
    11. Bram L. Gorissen & Hans Blanc & Dick den Hertog & Aharon Ben-Tal, 2014. "Technical Note---Deriving Robust and Globalized Robust Solutions of Uncertain Linear Programs with General Convex Uncertainty Sets," Operations Research, INFORMS, vol. 62(3), pages 672-679, June.
    12. Postek, Krzysztof & Ben-Tal, A. & den Hertog, Dick & Melenberg, Bertrand, 2015. "Exact Robust Counterparts of Ambiguous Stochastic Constraints Under Mean and Dispersion Information," Other publications TiSEM d718e419-a375-4707-b206-e, Tilburg University, School of Economics and Management.
    13. van Eekelen, Wouter, 2023. "Distributionally robust views on queues and related stochastic models," Other publications TiSEM 9b99fc05-9d68-48eb-ae8c-9, Tilburg University, School of Economics and Management.
    14. Haolin Ruan & Zhi Chen & Chin Pang Ho, 2023. "Adjustable Distributionally Robust Optimization with Infinitely Constrained Ambiguity Sets," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1002-1023, September.
    15. Lin, Jun & Ng, Tsan Sheng, 2011. "Robust multi-market newsvendor models with interval demand data," European Journal of Operational Research, Elsevier, vol. 212(2), pages 361-373, July.
    16. Jun-Ya Gotoh & Michael Jong Kim & Andrew E. B. Lim, 2017. "Calibration of Distributionally Robust Empirical Optimization Models," Papers 1711.06565, arXiv.org, revised May 2020.
    17. Nicholas G. Hall & Daniel Zhuoyu Long & Jin Qi & Melvyn Sim, 2015. "Managing Underperformance Risk in Project Portfolio Selection," Operations Research, INFORMS, vol. 63(3), pages 660-675, June.
    18. Ng, Tsan Sheng, 2013. "Robust regret for uncertain linear programs with application to co-production models," European Journal of Operational Research, Elsevier, vol. 227(3), pages 483-493.
    19. Yanikoglu, I. & den Hertog, D. & Kleijnen, Jack P.C., 2013. "Adjustable Robust Parameter Design with Unknown Distributions," Discussion Paper 2013-022, Tilburg University, Center for Economic Research.
    20. Yu, Pengfei & Gao, Ruotian & Xing, Wenxun, 2021. "Maximizing perturbation radii for robust convex quadratically constrained quadratic programs," European Journal of Operational Research, Elsevier, vol. 293(1), pages 50-64.

    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:eee:csdana:v:203:y:2025:i:c:s0167947324001610. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.