IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v322y2025i1p121-132.html
   My bibliography  Save this article

Ranking and selection with two-stage decision

Author

Listed:
  • Wang, Tianxiang
  • Xu, Jie
  • Branke, Juergen
  • Hu, Jian-Qiang
  • Chen, Chun-Hung

Abstract

Ranking & selection (R&S) is concerned with the selection of the best decision from a finite set of alternative decisions when the outcome of the decision has to be estimated using stochastic simulation. In this paper, we extend the R&S problem to a two-stage setting where after a first-stage decision has been made, some information may be observed and a second-stage decision then needs to be made based on the observed information to achieve the best outcome. We then extend two popular single-stage R&S algorithms, expected value of information (EVI) and optimal computing budget allocation (OCBA), to efficiently solve the new two-stage R&S problem. We prove the consistency of the new two-stage EVI (2S-EVI) and OCBA (2S-OCBA) algorithms. Experiment results on benchmark test problems and a two-stage multi-product assortment problem show that both algorithms outperform applying single-stage EVI and OCBA in the two-stage setting. Between 2S-EVI and 2S-OCBA, numerical results suggest that 2S-EVI tends to perform better with smaller number of decisions at first and second stage while 2S-OCBA has better performance for larger problems.

Suggested Citation

  • Wang, Tianxiang & Xu, Jie & Branke, Juergen & Hu, Jian-Qiang & Chen, Chun-Hung, 2025. "Ranking and selection with two-stage decision," European Journal of Operational Research, Elsevier, vol. 322(1), pages 121-132.
    • Handle: RePEc:eee:ejores:v:322:y:2025:i:1:p:121-132
    DOI: 10.1016/j.ejor.2024.11.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221724008555
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2024.11.005?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. Jianzhong Du & Siyang Gao & Chun-Hung Chen, 2024. "A Contextual Ranking and Selection Method for Personalized Medicine," Manufacturing & Service Operations Management, INFORMS, vol. 26(1), pages 167-181, January.
    2. Stephen E. Chick & Jürgen Branke & Christian Schmidt, 2010. "Sequential Sampling to Myopically Maximize the Expected Value of Information," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 71-80, February.
    3. M. El Agizy, 1967. "Two-Stage Programming under Uncertainty with Discrete Distribution Function," Operations Research, INFORMS, vol. 15(1), pages 55-70, February.
    4. Haihui Shen & L. Jeff Hong & Xiaowei Zhang, 2021. "Ranking and Selection with Covariates for Personalized Decision Making," INFORMS Journal on Computing, INFORMS, vol. 33(4), pages 1500-1519, October.
    5. Ma, Lijun & Zhao, Yingxue & Xue, Weili & Cheng, T.C.E. & Yan, Houmin, 2012. "Loss-averse newsvendor model with two ordering opportunities and market information updating," International Journal of Production Economics, Elsevier, vol. 140(2), pages 912-921.
    6. Weiwei Fan & L. Jeff Hong & Xiaowei Zhang, 2020. "Distributionally Robust Selection of the Best," Management Science, INFORMS, vol. 66(1), pages 190-208, January.
    7. Ilya O. Ryzhov, 2016. "On the Convergence Rates of Expected Improvement Methods," Operations Research, INFORMS, vol. 64(6), pages 1515-1528, December.
    8. Michael Arthur Leopold Pearce & Matthias Poloczek & Juergen Branke, 2022. "Bayesian Optimization Allowing for Common Random Numbers," Operations Research, INFORMS, vol. 70(6), pages 3457-3472, November.
    9. Eunhye Song & Barry L. Nelson, 2019. "Input–Output Uncertainty Comparisons for Discrete Optimization via Simulation," Operations Research, INFORMS, vol. 67(2), pages 562-576, March.
    10. Haitao Liu & Hui Xiao & Haobin Li & Loo Hay Lee & Ek Peng Chew, 2022. "Offline sequential learning via simulation," IISE Transactions, Taylor & Francis Journals, vol. 54(11), pages 1019-1032, November.
    11. Tianxiang Wang & Jie Xu & Jian-Qiang Hu, 2021. "A Study on Efficient Computing Budget Allocation for a Two-Stage Problem," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 38(02), pages 1-20, April.
    12. Siddharth Mahajan & Garrett van Ryzin, 2001. "Stocking Retail Assortments Under Dynamic Consumer Substitution," Operations Research, INFORMS, vol. 49(3), pages 334-351, June.
    13. Stephen E. Chick & Koichiro Inoue, 2001. "New Two-Stage and Sequential Procedures for Selecting the Best Simulated System," Operations Research, INFORMS, vol. 49(5), pages 732-743, October.
    14. Hui Xiao & Fei Gao & Loo Hay Lee, 2020. "Optimal computing budget allocation for complete ranking with input uncertainty," IISE Transactions, Taylor & Francis Journals, vol. 52(5), pages 489-499, May.
    15. Wang, Tianxiang & Xu, Jie & Hu, Jian-Qiang & Chen, Chun-Hung, 2023. "Efficient estimation of a risk measure requiring two-stage simulation optimization," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1355-1365.
    16. Russell R. Barton & Henry Lam & Eunhye Song, 2022. "Input Uncertainty in Stochastic Simulation," Springer Books, in: Saïd Salhi & John Boylan (ed.), The Palgrave Handbook of Operations Research, chapter 0, pages 573-620, Springer.
    17. Barry L. Nelson & Julie Swann & David Goldsman & Wheyming Song, 2001. "Simple Procedures for Selecting the Best Simulated System When the Number of Alternatives is Large," Operations Research, INFORMS, vol. 49(6), pages 950-963, December.
    18. Haidong Li & Henry Lam & Yijie Peng, 2024. "Efficient Learning for Clustering and Optimizing Context-Dependent Designs," Operations Research, INFORMS, vol. 72(2), pages 617-638, March.
    19. Jürgen Branke & Stephen E. Chick & Christian Schmidt, 2007. "Selecting a Selection Procedure," Management Science, INFORMS, vol. 53(12), pages 1916-1932, December.
    20. Di Wu & Yuhao Wang & Enlu Zhou, 2024. "Data-Driven Ranking and Selection Under Input Uncertainty," Operations Research, INFORMS, vol. 72(2), pages 781-795, March.
    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. L. Jeff Hong & Guangxin Jiang & Ying Zhong, 2022. "Solving Large-Scale Fixed-Budget Ranking and Selection Problems," INFORMS Journal on Computing, INFORMS, vol. 34(6), pages 2930-2949, November.
    2. Hu, Mingjie & Xu, Jie & Chen, Chun-Hung & Hu, Jian-Qiang, 2025. "Optimal computation budget allocation with Gaussian process regression," European Journal of Operational Research, Elsevier, vol. 322(1), pages 147-156.
    3. Gongbo Zhang & Yijie Peng & Jianghua Zhang & Enlu Zhou, 2023. "Asymptotically Optimal Sampling Policy for Selecting Top- m Alternatives," INFORMS Journal on Computing, INFORMS, vol. 35(6), pages 1261-1285, November.
    4. Jie Xu & Barry L. Nelson & L. Jeff Hong, 2013. "An Adaptive Hyperbox Algorithm for High-Dimensional Discrete Optimization via Simulation Problems," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 133-146, February.
    5. Zhongshun Shi & Siyang Gao & Hui Xiao & Weiwei Chen, 2019. "A worst‐case formulation for constrained ranking and selection with input uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(8), pages 648-662, December.
    6. Daniel Russo, 2020. "Simple Bayesian Algorithms for Best-Arm Identification," Operations Research, INFORMS, vol. 68(6), pages 1625-1647, November.
    7. Zhongshun Shi & Yijie Peng & Leyuan Shi & Chun-Hung Chen & Michael C. Fu, 2022. "Dynamic Sampling Allocation Under Finite Simulation Budget for Feasibility Determination," INFORMS Journal on Computing, INFORMS, vol. 34(1), pages 557-568, January.
    8. Peter I. Frazier, 2014. "A Fully Sequential Elimination Procedure for Indifference-Zone Ranking and Selection with Tight Bounds on Probability of Correct Selection," Operations Research, INFORMS, vol. 62(4), pages 926-942, August.
    9. Wang, Tianxiang & Xu, Jie & Hu, Jian-Qiang & Chen, Chun-Hung, 2023. "Efficient estimation of a risk measure requiring two-stage simulation optimization," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1355-1365.
    10. Batur, D. & Choobineh, F., 2010. "A quantile-based approach to system selection," European Journal of Operational Research, Elsevier, vol. 202(3), pages 764-772, May.
    11. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    12. Fei, Xin & Gülpınar, Nalân & Branke, Jürgen, 2019. "Efficient solution selection for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 277(3), pages 918-929.
    13. Cheng Li & Siyang Gao & Jianzhong Du, 2023. "Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 386-402, March.
    14. Juergen Branke & Wen Zhang, 2019. "Identifying efficient solutions via simulation: myopic multi-objective budget allocation for the bi-objective case," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(3), pages 831-865, September.
    15. Groves, Matthew & Branke, Juergen, 2019. "Top-κ selection with pairwise comparisons," European Journal of Operational Research, Elsevier, vol. 274(2), pages 615-626.
    16. Chen, E. Jack & Kelton, W. David, 2005. "Sequential selection procedures: Using sample means to improve efficiency," European Journal of Operational Research, Elsevier, vol. 166(1), pages 133-153, October.
    17. Ilya O. Ryzhov, 2016. "On the Convergence Rates of Expected Improvement Methods," Operations Research, INFORMS, vol. 64(6), pages 1515-1528, December.
    18. Stephen E. Chick & Peter Frazier, 2012. "Sequential Sampling with Economics of Selection Procedures," Management Science, INFORMS, vol. 58(3), pages 550-569, March.
    19. Kabirian, Alireza & Ólafsson, Sigurdur, 2011. "Continuous optimization via simulation using Golden Region search," European Journal of Operational Research, Elsevier, vol. 208(1), pages 19-27, January.
    20. Yijie Peng & Chun-Hung Chen & Michael C. Fu & Jian-Qiang Hu, 2016. "Dynamic Sampling Allocation and Design Selection," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 195-208, May.

    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:ejores:v:322:y:2025:i:1:p:121-132. 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/eor .

    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.