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Picking winners: Diversification through portfolio optimization

Author

Listed:
  • Ju Liu
  • Changchun Liu
  • Chung Piaw Teo

Abstract

We develop a general framework for selecting a small pool of candidate solutions to maximize the chances that one will be optimal for a combinatorial optimization problem, under a linear and additive random payoff function. We formulate this problem using a two‐stage distributionally robust model, with a mixed 0–1 semidefinite program. This approach allows us to exploit the “diversification” effect inherent in the problem to address how different candidate solutions can be selected to improve the chances that one will attain a high ex post payoff. More interestingly, using this distributionally robust optimization approach, our model recovers the “evil twin” strategy, well known in the field of football pool betting, under appropriate settings. We also address the computational challenges of scaling up our approach to construct a moderate number of candidate solutions to increase the chances of finding one that performs well. To this end, we develop a sequential optimization approach based on a compact semidefinite programming reformulation of the problem. Extensive numerical results show the superiority of our approach over existing methods.

Suggested Citation

  • Ju Liu & Changchun Liu & Chung Piaw Teo, 2023. "Picking winners: Diversification through portfolio optimization," Production and Operations Management, Production and Operations Management Society, vol. 32(9), pages 2864-2884, September.
  • Handle: RePEc:bla:popmgt:v:32:y:2023:i:9:p:2864-2884
    DOI: 10.1111/poms.14013
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    References listed on IDEAS

    as
    1. Xiaobo Li & Hailong Sun & Chung Piaw Teo, 2022. "Convex Optimization for Bundle Size Pricing Problem," Management Science, INFORMS, vol. 68(2), pages 1095-1106, February.
    2. Brown Mark & Sokol Joel, 2010. "An Improved LRMC Method for NCAA Basketball Prediction," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 6(3), pages 1-23, July.
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    6. Martin B. Haugh & Raghav Singal, 2021. "How to Play Fantasy Sports Strategically (and Win)," Management Science, INFORMS, vol. 67(1), pages 72-92, January.
    7. Karthik Natarajan & Chung Piaw Teo & Zhichao Zheng, 2011. "Mixed 0-1 Linear Programs Under Objective Uncertainty: A Completely Positive Representation," Operations Research, INFORMS, vol. 59(3), pages 713-728, June.
    8. Dimitris Bertsimas & Xuan Vinh Doan & Karthik Natarajan & Chung-Piaw Teo, 2010. "Models for Minimax Stochastic Linear Optimization Problems with Risk Aversion," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 580-602, August.
    9. David Bergman & Carlos Cardonha & Jason Imbrogno & Leonardo Lozano, 2023. "Optimizing the Expected Maximum of Two Linear Functions Defined on a Multivariate Gaussian Distribution," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 304-317, March.
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    13. Sarah Yini Gao & David Simchi-Levi & Chung-Piaw Teo & Zhenzhen Yan, 2019. "Disruption Risk Mitigation in Supply Chains: The Risk Exposure Index Revisited," Operations Research, INFORMS, vol. 67(3), pages 831-852, May.
    14. Zhenzhen Yan & Sarah Yini Gao & Chung Piaw Teo, 2018. "On the Design of Sparse but Efficient Structures in Operations," Management Science, INFORMS, vol. 64(7), pages 3421-3445, July.
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