Data-driven decision-making: Paradigms, methods, and challenges

Abstract

Data-driven decision-making plays an increasingly important role in engineering management and complex operational systems under uncertainty and dynamic environments. This article reviews the major paradigms in data-driven optimization, including offline learning and stochastic optimization, robust and distributionally robust optimization under small-data regimes, and adaptive online and reinforcement learning approaches. We examine the methodological foundations of these paradigms and discuss their applications in engineering management contexts. Finally, we highlight emerging research directions at the intersection of artificial intelligence and decision-making.

Graphical abstract

Keywords

data-driven optimization / stochastic optimization / distributionally robust optimization / online learning / reinforcement learning / AI for decision-making

References

[1] Abdul A T, Saravanos A D, Theodorou E A (2025). Nonlinear robust optimization for planning and control. In: 2025 IEEE 64th Conference on Decision and Control. 3383–3390

[2] AhmadiTeshnizi AGao WUdell M (2024). Optimus: Scalable optimization modeling with (MI)LP solvers and large language models. arXiv preprint arXiv:2402.10172

[3] Ahmed T, Choudhury S, (2024). LM4OPT: Unveiling the potential of Large Language Models in formulating mathematical optimization problems. INFOR, 62( 4): 559–572

[4] Alyousef M I, Sattar M U, Hasan R, Usman S, Hassan A, (2025). The Counterfactual–Dialectical Optimization Framework: A prescriptive approach to employee attrition management with empirical validation. Information, 16( 12): 1053

[5] Anis Lahoud A, Khan A S, Schaffernicht E, Trincavelli M, Stork J A, (2025). Predict-and-optimize techniques for data-driven optimization problems: A review. Neural Processing Letters, 57( 2): 40

[6] Aolaritei L, Shafiee S, Dörfler F, (2026). Wasserstein distributionally robust estimation in high dimensions: performance analysis and optimal hyperparameter tuning. Mathematical Programming, 2026: 1–85

[7] Aouali IBrunel V ERohde DKorba A (2024). Unified pac-bayesian study of pessimism for offline policy learning with regularized importance sampling. arXiv preprint arXiv:2406.03434

[8] Arora S, Hazan E, Kale S, (2012). The multiplicative weights update method: a meta-algorithm and applications. Theory of computing, 8( 1): 121–164

[9] Ban G Y, (2020). Confidence intervals for data-driven inventory policies with demand censoring. Operations Research, 68( 2): 309–326

[10] Ban G Y, Rudin C, (2019). The big data newsvendor: Practical insights from machine learning. Operations Research, 67( 1): 90–108

[11] Bayrak H İ, Koçyiğit Ç, Kuhn D, Pinar M C, (2025). Distributionally robust optimal allocation with costly verification. Operations Research, 73( 6): 3421–3439

[12] Ben-Gal S, Tzur M, (2025). Data-driven policies for the online ride-hailing problem with fairness. Transportation Science, 59( 3): 647–669

[13] Ben-Tal A, Den Hertog D, De Waegenaere A, Melenberg B, Rennen G, (2013). Robust solutions of optimization problems affected by uncertain probabilities. Management Science, 59( 2): 341–357

[14] Ben-Tal A, Nemirovski A, (1998). Robust convex optimization. Mathematics of Operations Research, 23( 4): 769–805

[15] Ben-Tal A, Nemirovski A, (1999). Robust solutions of uncertain linear programs. Operations Research Letters, 25( 1): 1–13

[16] Ben-Tal A, Nemirovski A, El Ghaoui L (2009). Robust Optimization. Princeton, NJ: Princeton University Press

[17] Bertsekas D P, (2024). Model predictive control and reinforcement learning: A unified framework based on dynamic programming. IFAC-PapersOnLine, 58( 18): 363–383

[18] Bertsimas D, Gupta V, Kallus N, (2018). Robust sample average approximation. Mathematical Programming, 171( 1): 217–282

[19] Bertsimas D, Kallus N, (2020). From predictive to prescriptive analytics. Management Science, 66( 3): 1025–1044

[20] Bertsimas D, Koduri N, (2022). Data-driven optimization: A reproducing kernel hilbert space approach. Operations Research, 70( 1): 454–471

[21] Bertsimas D, Shtern S, Sturt B, (2023). A data-driven approach to multistage stochastic linear optimization. Management Science, 69( 1): 51–74

[22] Bertsimas D, Thiele A, (2006). Robust and data-driven optimization: Modern decision making under uncertainty.

[23] Blanchet J, He F, Murthy K, (2020). On distributionally robust extreme value analysis. Extremes, 23( 2): 317–347

[24] Blanchet J, Kuhn D, Li J, Taskesen B, (2025a). .

[25] Blanchet J, Li J, Lin S, Zhang X, (2025b). Distributionally robust optimization and robust statistics. Statistical Science, 40( 3): 351–377

[26] Bubeck S, Cesa-Bianchi N, et al. (2012). Regret analysis of stochastic and nonstochastic multi-armed bandit problems. Foundations and Trends® in Machine Learning, 5( 1): 1–122

[27] Chen L, Sim M, (2025). Robust CARA optimization. Operations Research, 73( 3): 1459–1478

[28] Chen X, Miao S, Wang Y, (2023). Differential privacy in personalized pricing with nonparametric demand models. Operations Research, 71( 2): 581–602

[29] Chen Y, Xia J, Shao S, Ge D, Ye Y, (2026). Solver-informed RL: Grounding large language models for authentic optimization modeling. Advances in Neural Information Processing Systems, 38: 106027–106069

[30] Chen Z, Kuhn D, Wiesemann W, (2024). Data-driven chance constrained programs over Wasserstein balls. Operations Research, 72( 1): 410–424

[31] Cheung W C, Simchi-Levi D, (2019). Sampling-based approximation schemes for capacitated stochastic inventory control models. Mathematics of Operations Research, 44( 2): 668–692

[32] Coussement K, Abedin M Z, Kraus M, Maldonado S, Topuz K, (2024). Explainable AI for enhanced decision-making. Decision Support Systems, 184: 114276

[33] Davoodi M, Katehakis M N, Yang J, (2022). Dynamic inventory control with fixed setup costs and unknown discrete demand distribution. Operations Research, 70( 3): 1560–1576

[34] Diakonikolas I, Kane D M (2023). Algorithmic High-Dimensional Robust Statistics. Cambridge: Cambridge University Press

[35] Elmachtoub A N, Grigas P, (2022). Smart “predict, then optimize”. Management Science, 68( 1): 9–26

[36] Esteso A, Peidro D, Mula J, Díaz-Madroñero M, (2023). Reinforcement learning applied to production planning and control. International Journal of Production Research, 61( 16): 5772–5789

[37] Feng J, Ran L, Wang Z, Zhang M, (2024). Optimal energy scheduling of virtual power plant integrating electric vehicles and energy storage systems under uncertainty. Energy, 309: 132988

[38] Fügener A, Walzner D D, Gupta A, (2026). Roles of artificial intelligence in collaboration with humans: Automation, augmentation, and the future of work. Management Science, 72( 1): 538–557

[39] Gao R, Chen X, Kleywegt A J, (2024). Wasserstein distributionally robust optimization and variation regularization. Operations Research, 72( 3): 1177–1191

[40] Gao R, Kleywegt A, (2023). Distributionally robust stochastic optimization with Wasserstein distance. Mathematics of Operations Research, 48( 2): 603–655

[41] He Y, Fu H, Wu A Y, Wu H, Ding M, (2025). Enhancing resilience of distribution system under extreme weather: Two-stage energy storage system configuration strategy based on robust optimization. International Journal of Electrical Power & Energy Systems, 167: 110624

[42] Hu Y, Liu Q, Li S, Wu W, (2025). Robust emergency logistics network design for pandemic emergencies under demand uncertainty. Transportation Research Part E, Logistics and Transportation Review, 196: 103957

[43] Hu Z, Hong L J (2013). Kullback-Leibler divergence constrained distributionally robust optimization. Optimization Online, Available at the website of optimization-online.org

[44] Huang C, Tang Z, Hu S, Jiang R, Zheng X, Ge D, Wang B, Wang Z, (2025a). ORLM: A customizable framework in training large models for automated optimization modeling. Operations Research, 73( 6): 2986–3009

[45] Huang J, Shang K, Yang Y, Zhou W, Li Y, (2025b). Taylor approximation of inventory policies for one-warehouse, multi-retailer systems with demand feature information. Management Science, 71( 1): 879–897

[46] Jiang J, Ye Y, (2024). .

[47] Jiang S, Li Z, Bi S, Teo C P, Huang M, (2026). Dual sourcing made easy: distributionally robust optimization of inventory systems under independent demand. Operations Research,

[48] Jin G, Laeven R J A, den Hertog D, Ben-Tal A, (2024). .

[49] Kang Z, Li X, Li Z, Zhu S, (2019). Data-driven robust mean-CVaR portfolio selection under distribution ambiguity. Quantitative Finance, 19( 1): 105–121

[50] Kannan R, Bayraksan G, Luedtke J R, (2024). Residuals-based distributionally robust optimization with covariate information. Mathematical Programming, 207( 1): 369–425

[51] Kannan R, Bayraksan G, Luedtke J R, (2025). Data-driven sample average approximation with covariate information. Operations Research, 73( 6): 3245–3259

[52] Karimianfard H, (2025). A robust optimization framework for smart home energy management: Integrating photovoltaic storage, electric vehicle charging, and demand response. Journal of Energy Storage, 110: 115259

[53] Ke G Y, (2022). Managing reliable emergency logistics for hazardous materials: A two-stage robust optimization approach. Computers & Operations Research, 138: 105557

[54] Keyvanshokooh E, Kazemian P, Fattahi M, Van Oyen M P, (2022). Coordinated and priority-based surgical care: An integrated distributionally robust stochastic optimization approach. Production and Operations Management, 31( 4): 1510–1535

[55] Kronblad C, Essén A, Mähring M, (2024). When justice is blind to algorithms: Multilayered blackboxing of algorithmic decision-making in the public sector. Management Information Systems Quarterly, 48( 4): 1637–1662

[56] Kuhn D, Shafiee S, Wiesemann W, (2025). Distributionally robust optimization. Acta Numerica, 34: 579–804

[57] Lam H, Qian H (2018). Assessing solution quality in stochastic optimization via bootstrap aggregating. In: IEEE 2018 Winter Simulation Conference;2061–2071

[58] Levi R, Perakis G, Uichanco J, (2015). The data-driven newsvendor problem: New bounds and insights. Operations Research, 63( 6): 1294–1306

[59] Levi R, Roundy R O, Shmoys D B, (2007). Provably near-optimal sampling-based policies for stochastic inventory control models. Mathematics of Operations Research, 32( 4): 821–839

[60] Levy D, Carmon Y, Duchi J C, Sidford A, (2020). Large-scale methods for distributionally robust optimization. Advances in Neural Information Processing Systems, 33: 8847–8860

[61] Li J, Yuan J, Hao J, (2026). Distributionally robust optimal allocation of financial assets under the uncertainty and irrationality. European Journal of Operational Research, 331( 2): 666–685

[62] Li S, Tang H (2024). Multimodal alignment and fusion: A survey. arXiv preprint arXiv:2411.17040

[63] Liu F, Tong X, Yuan M, Lin X, Luo F, Wang Z, Lu Z, Zhang Q, (2024). .

[64] Liu J, Chen Z, Xu H, (2025a). Preference ambiguity and robustness in multistage decision making. Mathematical Programming, 214( 1): 847–939

[65] Liu J, Chen Z, Zhong Y, (2025b). .

[66] Liu O, Fu D, Yogatama D, Neiswanger W, (2025). Dellma: Decision making under uncertainty with large language models. International Conference on Learning Representations, 43850–43886

[67] Liyanage L H, Shanthikumar J G, (2005). A practical inventory control policy using operational statistics. Operations Research Letters, 33( 4): 341–348

[68] Long D Z, Qi J, Zhang A, (2024). Supermodularity in two-stage distributionally robust optimization. Management Science, 70( 3): 1394–1409

[69] Luo Q W, Xie M K, Wang Y, Huang S J, (2024). Optimistic critic reconstruction and constrained fine-tuning for general offline-to-online RL. Advances in Neural Information Processing Systems, 37: 108167–108207

[70] Lyu G, Teo C P, Wang Q, (2025). .

[71] Ma C, Li A, Du Y, Dong H, Yang Y, (2024). Efficient and scalable reinforcement learning for large-scale network control. Nature Machine Intelligence, 6( 9): 1006–1020

[72] Meng F, Xu H, (2006). A regularized sample average approximation method for stochastic mathematical programs with nonsmooth equality constraints. SIAM Journal on Optimization, 17( 3): 891–919

[73] Miao K E, Pesenti S M, (2025). Robust elicitable functionals. European Journal of Operational Research, 326( 2): 311–325

[74] Neria G, Tzur M, (2024). The dynamic pickup and allocation with fairness problem. Transportation Science, 58( 4): 821–840

[75] Notz P M, Pibernik R, (2022). Prescriptive analytics for flexible capacity management. Management Science, 68( 3): 1756–1775

[76] Pan J, Ye Z, Yang X, Yang X, Liu W, Wang L, Bian J, (2024). BPQP: A differentiable convex optimization framework for efficient end-to-end learning. Advances in Neural Information Processing Systems, 37: 77468–77493

[77] Passerini A, Gema A, Minervini P, Sayin B, Tentori K, (2025). Fostering effective hybrid human-LLM reasoning and decision making. Frontiers in Artificial Intelligence, 7: 1464690

[78] Pham V T D, Doan L, Binh H T T (2025). HSEvo: Elevating automatic heuristic design with diversity-driven harmony search and genetic algorithm using LLMs. In Proceedings of the 39th AAAI Conference on Artificial Intelligence,39(25), 26931–26938

[79] Putrama I M, Martinek P, (2024). Heterogeneous data integration: Challenges and opportunities. Data in Brief, 56: 110853

[80] Qin H, Simchi-Levi D, Wang L, (2022). Data-driven approximation schemes for joint pricing and inventory control models. Management Science, 68( 9): 6591–6609

[81] Remadi A, El Hage K, Hobeika Y, Bugiotti F, (2024). To prompt or not to prompt: Navigating the use of large language models for integrating and modeling heterogeneous data. Data & Knowledge Engineering, 152: 102313

[82] Sadana U, Chenreddy A, Delage E, Forel A, Frejinger E, Vidal T, (2025). A survey of contextual optimization methods for decision-making under uncertainty. European Journal of Operational Research, 320( 2): 271–289

[83] Scarf H E, Arrow K, Karlin S, (1957). .

[84] Shapiro A, Ruszczynski A, (2008). .

[85] Shehadeh K S, Cohn A E, Jiang R, (2020). A distributionally robust optimization approach for outpatient colonoscopy scheduling. European Journal of Operational Research, 283( 2): 549–561

[86] Shen H, Jiang R, (2023). Chance-constrained set covering with Wasserstein ambiguity. Mathematical Programming, 198( 1): 621–674

[87] Shin Y, Kim J, Jung W, Hong S, Yoon D, Jang Y, Kim G, Chae J, Sung Y, Lee K, Lim W, (2025). Online pre-training for offline-to-online reinforcement learning. arXiv preprint arXiv:2507.08387,

[88] Si N, Zhang F, Zhou Z, Blanchet J, (2023). Distributionally robust batch contextual bandits. Management Science, 69( 10): 5772–5793

[89] Slivkins A, Sankararaman K A, Foster D J (2023). Contextual bandits with packing and covering constraints: A modular lagrangian approach via regression. In: The 36th Annual Conference on Learning Theory, 4633–4656

[90] Smith J E, Winkler R L, (2006). The optimizer’s curse: Skepticism and postdecision surprise in decision analysis. Management Science, 52( 3): 311–322

[91] Sutter T, Van Parys B P, Kuhn D, (2020). .

[92] Terpin A, Lanzetti N, Dörfler F, (2024). Dynamic programming in probability spaces via optimal transport. SIAM Journal on Control and Optimization, 62( 2): 1183–1206

[93] Tu K, Chen Z, Yue M C, (2024). .

[94] Vredenburgh K, (2022). The right to explanation. Journal of Political Philosophy, 30( 2): 209–229

[95] Wachi A, Shen X, Sui Y, (2024). A survey of constraint formulations in safe reinforcement learning. arXiv preprint arXiv:2402.02025,

[96] Wan Y, Zhang L, Song M (2023). Improved dynamic regret for online frank-wolfe. In: the 36th Annual Conference on Learning Theory, 3304–3327

[97] Wang S, Si N, Blanchet J, Zhou Z, (2023). .

[98] Wang Y, Srivastava P R, Hanasusanto G A, Ho C P, (2026). On data-driven prescriptive analytics with side information: A regularized Nadaraya–Watson approach. Manufacturing & Service Operations Management, 28( 3): 841–859

[99] Wang Y, Yang W, Jiang W, Lu S, Wang B, Tang H, Wan Y, Zhang L, (2024a). Non-stationary projection-free online learning with dynamic and adaptive regret guarantees. Proceedings of the AAAI Conference on Artificial Intelligence, 38( 14): 15671–15679

[100] Wang Y, Zhou H, Mao D, Li L, Tan J, Han H, Yang Z, Wang A J, Li M (2024b). OR-PRM: A process reward model for algorithmic problem in operations research. The Fourteenth International Conference on Learning Representations

[101] Wang Z, Glynn P W, Ye Y, (2016). Likelihood robust optimization for data-driven problems. Computational Management Science, 13( 2): 241–261

[102] Wei J, Wang X, Schuurmans D, Bosma M, Ichter B, Xia F, Chi E, Le Q V, Zhou D, (2022). Chain-of-thought prompting elicits reasoning in large language models. Advances in Neural Information Processing Systems, 35: 24824–24837

[103] Xiao Z, Zhang D, Wu Y, Xu L, Wang Y J, Han X, Fu X, Zhong T, Zeng J, Song M, Gang C (2023). Chain-of-experts: When LLMs meet complex operations research problems. The 20th International Conference on Learning Representations

[104] Xu B, Yang G, (2025). Interpretability research of deep learning: A literature survey. Information Fusion, 115: 102721

[105] Ye H, Wang J, Cao Z, Berto F, Hua C, Kim H, Park J, Song G, (2024). Reevo: Large language models as hyper-heuristics with reflective evolution. Advances in Neural Information Processing Systems, 37: 43571–43608

[106] Ye T, Cheng S, Hijazi A, Van Hentenryck P, (2025). Contextual stochastic optimization for omnichannel multicourier order fulfillment under delivery time uncertainty. Manufacturing & Service Operations Management, 28( 4): 1068–1090

[107] Yu X, Basciftci B, (2026). Distributionally robust optimization with multimodal decision-dependent ambiguity sets. Mathematical Programming, 1: –51

[108] Zhang K, Gao X, Wang Z, Zhou S X, (2025a). Sampling-based approximation for series inventory systems. Management Science, 71( 10): 8200–8217

[109] Zhang L, Yang J, Gao R, (2024a). Optimal robust policy for feature-based newsvendor. Management Science, 70( 4): 2315–2329

[110] Zhang L, Yang J, Gao R, (2025b). A short and general duality proof for Wasserstein distributionally robust optimization. Operations Research, 73( 4): 2146–2155

[111] Zhang M, Jiao Z, Ran L, Zhang Y, (2023). Optimal energy and reserve scheduling in a renewable-dominant power system. Omega, 118: 102848

[112] Zhang X, Ye Z S, Haskell W B, (2025c). Error propagation in asymptotic analysis of the data-driven (s, S) inventory policy. Operations Research, 73( 1): 1–21

[113] Zhang Y, Dong J, (2022). Building load control using distributionally robust chance-constrained programs with right-hand side uncertainty and the risk-adjustable variants. INFORMS Journal on Computing, 34( 3): 1531–1547

[114] Zhang Y, Liu J, Li C, Niu Y, Yang Y, Liu Y, Ouyang W, (2024b). A perspective of q-value estimation on offline-to-online reinforcement learning. Proceedings of the AAAI Conference on Artificial Intelligence, 38( 15): 16908–16916

[115] Zhao M, Freeman N, Pan K, (2023). Robust sourcing under multilevel supply risks: analysis of random yield and capacity. INFORMS Journal on Computing, 35( 1): 178–195

[116] Zhong R, Xu Y, Zhang C, Yu J, (2024). Leveraging large language model to generate a novel metaheuristic algorithm with CRISPE framework. Cluster Computing, 27( 10): 13835–13869

[117] Zhou C, Xu T, Lin J, Ge D, (2025). StepORLM: A self-evolving framework with generative process supervision for operations research language models.

[118] Zinkevich M (2003). Online convex programming and generalized infinitesimal gradient ascent. In: Proceedings of the 20th international conference on machine learning; 928–936

RIGHTS & PERMISSIONS

Higher Education Press