My research lies at the interface of data analytics, operations research, and artificial intelligence. Many decision-making problems in today's real-world environments need to be informed by potentially unreliable, scarce, partially observable, and nonstationary data while considering complex objectives and constraints. In many circumstances, it remains unclear how to leverage this data in systematic and optimal ways. My research focuses on developing new data-driven optimization methods, as well as predictive and prescriptive models, to address these complex decision-making problems that arise in high-impact applications. I have successfully deployed these methods in a broad range of applications, including organ allocation, epidemic modeling and COVID vaccine prioritization, modeling and predicting rare events, WHO-EPI vaccine distribution, real-time resource allocation, and fairness and flexibility in supply chain operations. I served as the Principal Investigator for research grants from the National Science Foundation, Office of Naval Research and DARPA that supported my research. The following are some examples of the research themes that I have worked on.
Optimization and predictive analytics techniques for health policy
Data-driven optimization for complex data environment
Optimization approaches for supply chain design
Data-driven optimization for partially observable, nonstationary data environments: Conventional data-driven decision-making methods rely on complete, well-structured data. However, data can be noisy, partially observable, and nonstationary in practice. In many circumstances, it is challenging to leverage such data systematically and optimally. Therefore, I devised new paradigms for data-driven modeling and decision-making by combining ideas from robust/distributionally robust optimization, statistics, and machine learning. In [1,2,3], we develop joint learning and optimization frameworks that can handle issues brought by missing and nonstationary data and outperform traditional estimate-then-optimize paradigms. The core of these paradigms is distributionally robust optimization. These methods provide substantial modeling capacities and computational and theoretical enhancements.
Data-driven inventory policy: Learning from sequentially observed non-stationary data. K. Ren*, H. Bidkhori, and Z.J.M. Shen. OMEGA - The International Journal of Management Science, 2024.
A study on distributionally robust optimization with incomplete joint data. K. Ren*, and H. Bidkhori. European Journal of Operational Research, 2023 .
Data-driven two-stage stochastic programming with marginal data. K. Ren*, and H. Bidkhori. Proceedings of the Winter Simulation Conference (WSC), 2021.
Distributionally robust optimization as a scalable framework to characterize extreme value distributions and model rare events: Modeling rare and extreme events is critical across various disciplines, including finance, climate science, and medicine. Rare events, such as earthquakes, tsunamis, pandemics, stock market crashes, and currency crises, occur infrequently, yet their impact is profound when they do. Extreme value theory (EVT) provides statistical principles that can be used to extrapolate tail distributions and consequently, to estimate extreme quantiles. While powerful, these models are only asymptotically valid for large samples. However, since extreme data is scarce by definition, the potential for model misspecification error is inherent to these applications. To address this limitation, I worked together with students and postdocs and my colleagues Profs. Jose Blanchet (Stanford University) and Vahid Tarokh (Duke University) to develop distributionally robust optimization (DRO) estimators, specifically for multidimensional EVT statistics. To achieve computational tractability, we have studied both tractable convex formulations for some estimators of interest (e.g., conditional value-at-risk) and more general neural network-based estimators. We validated both approaches by using synthetically generated data, recovering prescribed characteristics, and verifying the efficacy of the proposed techniques. We applied the proposed method to a real dataset of financial returns for comparison to previous analyses.
Distributionally robust optimization as a scalable framework to characterize extreme value distributions. P. Kuiper*, V. Tarokh, W. Yang, J. Blanchet, A. Hasan*, Y. Ng*, and H. Bidkhori. The Conference on Uncertainty in Artificial Intelligence, 2024.
Utilizing optimization and predictive analytics techniques in kidney exchange: Patients with end-stage renal failure often find kidney donors who are willing to donate a life-saving kidney, but who are medically incompatible with the patient. Kidney exchange, a barter market, facilitates swaps between patients and donors. There are many sources of uncertainty in real kidney exchanges—due to medical, moral, and policy factors and can severely impact the outcome of an exchange. We have designed robust algorithms to reduce the impact of uncertainties [5,6,7] and increase the number of transplants resulting from kidney exchange. We considered two types of uncertainty: 1) weight uncertainty (the utility of matches is not known) and 2) failure uncertainty (planned trades can fail). Formulated as an optimization problem, the deterministic kidney exchange is NP-hard, and researchers have developed practical algorithms to solve this problem in a reasonable amount of time. Incorporating uncertainty into this optimization problem adds an additional layer of complexity to the original problem and makes it more computationally challenging. We devised computationally efficient optimization algorithms for kidney exchange under uncertainty and demonstrated these methods’ effectiveness using the United Network of Organ Sharing (UNOS) data.
5. Scalable robust kidney exchange. D.C. McElfresh*, H. Bidkhori, and J.P. Dickerson. Conference on Artificial Intelligence (AAAI), 2019.
6. Kidney exchange with inhomogeneous edge existence uncertainty. H. Bidkhori, J. P. Dickerson, D. C. McElfresh*, and K. Ren*. The Conference on Uncertainty in Artificial Intelligence, 2020.
7. Distributionally robust cycle and chain packing with application to organ exchange. D. C. McElfresh*, K. Ren*, H. Bidkhori, and J. P. Dickerson. Proceedings of the Winter Simulation Conference (WSC), 2021.
Utilizing optimization and predictive analytics techniques in epidemic analysis: The SEIR (susceptible-exposed-infected-recovered) model has become a valuable tool for studying infectious disease dynamics and predicting the spread of diseases, especially since it was used during the COVID pandemic. The existing SEIR models often oversimplify population characteristics and fail to account for differences in disease sensitivity and social contact rates that can vary significantly among individuals. Together with my Ph.D. student, Yingze Hou, we developed a new multi-feature SEIR model [8,9] that considers the heterogeneity of health conditions and social activity levels among populations affected by infectious diseases. We validated our model using data from confirmed COVID cases in Allegheny County (Pennsylvania, USA) and Hamilton County (Ohio, USA). The results demonstrated that our model outperforms traditional SEIR models in terms of forecasting and predictive accuracy. We also used our multi-feature SEIR model to propose and evaluate different vaccine prioritization strategies tailored to heterogeneous populations. We demonstrated that our new multi-feature SEIR model enhances existing models and provides a more accurate picture of disease dynamics, which can help inform public health interventions during pandemics and epidemics.
8. Multi-feature SEIR model for epidemic analysis and vaccine prioritization. Y. Hou*, and H. Bidkhori. PLOS ONE, 2024.
9. Feature-modified SEIR model for pandemic simulation and evaluation for intervention approaches. Y. Hou*, and H. Bidkhori. Proceedings of the Winter Simulation Conference (WSC), 2022. (Nominated for the best student paper award)
Robust and distributionally robust optimization for supply chain flexibility: Flexibility is one of the most important strategies companies employ to respond to uncertainties and changes. Various types of flexibility exist, such as process flexibility, which is defined as the ability to “build different types of products in the same plant at the same time.” While effective, full process flexibility requires a significant investment. Therefore, most companies (including car manufacturing companies) are only willing to implement sparse or limited flexibility designs. In [10], we designed new tools to analyze the performance of various process flexibility structures, taking a different approach to study the worst expected sales of flexibility structures under a class of stochastic demand distributions with limited information. We developed a distribution-free model to evaluate the performance of process flexibility structures when only the mean and partial expectations of the demand are known. In [11], we considered process flexibility under disruptions. Most existing literature on partial flexibility only considers demand uncertainty, yet many companies also face disruption uncertainty (e.g., natural disasters). Therefore, we considered various disruption scenarios and developed a robust optimization framework to address the question of designing profitable and resilient flexibility in the face of disruptions and demand uncertainty.
10. Analysis of process flexibility designs under disruptions. E. Mehmanchi*, H. Bidkhori, and O. Prokopyev. IISE Transactions, 2020.
11. Analyzing process flexibility: a distribution-free approach with partial expectation. H. Bidkhori, D. Simchi-Levi, and Y. Wei. Operations Research Letters, 44 (3), 291-296, 2016.
Robust optimization for equity-driven facility location problem: Over the past years, I have sought to develop the mathematical and computational tools necessary to apply these optimization frameworks to decision-making problems that arise in many application domains [12, 13]. In [12], together with collaborators at UBC, we considered issues of equity in robust facility location models to explore how uncertainty exacerbates inequity and to examine several equity measures for robust facility location modeling. We considered the p-median facility location problem. Including equity introduces complexity due to the involvement of piecewise linear functions. To address this challenge, we reframed the problem into a tractable two-stage robust optimization model. We explored various equity metrics, analyzed their cost implications, and provided a schematic representation for benchmark and clarity. From a methodological standpoint, we introduced two solution algorithms that underwent rigorous testing across a range of equity-driven models and network sizes. Our numerical analysis demonstrated the efficacy of the two-stage approach in handling the inherent complexity of the problem. We examined well-known literature benchmark datasets to highlight the effectiveness and applicability of our strategies.
12. Equity-driven facility location problem under uncertainty: a robust optimization approach. M. Li*, A. A. Digehsara, A. Ardestani-Jaafari, and H. Bidkhori. Computers & Operations Research, 2024.
13. On the performance of affine policies for two-stage adaptive optimization: a geometric perspective. D. Bertsimas, and H. Bidkhori. Mathematical Programming, 2015.