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Journal articleBertsimas D, Cory-Wright R, Lo S, et al., 2026,
Disjunctive branch-and-bound for certifiably optimal low-rank matrix completion
, INFORMS Journal on Computing, ISSN: 1091-9856Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly scalable and often identifying high-quality solutions, do not provide an instance-wise certificate of optimality. We reexamine matrix completion with an optimality-oriented eye. We reformulate low-rank matrix completion problems as convex problems over the non-convex set of projection matrices and implement a disjunctive branch-and-bound scheme that solves them to certifiable optimality. Further, we derive a novel and often near-exact class of convex relaxations by decomposing a low-rank matrix as a sum of rank-one matrices and incentivizing that two-by-two minors in each rank-one matrix have determinant zero. In numerical experiments, our new convex relaxations decrease the optimality gap by two orders of magnitude compared to existing attempts, and our disjunctive branch-and-bound scheme solves n×m rank-k matrix completion problems to certifiable optimality or near optimality in hours for max{m,n}≤2500 and k≤5. Moreover, this reduction in the training error translates into an average 2%--50% reduction in the test set error compared with alternating minimization-based methods.
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Journal articleShen Y, Chan C, Zheng F, et al., 2026,
Structural estimation of intertemporal externalities with application in ICU admissions
, Manufacturing & Service Operations Management, ISSN: 1523-4614Problem definition: In many service systems, the system manager needs to balance between addressing the needs of current customers and ensuring the system’s ability to serve future customers. Such balancing behavior is particularly important in capacity-constrained systems with heterogeneous service levels, in which the manager needs to decide which level of service to provide to the current customer, taking into account the intertemporal externalities of their decisions.Methodology/results: We develop a dynamic discrete choice model to describe the decision-making process in a gate keeper system with multiple classes of servers and customers. The discount factor in the model captures how much the decision-maker internalizes the intertemporal externalities of their customer routing decisions. In contrast to most empirical studies in the literature which use a pre-specified discount factor, we establish joint identification of the discount factor and the utility parameters from data. We then apply the model to empirically study the Intensive Care Unit (ICU)admission decisions for Emergency Department (ED) patients. Using a large hospitalization data set, we find that there is large heterogeneity in the estimated discount factors across hospitals. Via counterfactual simulations, we show that understanding the balancing behavior from data is important for hospitals to manage their ICU congestion.Managerial implications: Our results suggest that it is important to understand how the decision-maker internalizes the intertemporal externalities from data. In addition, the balancing behavior regarding current customers and future available capacity provides a potential channel for improving system performance.
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Journal articleLiu H, Wiesemann W, Yue M-C, 2026, , Operations Research, ISSN: 0030-364X
Factored Markov decision processes (MDPs) are a prominent paradigm within the artificial intelligence community for modeling and solving large-scale MDPs whose rewards and dynamics decompose into smaller, loosely interacting components. Through the use of value function approximations, dynamic Bayesian networks and context-specific independence, factored MDPs can achieve an exponential reduction in the state space of an MDP and thus scale to problem sizes that are beyond the reach of classical MDP algorithms. However, factored MDPs are typically solved using custom-designed algorithms that can require meticulous implementationsand considerable fine-tuning. In this paper, we propose a mathematical programming approach to solving factored MDPs. Unlike existing solution schemes, our approach leverages off-the-shelf solvers, which enables streamlined implementation and maintenance. Moreover, we exploit the factored structure in both state and action spaces, and we employ feature representations to unify existing methods while taking advantage of context-specific independence in problem classes that other approaches cannot solve efficiently. To further enhance scalability, we introduce a feature learning scheme that automatically identifies informative features and a dynamic basisapproximation scheme that adaptively refines our value function approximations. Our numerical experiments demonstrate the potential of our approach.
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Journal articleCao X, Hu C, Sun J, et al., 2026, , Manufacturing & Service Operations Management, Vol: 28, Pages: 1286-1306, ISSN: 1523-4614
Problem definition: Whereas artificial intelligence (AI) technologies are increasingly becoming powerful and useful in operations, human workers often resist adopting algorithms, known as algorithm aversion. This aversion can undermine the algorithm performance in practice. Whereas numerous studies explore short-term mitigation strategies for such aversion, this paper investigates whether and why forced interventions can promote AI adoption and reduce algorithm aversion in practice. Methodology/results: Data from a leading online education company reveal that sales workers underutilize a new matching algorithm and often selectively use it on low-quality leads. The company conducted a field experiment in which sales workers were forced to use or not use the algorithm for three weeks. Experimental results show that forcing workers to use the algorithm during the experiment causally increases their algorithm usage over the month after the experiment by 15.8 percentage points. We develop a theoretical model to derive empirical strategies for exploring the mechanisms behind this improvement. Contrary to the traditional literature focusing on habit formation, our findings suggest learning is a key driver for algorithm adoption among workers over the month after the experiment. Specifically, forced algorithm use allows workers to experience the unbiased algorithm performance and positively adjust their beliefs about it. Consequently, after the experiment, workers use the algorithm not only more frequently but also more on high-quality leads. Managerial implications: The study empirically shows that forced intervention can effectively improve persistent algorithm use after the intervention, which is crucial for continuous development of the algorithm. More importantly, forced intervention breaks the vicious cycle of biased beliefs and selective usage by enabling workers to form unbiased evaluation of the algorithm efficacy and mitigate selective adoption on low-quality case
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Journal articleHarutyunyan M, Koca E, 2026, , Management Science, Vol: 72, Pages: 4569-5489, ISSN: 0025-1909
In player-versus-player video games, players' natural desire to win and avoid losing has created an opportunity for game developers to sell ``pay-to-win'' add-ons, digital items that give buyers a competitive advantage against other players. In this paper, we investigate the pricing and design of a pay-to-win add-on, its effect on the base game and profit implications for the developer. When a large share of the players is less price sensitive and highly willing to buy the pay-to-win add-on, we find that, surprisingly, the developer may prefer not to introduce it. Further, when it is optimal to sell the add-on, the developer designs it to be less (more) powerful in games where players are highly (moderately) sensitive to losing. In practice, the developer may design rewards or penalties in the game to influence players' sensitivities to winning and losing, respectively. Our findings suggest that when selling a pay-to-win add-on, the developer ideally prefers players' loss-sensitivity to be neither too high nor too low, whereas high win-sensitivity tends to benefit the developer. The introduction of a pay-to-win add-on influences the optimal pricing and design of the base game. In particular, the developer decreases the base game price and may even sell it as a freemium. Despite the price reduction, investment in game quality may actually increase. From the players' perspective, our analysis shows that the introduction of a pay-to-win add-on can actually improve player surplus.In an extension of our core model, we show that the developer may prefer to customize player-to-player matching probabilities based on ownership of the pay-to-win add-on, making players who own it more likely to be matched against non-owners. However, such customization is not always optimal, and under some market conditions, the developer may optimally abstain from customizing matching probabilities. In another extension, we show that the developer may benefit from setting a negative price for
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Journal articleCollet K, Li B, Wiesemann W, et al., 2026,
A retrospective cohort study mapping real‑world psychosis care pathways and guideline adherence using integrated electronic health records
, BMJ Connections Mental HealthObjectives: To develop a systematic, data-driven approach to map patient journeys and apply this to care pathways, assessing alignment with published guidance and highlighting potential areas to improve service delivery, using the case study of first diagnosis of psychosis. Design: Using document review, an idealised patient journey was developed. Event data were extracted from electronic health records using a systematic process to map real-world patient journeys across care settings. Setting: North West London’s de-identified integrated care records system (Discover). Participants: 3,219 (mean age 37 years; 55% men) adult patients (18 to 64) registered in North West London in December 2024, with a first episode of psychosis recorded between 2016 and 2019. Main outcomes: Mapping full patient journeys, including care transitions and service contacts (i.e. psychiatric admissions, EIP involvement, and GP management). Comparison of real‑world pathways against NICE guidelines. Results: Case identification yielded demographic trends comparable with national and local level data. Two-thirds of cases had their diagnosis first recorded in primary care, with many already attending secondary care services (i.e. records may not reflect where diagnosis was clinically established). Only 18% had a clearly identifiable record of an early intervention in psychosis (EIP) service, and the recorded duration of EIP involvement varied widely. Psychiatric admission, readmission, and use of crisis and emergency services were frequent. A large proportion of patient records showed no recorded healthcare contact within either 30 days or 6 months following the index admission. The patient journey models highlighted the complexity and heterogeneity of psychosis care and were difficult to manage and visualise using available models (process maps and matrices). Conclusions: Real-world patient journeys in psychosis, as represented in electronic medical records, appear to diverge widely f
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Journal articleCory-Wright R, Pauphilet J, 2026,
Sparse PCA With multiple components
, Operations Research, ISSN: 0030-364XSparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves solving a sparsity and orthogonality constrained convex maximization problem, which is extremely computationally challenging. Most existing works address sparse PCA via methods-such as iteratively computing one sparse PC and deflating the covariance matrix-that do not guarantee the orthogonality, let alone the optimality, of the resulting solution when we seek multiple mutually orthogonal PCs. We challenge this status by reformulating the orthogonality conditions as rank constraints and optimizing over the sparsity and rank constraints simultaneously. We design tight semidefinite relaxations to supply high-quality upper bounds, which we strengthen via additional second-order cone inequalities when each PC's individual sparsity is specified. Further, we derive a combinatorial upper bound on the maximum amount of variance explained as a function of the support. We exploit these relaxations and bounds to propose exact methods and rounding mechanisms that, together, obtain solutions with a bound gap on the order of 0%-15% for real-world datasets with p = 100s or 1000s of features and r \in {2, 3} components. Numerically, our algorithms match (and sometimes surpass) the best performing methods in terms of fraction of variance explained and systematically return PCs that are sparse and orthogonal. In contrast, we find that existing methods like deflation return solutions that violate the orthogonality constraints, even when the data is generated according to sparse orthogonal PCs. Altogether, our approach solves sparse PCA problems with multiple components to certifiable (near) optimality in a practically tractable fashion.
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Journal articleTalluri K, Wang H, Li X, 2026,
Transformer choice net: a transformer neural network for choice prediction
, INFORMS Journal on Data ScienceDiscrete-choice models, such as Multinomial Logit, Probit, or Mixed-Logit, are widely used in Marketing, Economics, and Operations Research: given a set of alter natives, the customer is modeled as choosing one of the alternatives to maximize a (latent) utility function. However, extending such models to situations where the customer chooses more than one item (such as in e-commerce shopping) has proven problematic. While one can construct reasonable models of the customer’s behavior, estimating such models becomes very challenging because of a combinatorial explosion in the number of possible subsets of items. In this paper we develop a transformerneural network architecture, the Transformer Choice Net, that is suitable for predicting multiple choices. Transformer networks turn out to be especially suitable for this taskas they take into account not only the features of the customer and the items but also the context, which in this case could be the assortment as well as the customer’s past choices. On a range of benchmark datasets, our architecture shows uniformly superior out-of-sample prediction performance compared to the benchmark models in the literature, without requiring any custom modeling for each instance.Key words: Generative AI, Transformer, Choice Modeling, Deep Learning
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Journal articleShen Y, Chan CW, Zheng F, et al., 2026, , Production and Operations Management, Vol: 35, Pages: 2054-2072, ISSN: 1059-1478
In many service systems, an individual server’s workload can have a substantial impact on service time and quality. Such effects are particularly important in healthcare systems which often operate under resource and time constraints. In much of the literature, this effect of workload has been primarily considered at the system and instantaneous level rather than the individual and cumulative level. In this study, we investigate this relationship in the context of cardiac surgery, that is, how surgery duration and patient outcomes are affected by the individual surgeon’s daily workload. Using a detailed data set of more than 5,600 cardiac operations in a large hospital, we quantify how individual surgeon daily workload (the numberof operations performed by the focal surgeon) affects surgery duration and patient outcomes. To handle the endogeneity ofsurgeon daily workload, we construct instrumental variables using operational factors of the cardiac surgery department, including the regular surgery schedule of surgeons. We find that high daily workload for the focal surgeon is associated with longer surgery duration as well as post-surgery length-of-stay in the intensive care unit and hospital. These results highlight the potential negative impact of high individual surgeon workload. We develop a surgical scheduling model that incorporates the estimated impact of surgeon daily workload. We solve the model by mixed-integer quadratic programing and show that our proposed schedule can substantially reduce total operating room (OR) time and post-surgery length-of-stay. Our results suggest that hospitals should take into account the effects of individual surgeon daily workload when managing their ORs. Specifically, they can substantially improve patient flow and patient outcomes by smoothing individual surgeon’s workload across days.
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Journal articleMorton S, Manek R, Mohammadi N, et al., 2026, , British Journal of Anaesthesia, Vol: 136, Pages: 1546-1567, ISSN: 0007-0912
BackgroundOperating theatre performance is an essential component of healthcare resource optimisation. Because of its time-critical nature, emergency operating theatre performance is a problem distinct to that of elective surgery. Process performance can be quantified through the related terms: productivity, efficiency, and effectiveness. This systematic review examined the metrics used to quantify emergency operating theatre performance and the methodological quality of the associated literature.MethodsPubMed, ISI Web of Knowledge, and Embase were searched from inception to December 2024 using Medical Subject Headings terms relating to metric, performance, and operating theatre. Studies were reviewed independently for inclusion and quality (ROBINS-I and GRADE). Only clinical studies are presented here.ResultsIn total, 32 clinical studies were included, and 19 performance metrics were identified (six efficiency; 10 effectiveness; three productivity). The median (range) performance metrics per study was 4 (1–7). Frequently reported metrics were out-of-hours operating (19 studies; 59%), delay (17 studies; 53%), and utilisation (13 studies; 41%). Eleven (34%) studies were low quality and 21 (66%) were very low quality. Twenty-six (81%) studies used insufficient metrics, 30 (94%) studies used non-generalisable metrics, 29 (91%) studies did not quantify trade-off between metrics, and 16 (50%) studies had insufficient scope of investigation. Interventions evaluated included reallocating theatre time (eight studies; 25%), increasing emergency theatre capacity (eight studies; 25%), and instituting acute care surgery services (six studies; 19%).ConclusionsCurrently, there is no widely recognised framework to assess the quality of emergency theatre performance study designs. There is a tendency within clinical studies to focus on effectiveness rather than efficiency, potentially reflecting clinicians’ focus on patient outcome. Systematic biases that reduce evidenc
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