We deal with a retailer's multi-product inventory system where customers randomly seek acceptable substitutes if their initial requests are not satisfied. Unsuccessful quests for substitutes would result in lost sales. Motivated by a consulting project as well as other real practices, we also choose to deal with further challenges posed by initially unknown base demand distributions and substitution probabilities; moreover, we aim to develop an offline learning method that (i) takes advantage of given data derived from bygone decisions rather than of any learning-while-doing opportunity, (ii) makes inferences about base-demand distributions and pairwise substitution probabilities without knowing whether there have been demand arrivals after inventory depletions, and (iii) is unhindered by the lack of knowledge about the assortments faced by customers and their purchase-or-no-purchase decisions at their individual arrivals. To address these challenges, we propose an innovative approach based on the Kaplan-Meier estimator that circumvents unrealistic data requirements. Our substitution probability estimates employ carefully designed weighting schemes to facilitate rigorous theoretical analysis through tools such as the Cauchy-Schwartz inequality. Both one-time substitution scenarios and more complex Markov-chain substitution patterns would be accommodated. Using large deviation tools, we establish provably optimal convergence rates of our estimates on top of consistency. The precision in parameter estimates would translate into accuracy in replenishment decisions. For inventory management, we take advantage of a submodularity property to obtain an exact algorithm for the two-product case and a good heuristic for the general multi-product problem. Computational studies based on simulated and actual data confirm the merits of our approach.

Retail datasets often contain both numerical features and semantic labels, such as store locations, product names, and dates of sales, that implicitly encode external demand drivers but are typically treated as opaque categorical codes. We propose a Deep Fractile Newsvendor framework that combines decision-focused neural learning with LLM-based feature discovery. On the decision side, rather than training a neural network to predict order quantities directly, we use the empirical mixture distribution (EMD) as a distribution-side prior and the cost-implied critical ratio (fractile) as a decision-side prior. The network with feature input learns only a bounded, dimensionless adjustment around the cost-implied critical fractile, and the resulting adjusted fractile is mapped back through the EMD to obtain the order quantity. This formulation constrains decisions within the historical demand range, reduces scale sensitivity, and discourages large deviations, and is stabilized by Conditional Value-at-Risk (CVaR) regularization in limited-sample settings. On the feature side, an LLM serves as a semantic-to-source mapper: it interprets semantic labels and identifies verifiable external data sources (e.g., a meteorological API), from which numerical features are retrieved. A profit-based selection loop retains only features that improve profit. Across four datasets spanning three countries and three languages, adding quality-checked LLM-discovered external candidates followed by profitbased selection improves validation-period profit significantly when informative semantic labels, such as store locations, dates of sales, and product names, are present. In synthetic-data experiments, our fractile adjustment approach yields lower regret than the tested benchmarks when sample sizes are limited.

Retail data encompasses numerical variables and semantic labels (e.g., store locations, product names, and temporal data) that capture external demand drivers but are traditionally reduced to opaque categorical codes. The problem is twofold: we convert these semantic labels into informative features, then optimize data-driven newsvendor decisions. We propose a Deep Fractile Newsvendor framework integrating an LLM-based semantic-to-source mapper with decision-focused neural learning. The LLM identifies verifiable external data sources from semantic labels; numerical features are then retrieved and retained if they enhance profit. For ordering, we use the empirical mixture distribution (EMD) and the cost-implied critical fractile as priors; the model learns only a bounded, dimensionless fractile adjustment and maps it through the EMD to the order quantity. Across three real-world datasets, external-feature integration significantly improves out-of-sample profits in two cases; gains are marginal in the third because managers already captured key external drivers. Overall, the proposed fractile policy matches or outperforms established benchmarks. By utilizing LLMs to discover verifiable data sources---rather than generating demand forecasts or ordering decisions---this framework enables managers to enrich sparse operational data while maintaining transparent, stable, and auditable inventory policies.

We study the problem of appointment scheduling for outpatient clinical services, where patient arrivals, appointment cancellations, and attendance are inherently random, leading to high variability in patient flow. Analyzing dynamic scheduling decisions is particularly challenging due to the need to track confirmed appointments within the scheduling window. For planning with a long horizon, we show that a probabilistic allocation policy can be efficiently computed by optimizing a closed-form function. This policy ensures that the system's long-term profit asymptotically approaches the optimal profit in scalable settings. For a limited planning horizon, we propose a sequential assignment process implemented with a predetermined scheduling diagram. We characterize the conditions under which this scheduling diagram policy achieves optimality. Notably, an improved scheduling diagram policy emerges as a refinement of either a probabilistic allocation policy or a same-day scheduling policy, and we prove that it is optimal for two-day scheduling windows. The computation of the scheduling diagrams is straightforward, as it involves ranking the margins (i.e., first-order differences) of scalar profit functions, one for each day in the scheduling window. Extensive simulation analyses suggest that system efficiency can be achieved through a hybrid strategy, where a two-day policy is applied to a short scheduling window and an improved probabilistic policy is used for a long scheduling window.

We consider the single-item, periodic-review inventory system with stochastic demand, an all-or-nothing random yield pattern, and non-zero leadtimes, where the unmet demand is backlogged. The firm’s objective is to find an optimal ordering policy to minimize its total expected discounted cost. As the optimal policy remains unknown, we first develop a new heuristic that takes advantage of the all-or-nothing yield pattern and then propose a deep reinforcement learning (DRL) algorithm based on a tailored neural network model. The proposed DRL algorithm combines the results of existing heuristics to improve performance and stabilize the training process. Moreover, the total cost to be computed is convex in the decision variable, which facilitates the search. Extensive numerical experiments show that our new solution methods outperform known heuristics and demonstrate near-optimal performance when leadtimes are relatively short and the minimal cost can be achieved numerically.

Lifetime Value (LTV) prediction is critical in advertising, recommender systems, and e-commerce. In practice, LTV data patterns vary across decision scenarios. As a result, practitioners often build complex, scenario-specific pipelines and iterate over feature processing, objective design, and tuning. This process is expensive and hard to transfer. We propose AgentLTV, an agent-based unified search-and-evolution framework for automated LTV modeling. AgentLTV treats each candidate solution as an executable pipeline program. LLM-driven agents generate code, run and repair pipelines, and analyze execution feedback. Two decision agents coordinate a two-stage search. The Monte Carlo Tree Search (MCTS) stage explores a broad space of modeling choices under a fixed budget, guided by the Polynomial Upper Confidence bounds for Trees criterion and a Pareto-aware multi-metric value function. The Evolutionary Algorithm (EA) stage refines the best MCTS program via island-based evolution with crossover, mutation, and migration. Experiments on a large-scale proprietary dataset and a public benchmark show that AgentLTV consistently discovers strong models across ranking and error metrics. Online bucket-level analysis further indicates improved ranking consistency and value calibration, especially for high-value and negative-LTV segments. We summarize practitioner-oriented takeaways: use MCTS for rapid adaptation to new data patterns, use EA for stable refinement, and validate deployment readiness with bucket-level ranking and calibration diagnostics. The proposed AgentLTV has been successfully deployed online.

The gaming industry has emerged as a critical force in the digital content economy, yet managing user behavior to drive sustained activity and monetization remains a complex operational challenge. In this study, we propose a two-layer hidden Markov model to capture users' gameplay and payment behaviors by constructing a play-then-pay chain that links user engagement to subsequent purchase intention dynamics. Drawing on a real-world dataset, we uncover three levels of engagement states measuring the degree of stickiness with the focal game, as well as two levels of purchase intention states describing one's willingness to pay. We find that a higher engagement state is associated with a volatile transition pattern and leads to a higher upward transition tendency in purchase intention, while low and medium engagement states tend to maintain a low purchase intention state. We also examine several factors that affect the transitions of these psychological states. The analysis reveals that user activity in same-type games enhances upward transitions only among users in the medium engagement state, without affecting users in the high engagement state, and exhibits no significant effect on purchase intentions. In contrast, user activity in different types of games has a negative effect on users in both low and high engagement states. Our state-dependent outcomes suggest that the managers' strategies are more effective when targeted toward users with low engagement and purchase intention states. Further experimental analysis supports the effectiveness of the proposed play-then-pay chain for predicting users' behaviors. Our policy simulation demonstrates that traffic subsidization effectively redirects user attention to the focal game, with interventions targeting different-type games yielding greater improvements in propensities for both gameplay and payment behavior compared to same-type games. Our work provides managerial implications for platform managers.

Dynamic treatment regimes improve health outcomes by tailoring each treatment to a patient’s evolving condition, but they also allow providers to learn and game the system over time. How should insurers pay? We study this new class of reimbursement problems, where the provider can privately learn and manipulate the progression of the patient’s condition. (i) We characterize the optimal payment policy: it internalizes two intertemporal effects of each treatment, and rewards provider honesty with incentive pay; moreover, it admits a simple implementation of risk-adjusted cost-sharing policy. (ii) We show that, ignoring dynamic learning and gaming, the existing payment models may have overestimated the harm of information asymmetry. Using the optimal policy, insurers only need to pay for initial private information; they can exploit provider uncertainty and elicit future private information at no cost. (iii) Our study informs U.S. healthcare payment reform with new insights; using two sets of real data, our study also quantifies when and why the optimal policy outperforms the existing ones. By highlighting the critical role of dynamic learning and gaming, this study advances our understanding of healthcare payment theory and practice.

Background The adverse health impacts of ambient temperature have been well-documented, encompassing not only the mortality and morbidity burden but also mood and mental health disorders. However, the relationship between temperature and social isolation remains unexplored. The objective of the current study was to investigate the potential associations between ambient temperature and social isolation among the aging population. Methods We took advantage of a cross-sectional survey conducted between January 2017 and November 2018 from a community service program special for older adults aged ≥60 who lived in a central community of Hong Kong. The personal social isolation was assessed by the validated Lubben Social Network Scale-6 (LSNS-6), with a score ranging from 0 to 30 and score of less than 12 indicating social isolation. The environmental exposures, including ambient temperature, sunshine hours, rainfalls, and air pollution, were obtained from the nearby monitoring stations. The association of ambient temperature with LSNS-6 score or social isolation was examined by the generalized linear models while adjusting the potential confounding from other environmental exposures and personal sociodemographic factors. Results Among the 1,616 participants, the distribution of LSNS-6 score was approximately normal and the mean score was a bit higher on cool days than on hot days (13.0 vs. 12.2). Compared with cool temperatures (14.4–19.5oC), the independent effect estimates of hot ambient temperatures (24.5–28.7oC) was associated with a 2.38 (95%CI: 1.63–3.13) decrease in LSNS-6 score. Meanwhile, we observed statistically significant associations of sunshine exposure, gender, health status, marital status, living alone, religion, and housing type with LSNS-6 score or social isolation. Conclusions Our study revealed a clear association between ambient cool temperatures and reduced social isolation, as well as association between hot temperatures and social isolation among older Chinese adults residing in the urban community of Hong Kong.

In fashion, food processing, petrochemical production, and agriculture, products (items) are often bundled in a prefixed assortment, with a given ratio for each product. For example, one case of men’s shoes may contain 24 pairs of different sizes of the same design. Of the 24 pairs, there is one size 7 pair, four sizes 9, and so on. Moreover, those pairs of shoes are packaged independently for retailing. Retailers of such products order them in bundles and then resell them unbundled. In this study, we propose and analyze a newsvendor model in which a retailer decides the order quantity of the whole bundle before the uncertain demand for each product/item is realized. We call it a product unbundling newsvendor problem (PUNP): How should the retailer decide the ordering quantity of a product bundle to meet the unknown demands of individual items to maximize its expected profit? We approach this problem with a robust optimization approach that assumes the means and covariance matrix of stochastic demands but not the demand distributions. However, the robust approach that considers the worst-case demand scenario is perceived to be conservative. In this study, we incorporate the distributionally robust optimization with deep reinforcement learning (DRL) and propose a new paradigm of robust learning to improve the robust decision quality. We take this robust solution, that is, the order quantity and profit, as human domain knowledge and implement it into the decision-making process of DRL by designing a policy transfer mechanism. Unsurprisingly, the exact robust solution is computationally intractable; thus, we provide an approximate solution. Simulations were conducted based on limited data sizes, confirming that our approach effectively improves robust performance. Moreover, the hybrid approach significantly outperforms the DRL approach. In the meantime, reduced computing costs and increased interpretability of decision recommendations may facilitate the deployment of DRL algorithms in operational practice. Furthermore, the successful application of the hybrid approach in addressing several variants of the PUNP indicates that the proposed mechanism may provide a pathway for solving complex operational problems.

Abstract Background A large proportion of older adults suffer from chronic diseases. Health coaching is a promising intervention that enhances individuals’ health knowledge and supports changes in health behaviours. Even though health professionals usually conduct health coaching interventions, lay health workers from different backgrounds account for a growing segment of health coaches over the years. The planned study’s main objective is to investigate whether health coaching by lay health workers is as effective as that by health professionals. Methods The effects of health coaching intervention by lay health workers will be examined in comparison with that by health professionals within a single-blind, multi-centre, randomised controlled trial with a follow-up assessment after 3 months. A total of 380 community-dwelling older adults with chronic diseases will be recruited and randomly assigned using a 1:1 ratio into the intervention and control groups. The intervention group will receive a 3-month health coaching intervention delivered by lay health workers, whereas the control group will receive the intervention delivered by health professionals. Primary outcomes include patient activation, physical activity and nutrition behaviours. Discussion The expected findings of this study will advance the health coaching literature, research and practice by determining whether health coaching by lay health workers is as effective as that by health professionals in enhancing older adults’ knowledge, skills and confidence in chronic disease self-management and promoting changes in health behaviours. If proven effective, the inclusion of lay health workers in delivering effective self-management interventions should be advocated to reduce the over-reliance on health professionals in the primary healthcare system. Trial registration ISRCTN, ISRCTN73836238. Registered 8 November 2023.

ABSTRACTObjectiveEnhancing patient response to immune checkpoint inhibitors (ICIs) is crucial in cancer immunotherapy. We aim to create a data-driven mathematical model of the tumor immune microenvironment (TIME) and utilize deep reinforcement learning (DRL) to optimize patient-specific ICI therapy combined with chemotherapy (ICC).MethodsUsing patients’ genomic and transcriptomic data, we develop an ordinary differential equations (ODEs)-based TIME model to characterize interactions among chemotherapy, ICIs, immune cells, and cancer cells. A DRL algorithm is trained to determine the personalized optimal ICC therapy.ResultsNumerical experiments with real-world data demonstrates that the proposed TIME model can predict ICI therapy response. The DRL-derived personalized ICC therapy outperforms predefined fixed schedules. For tumors with extremely low CD8+T cell infiltration (“extremely cold tumors”), DRL recommends high-dosage chemotherapy alone. For tumors with higher CD8+T cell infiltration (“cold” and “hot tumors”), an appropriate chemotherapy dosage induces CD8+T cell proliferation, enhancing ICI therapy outcomes. Specifically, for “hot tumors,” chemotherapy and ICI are administered simultaneously, while for “cold tumors,” a mid-dosage of chemotherapy makes the TIME “hotter” before ICI administration. However, a number of “cold tumors” with rapid resistant cancer cell growth, ICC eventually fails.ConclusionThis study highlights the potential of utilizing real-world clinical data and DRL to develop personalized optimal ICC by understanding the complex biological dynamics of a patient’s TIME. Our ODE-based TIME model offers a theoretical framework for determining the best use of ICI, and the proposed DRL model may guide personalized ICC schedules.SIGNIFICANCE STATEMENTOur research presents a novel data-driven approach to personalized cancer treatment by combining artificial intelligence and mathematical models of the tumor’s surrounding environment, known as the tumor immune microenvironment (TIME). This innovative method allows for the optimization of patient-specific immune checkpoint inhibitors and combined chemotherapy therapy. By utilizing deep reinforcement learning, our approach can adapt and improve treatment strategies for individual patients, ultimately maximizing the effectiveness of cancer therapies. This pioneering work has the potential to significantly enhance clinical decision-making and improve patient outcomes, paving the way for personalized cancer immunotherapy.

BackgroundScreening for frequent hospitalizations in the community can help prevent super-utilizers from growing in the inpatient population. However, the determinants of frequent hospitalizations have not been systematically examined, their operational definitions have been inconsistent, and screening among community members lacks tools. Nor do we know if what determined frequent hospitalizations before COVID-19 continued to be the determinant of frequent hospitalizations at the height of the pandemic. Hence, the current study aims to identify determinants of frequent hospitalization and their screening items developed from the Comprehensive Geriatric Assessment (CGA), as our 273-item CGA is too lengthy to administer in full in community or primary care settings. The stability of the identified determinants will be examined in terms of the prospective validity of pre-COVID-selected items administered at the height of the pandemic.MethodsComprehensive Geriatric Assessments (CGAs) were administered between 2016 and 2018 in the homes of 1,611 older adults aged 65+ years. Learning models were deployed to select CGA items to maximize the classification of different operational definitions of frequent hospitalizations, ranging from the most inclusive definition, wherein two or more hospitalizations over 2 years, to the most exclusive, wherein two or more hospitalizations must appear during year two, reflecting different care needs. In addition, the CGA items selected by the best-performing learning model were then developed into a random-forest-based scoring system for assessing frequent hospitalization risk, the validity of which was tested during 2018 and again prospectively between 2022 and 2023 in a sample of 329 older adults recruited from a district adjacent to where the CGAs were initially performed.ResultsSeventeen items were selected from the CGA by our best-performing algorithm (DeepBoost), achieving 0.90 AUC in classifying operational definitions of frequent hospitalizations differing in temporal distributions and care needs. The number of medications prescribed and the need for assistance with emptying the bowel, housekeeping, transportation, and laundry were selected using the DeepBoost algorithm under the supervision of all operational definitions of frequent hospitalizations. On the other hand, reliance on walking aids, ability to balance on one’s own, history of chronic obstructive pulmonary disease (COPD), and usage of social services were selected in the top 10 by all but the operational definitions that reflect the greatest care needs. The prospective validation of the original risk-scoring system using a sample recruited from a different district during the COVID-19 pandemic achieved an AUC of 0.82 in differentiating those rehospitalized twice or more over 2 years from those who were not.ConclusionA small subset of CGA items representing one’s independence in aspects of (instrumental) activities of daily living, mobility, history of COPD, and social service utilization are sufficient for community members at risk of frequent hospitalization. The determinants of frequent hospitalization represented by the subset of CGA items remain relevant over the course of COVID-19 pandemic and across sociogeography.

BackgroundHomecare, a cornerstone of public health, is essential for health systems to achieve the Sustainable Development Goal (SDG) of universal health coverage while maintaining its own sustainability. Notwithstanding homecare’s system-level significance, there is a lack of economic evaluations of homecare services in terms of their system-wide cost-savings. Specifically, decisions informed by a joint medical-social budgetary perspective can maximize the allocative efficiency of assigning a diverse service mix to address the complex needs of the older adult population. However, little is known regarding which homecare service mix is most system-wide cost-effective when paired with which clinical profiles.MethodsValuation of homecare’s complex interventions was performed under a generalized cost-effectiveness analysis (GCEA) framework with proportional hazard-adjusted metrics representing the common numeraire between medical and social care.ResultsInstrumental homecare, on its own or combined with either one or both of the other homecare services, yielded the greatest cost savings compared to other services or the lack thereof. When expressed under a joint medical-social budgetary perspective, instrumental homecare can reduce medical costs of HK$34.53 (US$4.40) and HK$85.03 (US$10.84) for every HK$1 (US$0.13) invested in instrumental and instrumental-restorative homecare, respectively.ConclusionInstrumental homecare can increase hospitalization-free days among community-dwelling older adult and yield significant net system-wide cost savings. Thus, the current study demonstrated the feasibility of data-informed decision-making in system-wide resource allocation under a joint medical-social budget perspective.

Abstract Health coaching appears as a promising intervention to initiate behavioural change and improve health outcomes for outpatients (Krok-Schoen et al., 2017; Sharma et al., 2016). However, its effectiveness in improving self-management of chronic diseases were mainly examined in young and middle-aged adults with specific chronic diseases (Lin et al., 2021; Tülüce & Kutlutürkan, 2018). Whether health coaching is still effective in community-dwelling older adults, particular those with lower education and multiple chronic diseases, remains uncertain. This study thereby aims to examine the effects of a health coaching intervention in a sample of 194 older Hong Kong Chinese adults (Mage = 79.1, SD = 6.90, range = 62–95). Depending on their health needs, participants received 12 – 18-week home-based health coaching intervention during July 2022 – July 2024. Their patient activation, physical activity, nutrition behaviours, loneliness, and depression were measured before and immediately after the intervention. Repeated measures ANCOVAs showed that participation in the health coaching intervention significantly increased patient activation and nutrition-related health behaviours, and reduced loneliness and depression. Theses results remained significant even after controlling for age, sex, education, living arrangement, receipt of community centre and home care services, numbers of chronic diseases, polypharmacy, and frequency of intervention sessions. The findings of this study thus revealed beneficial effects of health coaching in enhancing older adults’ competence in managing their health, engagement in health behaviours, and psychological well-being. Policymakers and health-related professionals should implement health coaching in the primary healthcare system to maintain older adults’ well-being and promote ageing-in-place.