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Problem definition: Approximately 11,000 alleged illicit massage businesses (IMBs) exist across the United States hidden in plain sight among legitimate businesses. These illicit businesses frequently exploit workers, many of whom are victims of human trafficking, forced or coerced to provide commercial sex. Academic/practical relevance: Although IMB review boards like Rubmaps.ch can provide first-hand information to identify IMBs, these sites are likely to be closed by law enforcement. Open websites like Yelp.com provide more accessible and detailed information about a larger set of massage businesses. Reviews from these sites can be screened for risk factors of trafficking. Methodology: We develop a natural language processing approach to detect online customer reviews that indicate a massage business is likely engaged in human trafficking. We label data sets of Yelp reviews using knowledge of known IMBs. We develop a lexicon of key words/phrases related to human trafficking and commercial sex acts. We then build two classification models based on this lexicon. We also train two classification models using embeddings from the bidirectional encoder representations from transformers (BERT) model and the Doc2Vec model. Results: We evaluate the performance of these classification models and various ensemble models. The lexicon-based models achieve high precision, whereas the embedding-based models have relatively high recall. The ensemble models provide a compromise and achieve the best performance on the out-of-sample test. Our results verify the usefulness of ensemble methods for building robust models to detect risk factors of human trafficking in reviews on open websites like Yelp. Managerial implications: The proposed models can save countless hours in IMB investigations by automatically sorting through large quantities of data to flag potential illicit activity, eliminating the need for manual screening of these reviews by law enforcement and other stakeholders. Funding: This work was supported by the National Science Foundation [Grant 1936331]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2023.1196 .

We model the hierarchical and decentralized nature of product transitions using a mixed-integer bilevel program with two followers, a manufacturing unit and an engineering unit. The leader, corporate management, seeks to maximize revenue over a finite planning horizon. The manufacturing unit uses factory capacity to satisfy the demand for current products. The demand for new products, however, cannot be fulfilled until the engineering unit completes their development, which, in turn, requires factory capacity for prototype fabrication. We model this interdependency between the engineering and manufacturing units as a generalized Nash equilibrium game at the lower level of the proposed bilevel model. We present a reformulation where the interdependency between the followers is resolved through the leader’s coordination, and we derive a solution method based on constraint and column generation. Our computational experiments show that the proposed approach can solve realistic instances to optimality in a reasonable time. We provide managerial insights into how the allocation of decision authority between corporate leadership and functional units affects the objective function performance. This paper presents the first exact solution algorithm to mixed-integer bilevel programs with interdependent followers, providing a flexible framework to study decentralized, hierarchical decision-making problems.

This paper is concerned with the optimal influenza vaccine distribution in a heterogeneous population consisting of multiple subgroups. We employ a compartmental model for influenza transmission and formulate a mathematical program to minimize the number of vaccine doses distributed to effectively extinguish an emerging outbreak in its early stages. We propose an equity constraint to help public health authorities consider fairness when making vaccine distribution decisions. We develop an exact solution approach that generates a vaccine distribution policy with a solution quality guarantee. We perform sensitivity analyses on key epidemic parameters in order to illustrate the application of the proposed model. We then analyze the scalability of the solution approach for a population consisting of subgroups based on geographic location and age. We finally demonstrate the proposed model’s ability to consider vaccine coverage inequity and discuss a derivative-free optimization approach, as an alternative solution method which can consider various different objective functions and constraints. Our results indicate that consideration of group-specific transmission dynamics is paramount to the optimal distribution of influenza vaccines.

Emergency disaster managers are concerned with responding to disasters in a timely and efficient manner. We are concerned with determining the location and amount of disaster relief supplies to be ...

Sepsis is the body's adverse response to infection which can lead to septic shock and eventually death if not treated in a timely manner. Analyzing patterns in sepsis patients' health status over time can help predict septic shock before its onset allowing healthcare providers to be more proactive. Temporal pattern mining methods can be used to identify trends in a patient's health status over time. If these methods return too many patterns, however, this can hinder knowledge discovery and practical implementation at the bedside in acute care settings. We propose a framework to find a small number of relevant temporal patterns in electronic health records for the early prediction of septic shock. Our framework consists of a temporal pattern mining method and three pattern selection techniques based on non-contrasted group support (PST1), contrasted group support (PST2), and model predictive power (PST3, PST4). We find that model-based feature selection approaches PST3 and PST4 yield the best prediction performance among these techniques. However, PST2 identifies more multi-state patterns with abnormal health states, which can give healthcare providers indicators of patient deterioration towards septic shock. Hence, from a knowledge discovery perspective, it may be worthwhile to sacrifice a small amount of prediction power for actionable patient health information through the implementation of PST2.

Selecting model features that would ensure adequate out-of-sample classification is difficult in real life applications of classification often because there is a large number of candidate features. We propose a bilevel programming approach to feature selection problem for classification and develop a novel genetic algorithm as a solution approach. We implement the proposed framework in three different case studies where we classify influenza strains based on antigenic variety, distinguish between good and bad quality colposcopy images, and identify splice junction sites in genetic sequences. As a benchmark for the proposed genetic algorithm, we use a derivative-free optimization method to solve the bilevel feature selection problems in these case studies. The computational experiments show that the proposed bilevel framework improves the overall classification performance while selecting the most important features for the model.

To capture ALS progression in arm, leg, speech, swallowing, and breathing segments using a disease-specific staging system, namely tollgate-based ALS staging system (TASS), where tollgates refer to a set of critical clinical events including having slight weakness in arms, needing a wheelchair, needing a feeding tube, etc. METHODS: We compiled a longitudinal dataset from medical records including free-text clinical notes of 514 ALS patients from Mayo Clinic, Rochester-MN. We derived tollgate-based progression pathways of patients up to a 1-year period starting from the first clinic visit. We conducted Kaplan-Meier analyses to estimate the probability of passing each tollgate over time for each functional segment.At their first clinic visit, 93%, 77%, and 60% of patients displayed some level of limb, bulbar, and breathing weakness, respectively. The proportion of patients at milder tollgate levels (tollgate level 2) was smaller for arm and leg segments (38% and 46%, respectively) compared to others ( 65%). Patients showed non-uniform TASS pathways, i.e., the likelihood of passing a tollgate differed based on the affected segments at the initial visit. For instance, stratified by impaired segments at the initial visit, patients with limb and breathing impairment were more likely (62%) to use bi-level positive airway pressure device in a year compared to those with bulbar and breathing impairment (26%).Using TASS, clinicians can inform ALS patients about their individualized likelihood of having critical disabilities and assistive-device needs (e.g., being dependent on wheelchair/ventilation, needing walker/wheelchair or communication devices), and help them better prepare for future.

Background The progression of many degenerative diseases is tracked periodically using scales evaluating functionality in daily activities. Although estimating the timing of critical events (i.e., disease tollgates) during degenerative disease progression is desirable, the necessary data may not be readily available in scale records. Further, analysis of disease progression poses data challenges, such as censoring and misclassification errors, which need to be addressed to provide meaningful research findings and inform patients. Methods We developed a novel binary classification approach to map scale scores into disease tollgates to describe disease progression leveraging standard/modified Kaplan-Meier analyses. The approach is demonstrated by estimating progression pathways in amyotrophic lateral sclerosis (ALS). Tollgate-based ALS Staging System (TASS) specifies the critical events (i.e., tollgates) in ALS progression. We first developed a binary classification predicting whether each TASS tollgate was passed given the itemized ALSFRS-R scores using 514 ALS patients’ data from Mayo Clinic-Rochester. Then, we utilized the binary classification to translate/map the ALSFRS-R data of 3,264 patients from the PRO-ACT database into TASS. We derived the time trajectories of ALS progression through tollgates from the augmented PRO-ACT data using Kaplan-Meier analyses. The effects of misclassification errors, condition-dependent dropouts, and censored data in trajectory estimations were evaluated with Interval Censored Kaplan Meier Analysis and Multistate Model for Panel Data. Results The approach using Mayo Clinic data accurately estimated tollgate-passed states of patients given their itemized ALSFRS-R scores (AUCs > 0.90). The tollgate time trajectories derived from the augmented PRO-ACT dataset provide valuable insights; we predicted that the majority of the ALS patients would have modified arm function (67%) and require assistive devices for walking (53%) by the second year after ALS onset. By the third year, most (74%) ALS patients would occasionally use a wheelchair, while 48% of the ALS patients would be wheelchair-dependent by the fourth year. Assistive speech devices and feeding tubes were needed in 49% and 30% of the patients by the third year after ALS onset, respectively. The onset body region alters some tollgate passage time estimations by 1–2 years. Conclusions The estimated tollgate-based time trajectories inform patients and clinicians about prospective assistive device needs and life changes. More research is needed to personalize these estimations according to prognostic factors. Further, the approach can be leveraged in the progression of other diseases.

We develop an exact value function-based approach to solve a class of bilevel integer programs with stochastic right-hand sides. We first study structural properties and design two methods to efficiently construct the value function of a bilevel integer program. Most notably, we generalize the integer complementary slackness theorem to bilevel integer programs. We also show that the value function of a bilevel integer program can be characterized by its values on a set of so-called bilevel minimal vectors. We then solve the value function reformulation of the original bilevel integer program with stochastic right-hand sides using a branch-and-bound algorithm. We demonstrate the performance of our solution methods on a set of randomly generated instances. We also apply the proposed approach to a bilevel facility interdiction problem. Our computational experiments show that the proposed solution methods can efficiently optimize large-scale instances. The performance of our value function-based approach is relatively insensitive to the number of scenarios, but it is sensitive to the number of constraints with stochastic right-hand sides.Summary of Contribution: Bilevel integer programs arise in many different application areas of operations research including supply chain, energy, defense, and revenue management. This paper derives structural properties of the value functions of bilevel integer programs. Furthermore, it proposes exact solution algorithms for a class of bilevel integer programs with stochastic right-hand sides. These algorithms extend the applicability of bilevel integer programs to a larger set of decision-making problems under uncertainty.

For ambulances, quick response to a medical emergency is critical. Limiting response area for each ambulance may lead to shorter response times to emergency scenes and more evenly distributed workload for ambulances. We propose a two-stage stochastic mixed-integer programming model to address the service district design problem under uncertainty. The proposed model recommends how to locate ambulances to the waiting sites in the service area, and how to assign a set of demand zones to each ambulance at different backup levels. Our proposed Stochastic Service District Design (SSDD) model enables quick response times by jointly addressing the location and dispatching policies in a stochastic and dynamic environment. Each backup level is associated with a given response time threshold. The objective function is to maximize the expected number of covered calls while restricting the workload of each ambulance. The proposed model can be optimized offline as is commonly done for “patrol-beats” used in policing models. We evaluate the implementation of the proposed model via a discrete-event simulation, and compare the model with two baseline policies. Our computational results show a significant improvement in mean response time, reduction of 2 min, and statistically lower average workload of ambulances, of 4% on average, when the proposed model is fully implemented.

Pancreatic cancer is a low-incidence disease, where tumor progression studies using patient longitudinal data had limited sample sizes. Estimating the tumor inverse growth rate and its distribution are a challenge. Using a tumor progression model that incorporates the distribution of the inverse growth rate as the underlying assumption of the model, pancreatic cancer progression models were built assuming two distributions for the inverse growth rate: Uniform and Gamma. This study uses simulation to evaluate the effect of the tumor inverse growth rate distribution on the tumor progression models by examining tumor timelines. It was found that the tumor timeline is about nine months longer under the assumption that the inverse growth rate follows Gamma distribution. It was inconclusive whether tumor progression is faster or slower in older patients as the tumor progression models with the different underlying assumptions on the inverse growth rate yielded opposite results.

Complex interactions between workload variability, uncertain and increasing arrival rates, and resource constraints make it difficult to improve flow through emergency departments (EDs). This complexity causes crowded EDs, long patient lengths of stay, and burnout among care providers. One way to improve efficiency while maintaining high quality care is to switch from a siloed unit-based department to a team-based design or pod system. This paper seeks to compare a pod system against the unit-based design at Southeastern Health’s ED using a discrete event simulation. Robustness of the model under a selection of staffing designs will be tested with increased arrival rates and varying mixes of severity for incoming patients. Ultimately, it is shown the pod system maintains quality of care metrics while increasing resource utilization, establishing proof of concept that an optimized pod system can improve flow in the ED.

Motivated by the U.S. influenza vaccine market, we study the impact of random yield and production capacity on the number of firms, total supply, consumer surplus and social welfare in a market with identical suppliers. We formulate a two-stage game with endogenous entry, where each entering firm aims to maximize its profit under yield uncertainty subject to a production capacity constraint. We show that if firms produce full capacity in the equilibrium, then there are fewer firms in the equilibrium compared to the social optimum even for small levels of yield uncertainty. Furthermore, we prove that if firms do not produce full capacity in the equilibrium, they will not produce full capacity in the social optimum.

Influenza (flu) is a serious public health concern. The first line of defense is the flu shot, whose composition is updated annually to adjust for frequent mutations of the circulating viruses. The...

Emergency Medical Services (EMS) managers are concerned with responding to emergency calls in a timely manner. Redeployment and dispatching strategies can be used to improve coverage that pertains ...

We consider a class of bilevel linear mixed-integer programs (BMIPs), where the follower’s optimization problem is a linear program. A typical assumption in the literature for BMIPs is that the follower responds to the leader optimally, i.e., the lower-level problem is solved to optimality for a given leader’s decision. However, this assumption may be violated in adversarial settings, where the follower may be willing to give up a portion of his/her optimal objective function value, and thus select a suboptimal solution, in order to inflict more damage to the leader. To handle such adversarial settings we consider a modeling approach referred to as $$\alpha $$ -pessimistic BMIPs. The proposed method naturally encompasses as its special classes pessimistic BMIPs and max–min (or min–max) problems. Furthermore, we extend this new modeling approach by considering strong-weak bilevel programs, where the leader is not certain if the follower is collaborative or adversarial, and thus attempts to make a decision by taking into account both cases via a convex combination of the corresponding objective function values. We study basic properties of the proposed models and provide numerical examples with a class of the defender–attacker problems to illustrate the derived results. We also consider some related computational complexity issues, in particular, with respect to optimistic and pessimistic bilevel linear programs.

Inspired by the U.S. influenza vaccine market, we formulate a Cournot competition model with asymmetric firms facing capacity constraints and yield uncertainty. We derive the equilibrium of this model by defining a score that ranks firms based on their capacity, unit production cost, random yield mean, and variance. In particular, we show a threshold structure. Firms that have scores above a threshold produce at full capacity, while other firms produce less than their capacities in the equilibrium. Finally, for the case of symmetric firms, we correct mistakes in the analysis of Deo and Corbett [Deo S, Corbett CJ (2009) Cournot competition under yield uncertainty: The case of the U.S. influenza vaccine market. Manufacturing Service Oper. Management 11(4):563–576], showing that society can benefit from supplier diversification under weaker conditions. The online appendices are available at https://doi.org/10.1287/msom.2016.0610 .

We present an equivalent value function reformulation for a class of single-ratio Fractional Integer Programs (FIPs) with stochastic right-hand sides and propose a two-phase solution approach. The first phase constructs the value functions of FIPs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of the value functions of FIPs and utilize them in our algorithms. We show that in certain cases our approach can solve instances whose extensive forms have the same order of magnitude as the largest stochastic quadratic integer programs solved in the literature.

Many dynamic decision problems involving uncertainty can be appropriately modeled as multistage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of [B. Sandikci, N. Kong, and A. J. Schaefer, Math. Program., 138 (2013), pp. 253--272] on two-stage stochastic mixed-integer programs, this paper considers general multistage stochastic programs and develops a bounding method based on scenario decomposition. This method is broadly applicable, as it does not assume any problem structure including convexity. Moreover, it naturally fits into a distributed computing environment. Computational experiments with large-scale instances (with up to 100 million scenarios, about 1.5 billion decision variables---85% binary---and 800 million constraints) demonstrate that the proposed method scales nicely with problem size and has immense potential to obtain high-quality solutions...

Stochastic programming offers a flexible modeling framework for optimal decision-making problems under uncertainty. Most practical stochastic programming instances, however, quickly grow too large to solve on a single computer, especially due to memory limitations. This chapter reviews recent developments in solving large-scale stochastic programs, possibly with multiple stages and mixed-integer decision variables, and focuses on a scenario decomposition-based bounding method, which is broadly applicable as it does not rely on special problem structure and stands out as a natural candidate for implementation in a distributed fashion. In addition to discussing the method theoretically, this chapter examines issues related to a distributed implementation of the method on a modern computing grid. Using large-scale instances from the literature, this chapter demonstrates the potential of the method in obtaining high quality solutions to very large-scale stochastic programming instances within a reasonable time frame.

Objective We aim to investigate the hypothesis that using information about which variables are missing along with appropriate imputation improves the performance of severity of illness scoring systems used to predict critical patient outcomes. Study design and setting We quantify the impact of missing and imputed variables on the performance of prediction models used in the development of a sepsis-related severity of illness scoring system. Electronic health records (EHR) data were compiled from Christiana Care Health System (CCHS) on 119,968 adult patients hospitalized between July 2013 and December 2015. Two outcomes of interest were considered for prediction: (1) first transfer to intensive care unit (ICU) and (2) in-hospital mortality. Five different prediction models were employed. Indicators were utilized in these prediction models to identify when variables were missing and imputed. Results We observed statistically significant gains in prediction performance when moving from models that did not indicate missing information to those that did. Moreover, this increase was higher in models that use summary variables as predictors compared to those that use all variables. Conclusion When developing prediction models using longitudinal EHR data, researchers should explore the incorporation of indicators for missing variables along with appropriate imputation.

Influenza vaccine composition is reviewed before every flu season because influenza viruses constantly evolve through antigenic changes. To inform vaccine updates, laboratories that contribute to the World Health Organization Global Influenza Surveillance and Response System monitor the antigenic phenotypes of circulating viruses all year round. Vaccine strains are selected in anticipation of the upcoming influenza season to allow adequate time for production. A mismatch between vaccine strains and predominant strains in the flu season can significantly reduce vaccine effectiveness. Models for predicting the evolution of influenza based on the relationship of genetic mutations and antigenic characteristics of circulating viruses may inform vaccine strain selection decisions. We review the literature on state-of-the-art tools and prediction methodologies utilized in modeling the evolution of influenza to inform vaccine strain selection. We then discuss areas that are open for improvement and need further research.

In Multiplayer Online Battle Arena (MOBA) games, teams of players compete in combat to complete an objective and defeat the opposing team. To stay alive, players must closely monitor their character's status, especially remaining health. Understanding how health may change in the near future can be vital in determining what tactics a player may use. We analyzed replay logs of the game Defense of the Ancients 2 (DotA 2) to discover methods to predict how players' health evolves over time. For DotA 2, our results suggest that forecasting changes in a player's health can be done by viewing gameplay as two separate processes: normal gameplay flow in which changes in health are smaller and more regular, and less frequent but higher-impact events in which players experience larger changes in their health, such as team battles. We accomplished this by considering health data as two separate, but interleaved, time series in which separate processes govern low magnitude changes in health from high magnitude changes. In this paper, we present a value-split approach to predicting changes in health and describe the results of our approach using autoregressive moving-average models for low magnitude health changes and a combination of statistical models for the larger changes.

Individuals are prioritized based on their risk profiles when allocating limited vaccine stocks during an influenza pandemic. Computationally expensive but realistic agent-based simulations and fast but stylized compartmental models are typically used to derive effective vaccine allocation strategies. A detailed comparison of these two approaches, however, is often omitted. We derive age-specific vaccine allocation strategies to mitigate a pandemic influenza outbreak in Seattle by applying derivative-free optimization to an agent-based simulation and also to a compartmental model. We compare the strategies derived by these two approaches under various infection aggressiveness and vaccine coverage scenarios. We observe that both approaches primarily vaccinate school children, however they may allocate the remaining vaccines in different ways. The vaccine allocation strategies derived by using the agent-based simulation are associated with up to 70% decrease in total cost and 34% reduction in the number of infections compared to the strategies derived by using the compartmental model. Nevertheless, the latter approach may still be competitive for very low and/or very high infection aggressiveness. Our results provide insights about potential differences between the vaccine allocation strategies derived by using agent-based simulations and those derived by using compartmental models.

We study a class of nonlinear bilevel knapsack problems. The upper-level objective is a nonlinear integer function of both the leader's and the follower's decision variables. At the lower level the follower solves a linear binary knapsack problem, where the right-hand side of the knapsack constraint depends on the resource allocated by the leader. After discussing computational complexity issues, we propose an exact solution approach using an equivalent single-level value function reformulation. Extensive computational experiments are performed with quadratic and fractional binary objective functions.

Seasonal influenza is a major public health concern, and the first line of defense is the flu shot. Antigenic drifts and the high rate of influenza transmission require annual updates to the flu shot composition. The World Health Organization recommends which flu strains to include in the annual vaccine, based on surveillance and epidemiological analysis. There are two critical decisions regarding the flu shot design. One is its composition; currently, three strains constitute the flu shot, and they influence vaccine effectiveness. Another critical decision is the timing of the composition decisions, which affects the flu shot production. Both of these decisions have to be made under uncertainty many months before the flu season starts. We quantify the trade-offs involved through a multistage stochastic mixed-integer program that determines the optimal flu shot composition and its timing in a stochastic and dynamic environment.We incorporate risk sensitivity through mean-risk models. Our results provide valuable insights for pressing policy issues.

The most widely used progress measure for branch-and-bound (B&B) algorithms when solving mixed-integer programs (MIPs) is the MIP gap. We introduce a new progress measure that is often much smoother than the MIP gap. We propose a double exponential smoothing technique to predict the solution time of B&B algorithms and evaluate the prediction method using three MIP solvers. Our computational experiments show that accurate predictions of the solution time are possible, even in the early stages of B&B algorithms.

We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We propose a two-phase solution approach. The first phase constructs value functions of quadratic integer programs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms. We show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature.

We introduce the bilevel knapsack problem with stochastic right-hand sides, and provide necessary and sufficient conditions for the existence of an optimal solution. When the leader's decisions can take only integer values, we present an equivalent two-stage stochastic programming reformulation with binary recourse. We develop a branch-and-cut algorithm for solving this reformulation, and a branch-and-backtrack algorithm for solving the scenario subproblems. Computational experiments indicate that our approach can solve large instances in a reasonable amount of time.