Adam Diamant

The topic of learning to solve optimization problems has received interest from both the operations research and machine learning communities. In this paper, we combine ideas from both fields to address the problem of learning to generate decisions to instances of optimization problems with potentially nonlinear or nonconvex constraints where the feasible set varies with contextual features. We propose a novel framework for training a generative model to produce provably optimal decisions by combining interior point methods and adversarial learning, which we further embed within an iterative data generation algorithm. To this end, we first train a classifier to learn feasibility and then train the generative model to produce optimal decisions to an optimization problem using the classifier as a regularizer. We prove that decisions generated by our model satisfy in-sample and out-of-sample optimality guarantees. Furthermore, the learning models are embedded in an active learning loop in which synthetic instances are iteratively added to the training data; this allows us to progressively generate provably tighter optimal decisions. We investigate case studies in portfolio optimization and personalized treatment design, demonstrating that our approach yields advantages over predict-then-optimize and supervised deep learning techniques, respectively. In particular, our framework is more robust to parameter estimation error compared with the predict-then-optimize paradigm and can better adapt to domain shift as compared with supervised learning models.

Managers are increasingly being tasked with overseeing data-driven projects that incorporate prescriptive and predictive models. Furthermore, basic knowledge of the data analytics pipeline is a fundamental requirement in many modern organizations. Given the central importance of analytics in today’s business environment, there is a growing demand for educational pedagogies that give students the opportunity to learn the fundamentals while also familiarizing them with how such tools are applied. However, a tension exists between the introduction of real-world problems that students can analyze and extract insight from and the need for prerequisite knowledge of mathematical concepts and programming languages such as Python/R. As a consequence, this paper describes an application-focused course that uses Microsoft Excel and mathematical programming to introduce MBA students with nontechnical backgrounds to tools from both prescriptive and predictive analytics. While students’ gain proficiency in managing data and creating optimization and machine learning models, they are also exposed to broader business concepts. Teaching evaluations indicate that the course has helped students further develop their practical skills in Microsoft Excel, gain an appreciation of the real-world impact of data analytics, and has introduced them to a discipline they originally believed was best suited for more technically focused professionals.

Purpose
The authors determine how the scheduling and sequencing of surgeries by surgeons impacts the rate of post-surgical complications and patient length-of-stay in the hospital.

Design/methodology/approach
Leveraging a dataset of 29,169 surgeries performed by 111 surgeons from a large hospital network in Ontario, Canada, the authors perform a matched case-control regression analysis. The empirical findings are contextualized by interviews with surgeons from the authors’ dataset.

Findings
Surgical complications and longer hospital stays are more likely to occur in technically complex surgeries that follow a similarly complex surgery. The increased complication risk and length-of-hospital-stay is not mitigated by scheduling greater slack time between surgeries nor is it isolated to a few problematic surgery types, surgeons, surgical team configurations or temporal factors such as the timing of surgery within an operating day.

Research limitations/implications
There are four major limitations: (1) the inability to access data that reveals the cognition behind the behavior of the task performer and then directly links this behavior to quality outcomes; (2) the authors’ definition of task complexity may be too simplistic; (3) the authors’ analysis is predicated on the fact that surgeons in the study are independent contractors with hospital privileges and are responsible for scheduling the patients they operate on rather than outsourcing this responsibility to a scheduler (i.e. either a software system or an administrative professional); (4) although the empirical strategy attempts to control for confounding factors and selection bias in the estimate of the treatment effects, the authors cannot rule out that an unobserved confounder may be driving the results.

Practical implications
The study demonstrates that the scheduling and sequencing of patients can affect service quality outcomes (i.e. post-surgical complications) and investigates the effect that two operational levers have on performance. In particular, the authors find that introducing additional slack time between surgeries does not reduce the odds of back-to-back complications. This result runs counter to the traditional operations management perspective, which suggests scheduling more slack time between tasks may prevent or mitigate issues as they arise. However, the authors do find evidence suggesting that the risk of back-to-back complications may be reduced when surgical pairings are less complex and when the method involved in performing consecutive surgeries varies. Thus, interspersing procedures of different complexity levels may help to prevent poor quality outcomes.

Originality/value
The authors empirically connect choices made in scheduling work that varies in task complexity and to patient-centric health outcomes. The results have implications for achieving high-quality outcomes in settings where professionals deliver a variety of technically complex services.

Home care provides personalized medical care and social support to patients within their own homes. Our work proposes a dynamic scheduling framework to assist in the assignment of health practitioners (HPs) to patients who arrive stochastically over time and are heterogeneous with respect to their health requirements, service duration, and region of residence. We model the decision of which patients to assign to HPs as a discrete-time, rolling-horizon, infinite-stage Markov decision process. Due to the curse of dimensionality and the combinatorial structure associated with an HP’s travel, we propose an approximate dynamic programming (ADP) approach based on a one-step policy improvement heuristic. Four policies are investigated: The first two prioritize HP fairness by balancing service and travel times, respectively, while the other two are based on fluid approximations of the system. We show that the first fluid model is optimal if the number of patient arrivals is sufficiently large while the second performs better experimentally; both approaches leverage pricing and decomposition strategies. We compare our framework to more commonly implemented policies—constrained versions of the classical vehicle routing problem—in a simulation study using data collected from a Canadian home care provider. We show that, in contrast to these approaches, by accounting for future uncertainty, substantial cost savings can be obtained while a fewer number of referrals are rejected. We also find that well-performing policies assign patients to HPs operating within a small set of adjacent regions while considering the number of periods that a patient requires care for. Otherwise, HP workload may not be appropriately balanced over the long-term even if travel time is minimized.

Demand for Personal Protective Equipment (PPE) such as surgical masks, gloves, and gowns has increased significantly since the onset of the COVID-19 pandemic. In hospital settings, both medical staff and patients are required to wear PPE. As these facilities resume regular operations, staff will be required to wear PPE at all times while additional PPE will be mandated during medical procedures. This will put increased pressure on hospitals which have had problems predicting PPE usage and sourcing its supply. To meet this challenge, we propose an approach to predict demand for PPE. Specifically, we model the admission of patients to a medical department using multiple independent Mt/G/∞Mt/G/∞ queues. Each queue represents a class of patients with similar treatment plans and hospital length-of-stay. By estimating the total workload of each class, we derive closed-form estimates for the expected amount of PPE required over a specified time horizon using current PPE guidelines. We apply our approach to a data set of 22,039 patients admitted to the general internal medicine department at St. Michael’s hospital in Toronto, Canada from April 2010 to November 2019. We find that gloves and surgical masks represent approximately 90% of predicted PPE usage. We also find that while demand for gloves is driven entirely by patient-practitioner interactions, 86% of the predicted demand for surgical masks can be attributed to the requirement that medical practitioners will need to wear them when not interacting with patients.

We investigate the scheduling practices of multistage outpatient health programs that offer care plans customized to the needs of their patients. We formulate the scheduling problem as a Markov decision process (MDP) where patients can reschedule their appointment, may fail to show up, and may become ineligible. The MDP has an exponentially large state space and thus, we introduce a linear approximation to the value function. We then formulate an approximate dynamic program (ADP) and implement a dual variable aggregation procedure. This reduces the size of the ADP while still producing dual cost estimates that can be used to identify favorable scheduling actions. We use our scheduling model to study the effectiveness of customized-care plans for a heterogeneous patient population and find that system performance is better than clinics that do not offer such plans. We also demonstrate that our scheduling approach improves clinic profitability, increases throughput, and decreases practitioner idleness as compared to a policy that mimics human schedulers and a policy derived from a deep neural network. Finally, we show that our approach is fairly robust to errors introduced when practitioners inadvertently assign patients to the wrong care plan.

We investigate the trade-off between acquisition and retention efforts when customers are sensitive to the quality of service they receive, i.e., whether they get timely access to a company’s resources when requested. We model the problem as a multi-class queueing network with new and returning customers, time-dependent arrivals, and abandonment. We derive its fluid approximation; a system of ordinary linear differential equations with continuous, piecewise smooth, right-hand sides. Based on the fluid model, we propose a novel approach to determine optimal stationary staffing levels for new and returning customer queues in anticipation of future time-varying dynamics. Using system accessibility as a proxy for service quality and staffing levels as a proxy for investment, we demonstrate how to apply our approach to two families of time-varying arrival functions motivated by real-world applications: an advertising campaign and a clinical setting. In a numerical study, we demonstrate that our approach creates staffing policies that maximize throughput while balancing acquisition and retention efforts more effectively (i.e., equitable abandonment from each customer class) than commonly used near-stationary methods such as segmentation-based square-root staffing policies. Our model confirms that acquisition and retention efforts are intimately linked; this has been found in empirical studies but not captured in the operations literature. We suggest that in time-varying environments, focusing on either alone is not sufficient to maintain high levels of throughput and service quality.

We determine how prediction methods combine with optimization methods in two-stage knowledge-based planning (KBP) pipelines to produce radiation therapy treatment plans. We trained two dose prediction methods, a generative adversarial network (GAN) and a random forest (RF) with the same 130 treatment plans. The models were applied to 87 out-of-sample patients to create two sets of predicted dose distributions that were used as input to two optimization models. The first optimization model, inverse planning (IP), estimates weights for dose-objectives from a predicted dose distribution and generates new plans using conventional inverse planning. The second optimization model, dose mimicking (DM), minimizes the sum of one-sided quadratic penalties between the predictions and the generated plans using several dose-objectives. Altogether, four KBP pipelines (GAN-IP, GAN-DM, RF-IP, and RF-DM) were constructed and benchmarked against the corresponding clinical plans using clinical criteria; the error of both prediction methods was also evaluated. The best performing plans were GAN-IP plans, which satisfied the same criteria as their corresponding clinical plans (78%) more often than any other KBP pipeline. However, GAN did not necessarily provide the best prediction for the second-stage optimization models. Specifically, both the RF-IP and RF-DM plans satisfied the same criteria as the clinical plans 25% and 15% more often than GAN-DM plans (the worst performing plans), respectively. GAN predictions also had a higher mean absolute error (3.9 Gy) than those from RF (3.6 Gy). We find that state-of-the-art prediction methods when paired with different optimization algorithms, produce treatment plans with considerable variation in quality.

We present an MCMC algorithm for sampling from the complement of a polyhedron. Our approach is based on the Shake-and-bake algorithm for sampling from the boundary of a set and provably covers the complement. We use this algorithm for data augmentation in a machine learning task of classifying a hidden feasible set in a data-driven optimization pipeline. Numerical results on simulated and MIPLIB instances demonstrate that our algorithm, along with a supervised learning technique, outperforms conventional unsupervised baselines.

Surgery is a knowledge intensive, high‐risk professional service. Most hospitals give surgeons considerable autonomy in deciding which patients to operate on and when. In theory, this allows surgeons the operational flexibility to prioritize surgeries based on intimate knowledge of their patient’s clinical needs. At odds with this strategy is the operations management literature, which favors the standardization and centralization of scheduling focused on achieving the efficient use of all resources, such as operating room capacity. Unfortunately, a little is known as to how surgeons customize their schedules and why they value such control. To this end, we conduct an exploratory qualitative study of the scheduling behavior of surgeons at a large Canadian teaching hospital. We identify significant differences between surgeons as to their priorities when scheduling. Two constructs are formative in surgeon decision‐making: the timeliness of treatment for their patients and idiosyncratic personal priorities. Our work has implications for achieving surgeon support for initiatives to standardize and centralize routines for patient scheduling. Accordingly, we formulate propositions that address the conditions under which such efforts will achieve the desired balance between flexibility and efficiency.

We analyze a double-sided queue with priority that serves patient customers and customers with zero patience (i.e., impatient customers). In a two-sided market, high and low priority customers arrive to one side and match with queued customers on the opposite side. Impatient customers match with queued patient customers; when there is no queue, they leave the system unmatched. All arrivals follow independent Poisson processes. We derive exact formulae for the stationary queue length distribution and several steady-state performance measures.

We investigate the scheduling practices of a medical school that must assign a cohort of students to a series of clinical rotations, while respecting both operational and quality‐of‐service requirements. Students become available to start clerkship progressively throughout the year and can complete rotations at hospitals in different geographic regions. Each hospital may offer a subset of the clinical rotations, with different start dates, capacities, and cost rates. We propose a novel network‐flow model based on decision diagrams, a graphical structure that compresses the state space of a dynamic program, to model feasible schedules. We demonstrate that our network model has several interesting structural features, is computationally superior as compared to a classical mixed‐integer linear program, and can be used to generate useful insights that can aid in managerial decision‐making. Using a dataset collected from the American University of the Caribbean, we perform a counterfactual analysis which shows that had our scheduling approach been implemented, a cost reduction of approximately 19% on average could have been achieved. To understand how assignment decisions can affect future costs, we develop a discrete‐event simulation of the licensing examination and clerkship scheduling process. We then compare our exact scheduling approach with current practice and achieve an average cost reduction of 25%. We also show that this cost reduction is robust with respect to estimation and forecast uncertainty, specifically, the licensing exam failure rate and the future cohort size.

We investigate the inventory management practices for reusable surgical instruments that must be sterilized between uses. We study a hospital that outsources their sterilization services and model the inventory process as a discrete-time Markov chain. We present two base-stock inventory models, one that considers stockout-based substitution and one that does not. We derive the optimal base-stock level for the number of reusable instruments to hold in inventory, the expected service level, and investigate the implied cost of a stockout. We apply our theoretical results to a dataset collected from a surgical unit at a large tertiary care hospital specializing in colorectal operations. We demonstrate how to implement our model when determining base-stock levels for future capacity expansion and when considering alternative stockout protocols. Our analysis suggests that the hospital can reduce the number of reusable instrument sets held in inventory if on-site sterilization techniques (e.g., flash sterilization) are employed. Our results will guide future procurement decisions for surgical units based on costs and desired service levels.

We investigate the scheduling practices of a multidisciplinary, multistage, outpatient health care program. Patients undergo a series of assessments before being eligible for elective surgery. Such systems often suffer from high rates of attrition and appointment no‐shows leading to capacity underutilization and treatment delays. We propose a new scheduling model where the clinic assigns patients to an appointment day but postpones the decision of which assessments patients undergo pending the observation of who arrives. In doing so, the clinic gains flexibility to improve system performance. We formulate the scheduling problem as a Markov decision process and use approximate dynamic programming to solve it. We apply our approach to a dataset collected from a bariatric surgery program at a large tertiary hospital in Toronto, Canada. We examine the quality of our solutions via structural results and compare them with heuristic scheduling practices using a discrete‐event simulation. By allowing multiple assessments, delaying their scheduling, and by optimizing over an appointment book, we show significant improvements in patient throughput, clinic profit, use of overtime, and staff utilization.

Increasing rates of obesity have led to growing demand for bariatric surgery. This has implications for wait times, particularly in publicly funded programs. This study examined the impact of patient and operational factors on wait times in a multidisciplinary bariatric surgery program. Methods: A retrospective study was conducted involving patients who were referred to a tertiary care centre (University Health Network, Toronto Western Hospital, Toronto) for bariatric surgery between June 2008 and July 2011. Patient characteristics, dates of clinical assessments and records describing operational changes were collected. Univariable analysis and multivariable log-linear and parametric time-to-event regressions were performed to determine whether patient and operational covariates were associated with the wait time for bariatric surgery (i.e., length of preoperative evaluation). Results: Of the 1664 patients included in the analysis, 724 underwent surgery with a mean wait time of 440 (standard deviation 198) days and a median wait time of 445 (interquartile range 298−533) days. Wait times ranged from 3 months to 4 years. Univariable and multivariable analyses showed that patients with active substance use (β =  0.3482, p  =  0.02) and individuals who entered the program in more recent operational periods (β = 0.2028, p).

We study a double-sided queue with batch arrivals and abandonment. There are two types of customers, patient ones who queue but may later abandon, and impatient ones who depart immediately if their order is not filled. The system matches units from opposite sides of the queue based on a first-come first-served policy. The model is particularly applicable to a class of alternative trading systems called crossing networks that are increasingly important in the operation of modern financial markets. We characterize, in closed form, the steady-state queue length distribution and the system-level average system time and fill rate. These appear to be the first closed-form results for a double-sided queuing model with batch arrivals and abandonment. For a customer who arrives to the system in steady state, we derive formulae for the expected fill rate and system time as a function of her order size and deadline. We compare these system- and customer-level results for our model that captures abandonment in aggregate, to simulation results for a system in which customers abandon after some random deadline. We find close correspondence between the predicted performance based on our analytical results and the performance observed in the simulation. Our model is particularly accurate in approximating the performance in systems with low fill rates, which are representative of crossing networks.

Obesity is a global epidemic, and several surgical programs have been created to combat this public health issue. Although demand for bariatric surgery has grown, so too has the attrition rate. In this study we identify patient characteristics and operational interventions that have contributed to high attrition in a multistage, multidisciplinary bariatric surgery program. Study Design
A retrospective study was conducted of 1,682 patients referred for bariatric surgery at the University Health Network in Toronto, Canada, from June 2008 to July 2011. Demographic information, presurgical assessment dates, and records describing operational changes were collected. Several penalized likelihood and mixed effects multivariable logistic regression models were used to determine whether patient characteristics, operational changes, and previous experience affected program completion and intermediate transitions between assessments. Results
Although the majority of attrition appears to be the result of patient self-removal, males (odds ratio [OR] 0.511, 95% CI 0.392 to 0.663, p < 0.001), and individuals with active substance use (OR 0.223, 95% CI 0.096 to 0.471, p < 0.001) were less likely to undergo surgery. Operational practices had a detrimental effect on program completion (OR 0.590, 95% CI 0.456 to 0.762, p < 0.001). Conversely, patients with a BMI > 40 kg/m2 (OR 1.756, 95% CI 1.233 to 2.515, p = 0.002) and those who lived within 25 to 300 km of the center (OR > 1.633, p < 0.001) were more likely to undergo surgery.