Denton, Brian T.

This paper presents a new model for online decision making. Motivated by the healthcare delivery application of dynamically allocating patients to procedure rooms in outpatient procedure centers, the online stochastic extensible bin-packing problem is described. The objective is to minimize the combined costs of opening procedure rooms and utilizing overtime to complete a day’s procedures. The dynamic patient-allocation decisions are made in an uncertain environment where the number of patients scheduled and the procedure durations are not known in advance. The resulting optimization model’s tractability focuses the paper’s attention on approximation methods and a special case that is amenable to decomposition-based solution methods. Theoretical performance guarantees are presented for list-based approximation methods as well as an approximation that is common in practice, where procedure rooms are reserved for patient groups in advance. Numerical results based on a real outpatient procedure center demonstrate the favorable results of the list-based approximations based on their average and worst case performances, as well as their computational requirements. Further, the numerical experiments show that the policy of reserving procedure rooms for patient groups in advance can perform poorly. These results are contrary to common practice and favor alternative, and still easy-to-implement, policies. The online supplement is available at https://doi.org/10.1287/ijoc.2017.0750 .

OBJECTIVE While metformin is generally accepted as the first-line agent in treatment of type 2 diabetes, there are insufficient evidence and extensive debate about the best second-line agent. We aimed to assess the benefits and harms of four commonly used antihyperglycemia treatment regimens considering clinical effectiveness, quality of life, and cost. RESEARCH DESIGN AND METHODS We developed and validated a new population-based glycemic control Markov model that simulates natural variation in HbA1c progression. The model was calibrated using a U.S. data set of privately insured individuals diagnosed with type 2 diabetes. We compared treatment intensification of metformin monotherapy with sulfonylurea, dipeptidyl peptidase-4 inhibitor, glucagon-like peptide-1 receptor agonist, or insulin. Outcome measures included life-years (LYs), quality-adjusted life-years (QALYs), mean time to insulin dependence, and expected medication cost per QALY from diagnosis to first diabetes complication (ischemic heart disease, myocardial infarction, congestive heart failure, stroke, blindness, renal failure, amputation) or death. RESULTS According to our model, all regimens resulted in similar LYs and QALYs regardless of glycemic control goal, but the regimen with sulfonylurea incurred significantly lower cost per QALY and resulted in the longest time to insulin dependence. An HbA1c goal of 7% (53 mmol/mol) produced higher QALYs compared with a goal of 8% (64 mmol/mol) for all regimens. CONCLUSIONS Use of sulfonylurea as second-line therapy for type 2 diabetes generated glycemic control and QALYs comparable with those associated with other agents but at lower cost. A model that incorporates HbA1c and diabetes complications can serve as a useful clinical decision tool for selection of treatment options.

Prostate cancer is the most common solid tumor in American men and is screened for using prostate-specific antigen (PSA) tests. We report on a nonstationary partially observable Markov decision process (POMDP) for prostate biopsy referral decisions. The core states are the patients' prostate cancer related health states, and PSA test results are the observations. Transition probabilities and rewards are inferred from the Mayo Clinic Radical Prostatectomy Registry and the medical literature. The objective of our model is to maximize expected quality-adjusted life years. We solve the POMDP model to obtain an age and belief (probability of having prostate cancer) dependent optimal biopsy referral policy. We also prove a number of structural properties including the existence of a control-limit type policy for the biopsy referral decision. Our empirical results demonstrate a nondecreasing belief threshold in age, and we provide sufficient conditions under which PSA screening should be discontinued for older patients. Finally, the benefits of screening under the optimal biopsy referral policy are estimated, and sensitivity analysis is used to prioritize the model parameters that would benefit from additional data collection.

Discrete-event simulation (DES) is an effective tool to for analyzing and improving healthcare processes. In this chapter we discuss the use of simulation to improve patient flow at an outpatient procedure center (OPC) at Mayo Clinic. The OPC addressed is the Pain Clinic, which was faced with high patient volumes in a new, untested facility. Simulation was particularly useful due to the uncertain patient procedure and recovery times. We discuss the simulation process and show how it helped reduce patient waiting time while ensuring the clinic could meet its target patient volumes.

Objective. To estimate the benefit of PSA-based screening for prostate cancer from the patient and societal perspectives. Method. A partially observable Markov decision process model was used to optimize PSA screening decisions. Age-specific prostate cancer incidence rates and the mortality rates from prostate cancer and competing causes were considered. The model trades off the potential benefit of early detection with the cost of screening and loss of patient quality of life due to screening and treatment. PSA testing and biopsy decisions are made based on the patient’s probability of having prostate cancer. Probabilities are inferred based on the patient’s complete PSA history using Bayesian updating. Data Sources. The results of all PSA tests and biopsies done in Olmsted County, Minnesota, from 1993 to 2005 (11,872 men and 50,589 PSA test results). Outcome Measures. Patients’ perspective: to maximize expected quality-adjusted life years (QALYs); societal perspective: to maximize the expected monetary value based on societal willingness to pay for QALYs and the cost of PSA testing, prostate biopsies, and treatment. Results. From the patient perspective, the optimal policy recommends stopping PSA testing and biopsy at age 76. From the societal perspective, the stopping age is 71. The expected incremental benefit of optimal screening over the traditional guideline of annual PSA screening with threshold 4.0 ng/mL for biopsy is estimated to be 0.165 QALYs per person from the patient perspective and 0.161 QALYs per person from the societal perspective. PSA screening based on traditional guidelines is found to be worse than no screening at all. Conclusions. PSA testing done with traditional guidelines underperforms and therefore underestimates the potential benefit of screening. Optimal screening guidelines differ significantly depending on the perspective of the decision maker.

Uncertainty in the duration of surgical procedures can cause long patient wait times, poor utilization of resources, and high overtime costs. We compare several heuristics for scheduling an Outpatient Procedure Center. First, a discrete event simulation model is used to evaluate how 12 different sequencing and patient appointment time‐setting heuristics perform with respect to the competing criteria of expected patient waiting time and expected surgical suite overtime for a single day compared with current practice. Second, a bi‐criteria genetic algorithm (GA) is used to determine if better solutions can be obtained for this single day scheduling problem. Third, we investigate the efficacy of the bi‐criteria GA when surgeries are allowed to be moved to other days. We present numerical experiments based on real data from a large health care provider. Our analysis provides insight into the best scheduling heuristics, and the trade‐off between patient and health care provider‐based criteria. Finally, we summarize several important managerial insights based on our findings.

Operating room (OR) scheduling is an important operational problem for most hospitals. In this study, we present a novel two-stage stochastic mixed-integer programming model to minimize total expected operating cost given that scheduling decisions are made before the resolution of uncertainty in surgery durations. We use this model to quantify the benefit of pooling ORs as a shared resource and to illustrate the impact of parallel surgery processing on surgery schedules. Decisions in our model include the number of ORs to open each day, the allocation of surgeries to ORs, the sequence of surgeries within each OR, and the start time for each surgeon. Realistic-sized instances of our model are difficult or impossible to solve with standard stochastic programming techniques. Therefore, we exploit several structural properties of the model to achieve computational advantages. Furthermore, we describe a novel set of widely applicable valid inequalities that make it possible to solve practical instances. Based on our results for different resource usage schemes, we conclude that the impact of parallel surgery processing and the benefit of OR pooling are significant. The latter may lead to total cost reductions between 21% and 59% on average.

The allocation of surgeries to operating rooms (ORs) is a challenging combinatorial optimization problem. There is also significant uncertainty in the duration of surgical procedures, which further complicates assignment decisions. In this paper, we present stochastic optimization models for the assignment of surgeries to ORs on a given day of surgery. The objective includes a fixed cost of opening ORs and a variable cost of overtime relative to a fixed length-of-day. We describe two types of models. The first is a two-stage stochastic linear program with binary decisions in the first stage and simple recourse in the second stage. The second is its robust counterpart, in which the objective is to minimize the maximum cost associated with an uncertainty set for surgery durations. We describe the mathematical models, bounds on the optimal solution, and solution methodologies, including an easy-to-implement heuristic. Numerical experiments based on real data from a large health-care provider are used to contrast the results for the two models and illustrate the potential for impact in practice. Based on our numerical experimentation, we find that a fast and easy-to-implement heuristic works fairly well, on average, across many instances. We also find that the robust method performs approximately as well as the heuristic, is much faster than solving the stochastic recourse model, and has the benefit of limiting the worst-case outcome of the recourse problem.