Brian T. Denton

A SEQUENTIAL BOUNDING APPROACH FOR OPTIMAL APPOINTMENT SCHEDULING

This study is concerned with the determination of optimal appointment times for a sequence of jobs with uncertain durations. Such appointment systems are used in many customer service applications to increase the utilization of resources, match workload to available capacity, and smooth the flow of customers. We show that the problem can be expressed as a two-stage stochastic linear program that includes the expected cost of customer waiting, server idling, and a cost of tardiness with respect to a chosen session length. We exploit the problem structure to derive upper bounds that are independent of job duration distribution type. These upper bounds are used in a variation of the standard L-shaped algorithm to obtain optimal solutions via successively finer partitions of the support of job durations. We present new analytical insights into the problem as well as a series of numerical experiments that illustrate properties of the optimal solution with respect to distribution type, cost structure, and number of jobs.

Optimal Allocation of Surgery Blocks to Operating Rooms Under Uncertainty

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.

Operating Room Pooling and Parallel Surgery Processing Under Uncertainty

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.

Simulation of a multiple operating room surgical suite

Outpatient surgery scheduling involves the coordination of several activities in an uncertain environment. Due to the very customized nature of surgical procedures there is significant uncertainty in the duration of activities related to the intake process, surgical procedure, and recovery process. Furthermore, there are multiple criteria which must be traded off when considering how to schedule surgical procedures including patient waiting, operating room (OR) team waiting, OR idling, and overtime for the surgical suite. Uncertainty combined with the need to tradeoff many criteria makes scheduling a complex task for OR managers. In this article we present a simulation model for a multiple OR surgical suite, describe some of the scheduling challenges, and illustrate how the model can be used as a decisions aid to improve strategic and operational decision making relating to the delivery of surgical services. All results presented are based on real data collected at Mayo Clinic in Rochester, MN

Dynamic Appointment Scheduling of a Stochastic Server with Uncertain Demand

We formulate and solve two new stochastic linear programming formulations of appointment scheduling problems that are motivated by the management of health services. We assume that service durations and the number of customers to be served on a particular day are uncertain. In the first model, customers may fail to show up for their appointments “no-show”. This model is formulated as a two-stage stochastic linear program. In the second model, customers are scheduled dynamically, one at a time, as they request appointments. This model is formulated as a multistage stochastic linear program with stages defined by customer appointment requests. We analyze the structure of the models and adapt decomposition-based algorithms to solve the problems efficiently. We present numerical results that illustrate the impact of uncertainty on dynamic appointment scheduling, and we identify useful insights that can be applied in practice. We also present a case study based on real data for an outpatient procedure center.

A Discrete Event Simulation Model to Evaluate Operational Performance of a Colonoscopy Suite

Background and Aims. Colorectal cancer, a leading cause of cancer death, is preventable with colonoscopic screening. Colonoscopy cost is high, and optimizing resource utilization for colonoscopy is important. This study’s aim is to evaluate resource allocation for optimal use of facilities for colonoscopy screening. Method. The authors used data from a computerized colonoscopy database to develop a discrete event simulation model of a colonoscopy suite. Operational configurations were compared by varying the number of endoscopists, procedure rooms, the patient arrival times, and procedure room turnaround time. Performance measures included the number of patients served during the clinic day and utilization of key resources. Further analysis included considering patient waiting time tradeoffs as well as the sensitivity of the system to procedure room turnaround time. Results. The maximum number of patients served is linearly related to the number of procedure rooms in the colonoscopy suite, with a fixed room to endoscopist ratio. Utilization of intake and recovery resources becomes more efficient as the number of procedure rooms increases, indicating the potential benefits of large colonoscopy suites. Procedure room turnaround time has a significant influence on patient throughput, procedure room utilization, and endoscopist utilization for varying ratios between 1:1 and 2:1 rooms per endoscopist. Finally, changes in the patient arrival schedule can reduce patient waiting time while not requiring a longer clinic day. Conclusions. Suite managers should keep a procedure room to endoscopist ratio between 1:1 and 2:1 while considering the utilization of related key resources as a decision factor as well. The sensitivity of the system to processes such as turnaround time should be evaluated before improvement efforts are made.

Optimizing the Start Time of Statin Therapy for Patients with Diabetes

Background . Clinicians often use validated risk models to guide treatment decisions for cardiovascular risk reduction. The most common risk models for predicting cardiovascular risk are the UKPDS, Framingham, and Archimedes models. In this article, the authors propose a model to optimize the selection of patients for statin therapy of hypercholesterolemia, for patients with type 2 diabetes, using each of the risk models. For each model, they evaluate the role of age, gender, and metabolic state on the optimal start time for statins. Method . Using clinical data from the Mayo Clinic electronic medical record, the authors construct a Markov decision process model with health states composed of cardiovascular events and metabolic factors such as total cholesterol and high-density lipoproteins. They use it to evaluate the optimal start time of statin treatment for different combinations of cardiovascular risk models and patient attributes. Results . The authors find that treatment decisions depend on the cardiovascular risk model used and the age, gender, and metabolic state of the patient. Using the UKPDS risk model to estimate the probability of coronary heart disease and stroke events, they find that all white male patients should eventually start statin therapy; however, using Framingham and Archimedes models in place of UKPDS, they find that for male patients at lower risk, it is never optimal to initiate statins. For white female patients, the authors also find some patients for whom it is never optimal to initiate statins. Assuming that age 40 is the earliest possible start time, the authors find that the earliest optimal start times for UKPDS, Framingham, and Archimedes are 50, 46, and 40, respectively, for women. For men, the earliest optimal start times are 40, 40, and 40, respectively. Conclusions . In addition to age, gender, and metabolic state, the choice of cardiovascular risk model influences the apparent optimal time for starting statins in patients with diabetes.

Second-line Agents for Glycemic Control for Type 2 Diabetes: Are Newer Agents Better?

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.

Optimal booking and scheduling in outpatient procedure centers

Patient appointment booking, sequencing, and scheduling decisions are challenging for outpatient procedure centers due to uncertainty in procedure times and patient attendance. We extend a previously developed appointment scheduling model to formulate a model based on a two-stage stochastic mixed integer program for optimizing booking and appointment times in the presence of uncertainty. The objective is to maximize expected profit. Analytical insights are reported for special cases and experimental results show that they provide useful rules of thumb for more general problems. Three solution methods are described which take advantage of the underlying structure of the stochastic program, and a series of experiments are performed to determine the best method. A case study based on an endoscopy suite at a large medical center is used to draw a number of useful managerial insights for procedure center managers.

IBM Solves a Mixed-Integer Program to Optimize Its Semiconductor Supply Chain

IBM Systems and Technology Group uses operations research models and methods extensively for solving large-scale supply chain optimization (SCO) problems for planning its extended enterprise semiconductor supply chain. The large-scale nature of these problems necessitates the use of computationally efficient solution methods. However, the complexity of the models makes developing robust solution methods a challenge. We developed a mixed-integer programming (MIP) model and supporting heuristics for optimizing IBMs semiconductor supply chain. We designed three heuristics, driven by practical applications, for capturing the discrete aspects of the MIP. We leverage the model structure to overcome computational hurdles resulting from the large-scale problem. IBM uses the model and method daily for operational and strategic planning decisions and has saved substantial costs.