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Diabetes is a chronic disease that requires lifelong management and care, affecting around 422 million people worldwide and roughly 37 million in the United States. Patients newly diagnosed with diabetes must work with health care providers to formulate a management plan, including lifestyle modifications and regular office visits, to improve metabolic control, prevent or delay complications, optimize quality of life, and promote well-being. Our aim is to investigate one component of system-wide access to timely health care for people with diabetes in New York City (NYC), namely the length of time for someone with newly diagnosed diabetes to obtain an appointment with 3 diabetes care specialists: a cardiologist, an endocrinologist, and an ophthalmologist, respectively. We contacted the offices of 3 different kinds of specialists: cardiologists, endocrinologists, and ophthalmologists, by telephone, for this descriptive cross-sectional study, to determine the number of days required to schedule an appointment for a new patient with diabetes. The sampling frame included all specialists affiliated with any private or public hospital in NYC. The number of days to obtain an appointment with each specialist was documented, along with \"time on hold\" when attempting to schedule an appointment and the presence of online booking capabilities. Of the 1639 unique physicians affiliated with (private and public) hospitals in the 3 subspecialties, 1032 (cardiologists, endocrinologists, and ophthalmologists) were in active practice and did not require a referral. The mean wait time for scheduling an appointment was 36 (SD 36.4; IQR 12-51.5) days for cardiologists; 82 (SD 47; IQR 56-101) days for endocrinologists; and 50.4 (SD 56; IQR 10-72) days for ophthalmologists. The median wait time was 27 days for cardiologists, 72 days for endocrinologists, and 30 days for ophthalmologists. The mean time on hold while attempting to schedule an appointment with these specialists was 2.6 (SD 5.5) minutes for cardiologists, 5.4 (SD 4.3) minutes for endocrinologists, and 3.2 (SD 4.8) minutes for ophthalmologists, respectively. Over 46% (158/341) of cardiologists enabled patients to schedule an appointment on the web, and over 55% (128/228) of endocrinologists enabled patients to schedule an appointment on the web. In contrast, only approximately 25% (117/463) of ophthalmologists offered web-based appointment scheduling options. The results indicate considerable variation in wait times between and within the 3 specialties examined for a new patient in NYC. Given the paucity of research on wait times for newly diagnosed people with diabetes to obtain an appointment with different specialists, this study provides preliminary estimates that can serve as an initial reference. Additional research is needed to document the extent to which wait times are associated with complications and the demographic and socio-economic characteristics of people served by different providers.

Purpose: This study is to develop a systematic approach for determining the most efficient patient appointment scheduling (PAS) model for a specific healthcare setting with its multiple appointments requests characteristics in order to increase patients’ accessibility and resource utilization, and reduce operation cost. In this study, three general appointment scheduling models, centralized scheduling model (CSM), decentralized scheduling model (DSM) and hybrid scheduling model (HSM), are considered. Design/methodology/approach: The integration of discrete event simulation and data envelopment analysis (DEA) is applied to determine the most efficient PAS model. Simulation analysis is used to obtain the outputs of different configurations of PAS, and the DEA based on the simulation outputs is applied to select the best configuration in the presence of multiple and contrary performance measures. The best PAS configuration provides an optimal balance between patient satisfaction, schedulers’ utilization and the cost of the scheduling system and schedulers’ training. Findings: In the presence of high proportion (more than 70%) of requests for multiple appointments, CSM is the best PAS model. If the proportion of requests for multiple appointments is medium (25%-50%), HSM is the best. Finally, if the proportion of requests for multiple appointments is low (less than 15%), DSM is the best. If the proportion is in the interval from 15% to 25% the selected PAS model could be either DSM or HSM based on expert idea. Similarly, if the proportion is in the interval from 50% to 70% the best PAS model could be either CSM or HSM. Originality/value: This is the first study that determines the best PAS model for a particular healthcare setting. The proposed approach can be used in a variety of the healthcare settings. Keywords: data envelopment analysis, discrete event simulation, patient appointment scheduling, multiple appointments, centralized scheduling model, decentralized scheduling model, hybrid scheduling model

This paper studies how to schedule medical appointments with time-dependent patient no-show behavior and random service times. The problem is motivated by our studies of independent datasets from countries in two continents that unanimously identify a significant time-of-day effect on patient show-up probabilities. We deploy a distributionally robust model, which minimizes the worst-case total expected costs of patient waiting and service provider’s idling and overtime, by optimizing the scheduled arrival times of patients. This model is challenging because evaluating the total cost for a given schedule involves a linear program with uncertainties present in both the objective function and the right-hand side of the constraints. In addition, the ambiguity set considered contains discrete uncertainties and complementary functional relationships among these uncertainties (namely, patient no-shows and service durations). We show that when patient no-shows are exogenous (i.e., time-independent), the problem can be reformulated as a copositive program and then be approximated by semidefinite programs. When patient no-shows are endogenous on time (and hence on the schedule), the problem becomes a bilinear copositive program. We construct a set of dual prices to guide the search for a good schedule and use the technique iteratively to obtain a near-optimal solution. Our computational studies reveal a significant reduction in total expected cost by taking into account the time-of-day variation in patient show-up probabilities as opposed to ignoring it. This paper was accepted by David Simchi-Levi, optimization.

In this paper, we develop distribution-free models that solve the appointment sequencing and scheduling problem by assuming only moments information of job durations. We show that our min-max appointment scheduling models, which minimize the worst-case expected waiting and overtime costs out of all probability distributions with the given marginal moments, can be exactly formulated as tractable conic programs. These formulations are obtained by exploiting hidden convexity of the problem. In the special case where only the first two marginal moments are given, the problem can be reformulated as a second-order cone program. Based on the structural properties of this formulation, under a mild condition, we derive the optimal time allowances in closed form and prove that it is optimal to sequence jobs in increasing order of job duration variance. We also prove similar results regarding the optimal time allowances and sequence for the case where only means and supports of job durations are known. This paper was accepted by Dimitris Bertsimas, optimization .

Patients nationwide experience difficulties in accessing medical care in a timely manner due to long backlogs of appointments. Medical practices aim to utilize their valuable resources efficiently, deliver timely access to care, and at the same time they strive to provide short waiting times for patients present at the medical facility. We address the joint problem of determining the panel size of a medical practice and the number of offered appointment slots per day, so that patients do not face long backlogs and the clinic is not overcrowded. We explicitly model the two time scales involved in accessing medical care: appointment delay (order of days, weeks) and clinic delay (order of minutes, hours). Closed-form expressions are derived for the performance measures of interest based on diffusion approximations. Our model captures many features of the complex reality of outpatient care, including patient no-shows, balking behavior, and random service times. Our analysis provides theoretical and numerical support for the optimality of an “open access” policy in outpatient scheduling when we account for both types of delay, and it demonstrates the importance of considering panel sizing and scheduling decisions in a joint framework. This paper was accepted by Noah Gans, stochastic models and simulation .

Despite the prevalence and significance of walk-ins in healthcare, we know relatively little about how to plan and manage the daily operations of a healthcare facility that accepts both scheduled and walk-in patients. In this paper, we take a data-analytics approach and develop an optimization model to determine the optimal appointment schedule in the presence of potential walk-ins. Our model is the first known approach that can jointly handle general walk-in processes and heterogeneous, time-dependent no-show behaviors. We demonstrate that, with walk-ins, the optimal schedules are fundamentally different from those without. Our numerical study reveals that walk-ins introduce a new source of uncertainties to the system and cannot be viewed as a simple solution to compensate for patient no-shows. Scheduling, however, is an effective way to counter some of the negative impact from uncertain patient behaviors. Using data from practice, we predict a significant cost reduction (42%–73% on average) if the providers were to switch from current practice (which tends to overlook walk-ins in planning) to our proposed schedules. Although our work is motivated by healthcare, our models and insights can also be applied to general appointment-based services with walk-ins. This paper was accepted by Gad Allon, operations management.

Data availability enables clinics to use predictive analytics to improve appointment scheduling and overbooking decisions based on the predicted likelihood of patients missing their appointment (no-shows). Analyzing data using machine learning can uncover hidden patterns and provide valuable business insights to devise new business models to better meet consumers’ needs and seek a competitive advantage in healthcare. The innovative application of machine learning and analytics can significantly increase the operational efficiency of online scheduling. This study offers an intelligent, yet explainable, analytics framework in scheduling systems for primary-care clinics considering individual patients’ no-show rates that may vary for each appointment day and time while generating appointment and overbooking decisions. We use the predicted individual no-show rates in two ways: (1) a probability-based greedy approach to schedule patients in time slots with the lowest no-show likelihood, and (2) marginal analysis to identify the number of overbookings based on the no-show probabilities of the regularly-scheduled patients. We find that the summary measures of profit and cost are considerably improved with the proposed scheduling approach as well as an increase in the number of patients served due to a substantial decrease in the no-show rate. Sensitivity analysis confirms the effectiveness of the proposed dynamic scheduling framework even further.

Motivated by the rising popularity of electronic appointment booking systems, we develop appointment scheduling models that take into account the patient preferences regarding when they would like to be seen. The service provider dynamically decides which appointment days to make available for the patients. Patients arriving with appointment requests may choose one of the days offered to them or leave without an appointment. Patients with scheduled appointments may cancel or not show up for the service. The service provider collects a \"revenue\" from each patient who shows up and incurs a \"service cost\" that depends on the number of scheduled appointments. The objective is to maximize the expected net \"profit\" per day. We begin by developing a static model that does not consider the current state of the scheduled appointments. We give a characterization of the optimal policy under the static model and bound its optimality gap. Building on the static model, we develop a dynamic model that considers the current state of the scheduled appointments, and we propose a heuristic solution procedure. In our computational experiments, we test the performance of our models under the patient preferences estimated through a discrete choice experiment that we conduct in a large community health center. Our computational experiments reveal that the policies we propose perform well under a variety of conditions.

This paper examines patient preferences and choice behavior in scheduling medical appointments. We conduct four discrete choice experiments on two distinct populations and identify several “operational” attributes (e.g., delay to care and choice of doctor) that affect patient choice. We observe an interesting gender effect with respect to how patients trade off speed (delay to care) and quality (doctor of choice), and demonstrate that risk attitudes mediate the impact of gender on the perception of speed and quality. Specifically, females (versus males) are more averse to not seeing their own doctor, and, when delay to care is relatively long, females perceive greater utility loss than males. As many operational strategies in outpatient care aim to improve the patient experience by making trade-offs between speed and quality, we make suggestions for when managers should intervene to improve their practice and how such interventions might look based on the patient mix and current delay level. The online appendix is available at https://doi.org/10.1287/mnsc.2016.2704 . This paper was accepted by Gad Allon, operations management.

Service systems are often stochastic and preplanned by appointments, yet implementations of their appointment systems are prevalently deterministic. At the planning stage of healthcare services, for example, customer punctuality and service durations are often assumed equal their means—and this gap, between planned and reality, motivated our research. Specifically, we consider appointment scheduling and sequencing under a time-varying number of servers, in a data-rich environment where service durations and punctuality are uncertain. Our data-driven approach, based on infinite-server queues, yields tractable and scalable solutions that accommodate hundreds of jobs and servers. We successfully test our approach against near-optimal algorithms (which exist for merely single-servers). This entails the development of a data-driven robust optimization approach with novel uncertainty sets. To test for practical performance, we leverage a unique data set from a cancer center that combines real-time locations, electronic health records, and appointments log. Focusing on one of the center’s infusion units (roughly 90 daily appointments, 25+ infusion chairs), we reduce cost (waiting plus overtime) on the order of 15%–40% consistently, under a wide range of experimental setups. This paper was accepted by Assaf Zeevi, stochastic models and simulation.