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Optimising the queuing system for an ear, nose and throat outpatient clinic
Journal of Applied Statistics
Abstract
Several authors have considered the problem of the efficient running of hospital outpatient clinics. The first solution was probably by Welch & Bailey (1952). More recent authors include Fetter & Thompson (1966), Vissers (1979), Stafford & Aggarwal (1979). The Ear, Nose and Throat outpatient clinic presents a special case due to the complex queuing structure involved, which is described in the next section. A simulation of this special clinic was undertaken, any useful theoretical results being impossible to obtain.
... Previous studies have also investigated allocation decisions that assign fixed appointment intervals with fixed block sizes, as well as a more complex system with varying block sizes (Cox, Birchall, & Wong, 1985;Fetter & Thompson, 1966;Fries & Marathe, 1981;Srinivas & Ravindran, 2020). Fries and Marathe (1981) introduced the variable block fixed interval allocation system and showed that it could reduce the weighted cost by up to 40% as opposed to a multi-block assignment. ...
... On the other hand, several works accounted for the distinct classes in the patient population and used them to develop sequencing rules (Cayirli & Veral, 2003). Some of the classes used to sequence patients include patient status (new vs. return patients), service time variability (i.e., low vs. high variance), and type of procedure (Cox et al., 1985;Lau & Lau, 2000;Lehaney, Clarke, & Paul, 1999). For instance, Cayirli and Veral (2003) showed that sequencing new patients from the beginning perform well for multi-block fixed interval rules, while sequencing return patients from the beginning is best suited for individual block fixed interval allocation system. ...
... Moreover, to maintain continuity of care, the clinic typically allows a provider to serve only his/her own patients. Therefore, similar to prior works, this clinic can be represented as a single-stage single-server system (Cox et al., 1985;Rising, Baron, & Averill, 1973). The clinic experiences an average noshow rate of 30% and double-books proportional to it to compensate for missed appointments. ...
This research considers the design of an appointment system (AS) for sequentially scheduling patients in the presence of stochastic factors (no-show and service time uncertainty) and two patient classes. Although studies on AS design are prevalent in literature, most prior works do not consider heterogeneous patient characteristics (e.g., patient-specific no-show risk and service time duration) and sequential patient call-ins together. This research integrates patient-specific uncertainty estimates into the AS design and assess its impact on AS efficiency (measured as the weighted sum of patient waiting time, doctor idle time, and overtime). Specifically, the patients are scheduled as they sequentially call the clinic for appointments based on their risk of no-show and estimated consultation duration. For this setting, a predict-then-schedule framework is proposed. In the predict step, patient-specific no-show risk and service duration are estimated using a machine learning model. The schedule step determines each patient’s appointment time and interval by integrating the predictions with three scheduling decisions (allocation, sequencing, and overbooking). As a result, new sequencing rules are employed. Results indicate that adopting the predict-then-schedule approach in a sequential framework always dominates conventional approaches and could improve the efficiency by 60%.
... Treatment strategy: Priority first come, first served (PFCFS) is popularly used in studies of health systems [17]. In PFCFS, patients with appointment are prioritized over walk-ins and within their respective groups, patients are served in order of their arrival, i.e., FCFS; compare [56,19]. Patients that arrive before the beginning o(λ) ∈ T of session λ ∈ Λ have to wait and the physician does not start treatments until the session has officially begun. ...
... SiM-Care accounts for the age dependency of various patient characteristics through the concept of age classes. The baseline scenario differentiates three patient age classes: young (16)(17)(18)(19)(20)(21)(22)(23)(24), middleaged , and elderly (>65). The characteristics of the modeled age classes A are shown in Table 7. Young patients (16)(17)(18)(19)(20)(21)(22)(23)(24) are, on average, the healthiest among all patients. ...
... The baseline scenario differentiates three patient age classes: young (16)(17)(18)(19)(20)(21)(22)(23)(24), middleaged , and elderly (>65). The characteristics of the modeled age classes A are shown in Table 7. Young patients (16)(17)(18)(19)(20)(21)(22)(23)(24) are, on average, the healthiest among all patients. Thus, they are expected to develop the fewest acute illnesses per year from which they recover relatively quickly. ...
Demand for health care is constantly increasing due to the ongoing demographic change, while at the same time health service providers face difficulties in finding skilled personnel. This creates pressure on health care systems around the world, such that the efficient, nationwide provision of primary health care has become one of society's greatest challenges. Due to the complexity of health care systems, unforeseen future events, and a frequent lack of data, analyzing and optimizing the performance of health care systems means tackling a wicked problem. To support this task for primary care, this paper introduces the hybrid agent-based simulation model SiM-Care. SiM-Care models the interactions of patients and primary care physicians on an individual level. By tracking agent interactions, it enables modelers to assess multiple key indicators such as patient waiting times and physician utilization. Based on these indicators, primary care systems can be assessed and compared. Moreover, changes in the infrastructure, patient behavior, and service design can be directly evaluated. To showcase the opportunities offered by SiM-Care and aid model validation, we present a case study for a primary care system in Germany. Specifically, we investigate the effects of an aging population, a decrease in the number of physicians, as well as the combined effects.
... Earlier works usually investigate the added value of patient classification over a single appointment rule using limited criteria based on service time characteristics only. Some commonly used classification schemes include "new/return," "long/short consultation," and "low/high variance" patients (Walter 1973;Cox et al. 1985;Klassen and Rohleder 1996;Vanden Bosch and Dietz 2000;Cayirli et al. 2006Cayirli et al. , 2008. ...
... 274-295, © 2014 INFORMS as the patient's age, physical mobility, or type of service. Cox et al. (1985) investigate several approaches on sequencing new and return patients in an ear, nose, and throat clinic, and they report that the proposed AS improves clinic performance in terms of utilization and patient wait times. Klassen and Rohleder (1996) use simulation to test sequencing approaches for patient groups with different service time variances but equal mean service times. ...
... The latter scenario represents a more adverse situation where 50% of patients are late. These parameters are chosen within the ranges reported by empirical studies, which confirm that patients are usually on time or early for their appointments (Blanco White and Pike 1964, Fetter and Thompson 1966, Cox et al. 1985, Harper and Gamlin 2003, Williams et al. 2014. ...
This study evaluates patient classification for scheduling and sequencing appointments for patients differentiated by their mean and standard deviation of service times, no-show, and walk-in probabilities. Alternative appointment systems are tested through simulation using a universal Dome rule and some of the best traditional appointment rules in the literature. Our findings show that the universal Dome rule performs better in terms of reducing the total cost of patient's waiting time, doctor's idle time, and overtime, and its performance improves further with the right sequencing of patient groups. Although it is a challenge to find the best sequence, we propose a heuristic rule that successfully identifies the best sequence with an accuracy level of 98% for the universal Dome rule. Sensitivity analyses further confirm that our findings are valid even when assumptions on patient punctuality and service time distributions are relaxed. To facilitate the use of our proposed appointment system, an open source online tool is developed to support practitioners in designing their appointment schedules for real clinics.
... Earlier works usually investigate the added value of patient classification over a single appointment rule using limited criteria based on service time characteristics only. Some commonly used classification schemes include "new/return," "long/short consultation," and "low/high variance" patients (Walter 1973;Cox et al. 1985;Klassen and Rohleder 1996;Vanden Bosch and Dietz 2000;Cayirli et al. 2006Cayirli et al. , 2008. ...
... 274-295, © 2014 INFORMS as the patient's age, physical mobility, or type of service. Cox et al. (1985) investigate several approaches on sequencing new and return patients in an ear, nose, and throat clinic, and they report that the proposed AS improves clinic performance in terms of utilization and patient wait times. Klassen and Rohleder (1996) use simulation to test sequencing approaches for patient groups with different service time variances but equal mean service times. ...
... The latter scenario represents a more adverse situation where 50% of patients are late. These parameters are chosen within the ranges reported by empirical studies, which confirm that patients are usually on time or early for their appointments (Blanco White and Pike 1964, Fetter and Thompson 1966, Cox et al. 1985, Harper and Gamlin 2003, Williams et al. 2014. ...
This study evaluates patient classification for scheduling and sequencing appointments for patients differentiated by their mean and standard deviation of service times, no-show and walk-in probabilities. Alternative appointment systems are tested through simulation, using a universal Dome rule and some of the best traditional appointment rules in the literature. Our findings show that the universal Dome rule performs better in terms of reducing the total cost of patient’s waiting time, doctor’s idle time and overtime and its performance improves further with the right sequencing of patient groups. While it is a challenge to find the best sequence, we propose a heuristic rule which successfully identify the best sequence with an accuracy level of 98% for the universal Dome rule. Sensitivity analyses further confirm that our findings are valid even when assumptions on patient punctuality and service time distributions are relaxed. To facilitate the use of our proposed appointment system, an open source online tool is developed to support practitioners in designing their appointment schedules for real clinics.
... The baseline scenario differentiates three patient age classes: young (16)(17)(18)(19)(20)(21)(22)(23)(24), middle-aged , and elderly (> 65). The characteristics of the modeled age classes A are shown in Table 9. ...
... The priority first come, first served (PFCFS) treatment strategy is popularly used in studies of health systems [17]. In PFCFS, patients with appointment are prioritized over walk-ins and within their respective groups, patients are served in order of their arrival, i.e., FCFS; compare [19,52]. Patients that arrive before the beginning o(λ) ∈ T of session λ ∈ have to wait and the physician does not start treatments until the session has officially begun. ...
Primary care systems are a cornerstone of universally accessible health care. The planning, analysis, and adaptation of primary care systems is a highly non-trivial problem due to the systems’ inherent complexity, unforeseen future events, and scarcity of data. To support the search for solutions, this paper introduces the hybrid agent-based simulation model SiM-Care. SiM-Care models and tracks the micro-interactions of patients and primary care physicians on an individual level. At the same time, it models the progression of time via the discrete-event paradigm. Thereby, it enables modelers to analyze multiple key indicators such as patient waiting times and physician utilization to assess and compare primary care systems. Moreover, SiM-Care can evaluate changes in the infrastructure, patient behavior, and service design. To showcase SiM-Care and its validation through expert input and empirical data, we present a case study for a primary care system in Germany. Specifically, we study the immanent implications of demographic change on rural primary care and investigate the effects of an aging population and a decrease in the number of physicians, as well as their combined effects.
... Bailey's rule has been found to perform well in many situations (Blanco White and Pike, 1964;Ho and Lau, 1992). Multiple block fixed interval (MBFI) appointment rules in which an equal number of multiple patients are allocated to each appointment slot of equal length have been proposed by Soriano (1966), Blanco White and Pike (1964), Cox et al. (1985), and Liu and Liu (1998). Multiple block variable interval (MBVI) rules have also been proposed in the literature (Fries and Marathe, 1981). ...
... According to the classification of the patients, different sequencing rules and also different lengths of the appointment intervals may be decided (Cayirli et al., 2008). Patients may be distinct in terms of characteristics, such as arrival rates, service time distribution, mean service time, service time variability, no-show probability and punctuality (Cox et al., 1985;Rohleder and Klassen, 2000;Vanden Bosch and Dietz, 2000;Turkcan et al., 2011;Akin et al., 2013). Other factors for classifying patients, such as patient's age, sex and type of investigation/procedure, and the source of arrival of patients (outpatients, inpatients, emergency) and priorities based on urgency have also been suggested in the literature (Green et al., 2006;Patrick and Puterman, 2007;Sickinger and Kolish, 2009;Min and Yih, 2010;Qu et al., 2013). ...
Appointment scheduling plays a key role in improving the performance of a healthcare facility and increasing patient access to healthcare. However, appointment systems in hospitals may receive requests for services from walk-ins and emergency arrivals in addition to the scheduled arrivals. Emergency arrivals need urgent care, and hence have higher priority to be served over the scheduled arrivals. Such emergency arrivals disrupt the scheduled appointments, and may increase the waiting times of scheduled patients and the overtime of the appointment session. Walk-ins have lower priority to be served. However, it is desirable to serve walk-ins in order to increase the utilization of the server keeping the waiting times of scheduled patients as short as possible. In this research work, appropriate sequencing and appointment rules are identified for a Computed tomography (CT) – scan facility that experiences walk-in and emergency arrivals apart from regular scheduled arrivals. Several scheduling rules are evaluated under different patterns of walk-ins and emergency arrivals. In addition, the main and interaction effects of scheduling rules and arrival patterns of unscheduled patients are explored. It is found that the scheduling rules are more influential than the arrival patterns of unscheduled patients.
... Recently, Tai and Williams (2012) model patient unpunctuality as a constructed F3 distribution, which is a combination of some common distributions (normal and lognormal distributions) and their modified forms with consideration of various patient behaviour patterns. Some studies also use empirical data to approximate this distribution, for example, the family of Johnson distribution (Alexopoulos et al. 2008), normal distribution Rosen 2006, 2008) or exponential distribution (Cox, Birchall, and Wong 1985). Koeleman and Koole (2012) noted that most papers on the design of appointment scheduling systems assume patient punctuality. ...
... Now we assume that the patient unpunctuality which is the time difference between their actual arrival and appointment time follows a general distribution. Some studies use empirical data to approximate this distribution, for example, family of Johnson distribution (Alexopoulos et al. (2008)), normal distribution (Cayirli, Veral, and Rosen (2006) and Cayirli, Veral, and Rosen (2008)), or exponential distribution (Cox, Birchall, and Wong (1985)). ...
This study examines the design of appointment scheduling policies with considerations of not only the conventional factors, for example, the random consultation time and multiple patient types, but also of a new factor, particularly, patient unpunctuality, that is, one patient may arrive earlier or later than the appointment time. Patient unpunctuality negatively affects the appointment scheduling system, for example, such behaviour, reduces provider productivity and clinical efficiency, increases health care costs, and limits the ability of a clinic to serve its patients population by reducing the clinic’s effective capacity. In this study, while considering patient unpunctuality, we first introduce an analytical model and show the optimality of a fixed-interval policy for a simplified two-patient model. Motivated by the result, we propose an easy-to-implement heuristic policy with a simple structure using a simulation framework to improve the performance of the appointment scheduling system. The simulation result shows that our policy is overwhelmingly preponderant in current practice. We also measure the effect of patient unpunctuality and other factors. Actual data are used to add realism to the input parameters, and practical guidelines are developed for appointment scheduling.
... Queuing and waiting time in healthcare have recently received considerable attention in academia, with the research broadly falling into three categories. Firstly, the literature on the queuing approach provides optimal appointment scheduling (Cox et al., 1985;Luo et al., 2012). Secondly, research on patient waiting time satisfaction and dissatisfaction mitigation through information-based mechanisms (Haraden and Resar, 2004;Kumar and Krishnamurthy, 2008). ...
Purpose
Waiting time, as an important predictor of queue abandonment and patient satisfaction, is important for resource utilization and patient experience management. Medical institutions have given top priority to reforming the appointment system for many years; however, whether the increased information transparency brought about by the appointment scheduling mechanism could improve patient waiting time is not well understood. In this study, the authors examine the effects of information transparency in reducing patient waiting time from an uncertainty perspective.
Design/methodology/approach
Leveraging a quasi-natural experiment in a tertiary academic hospital, the authors analyze over one million observational patient visit records and design the propensity score matching plus the difference in difference (PSM-DID) model and hierarchical linear modeling (HLM) to address this issue.
Findings
The authors confirm that, on average, improved information transparency significantly reduces the waiting time for patients by approximately 6.43 min, a 4.90% reduction. The authors identify three types of uncertainties (resource, process and outcome uncertainty) in the patient visit process that affect patients' waiting time. Moreover, information transparency moderates the relationship between three sources of uncertainties and waiting time.
Originality/value
The authors’ work not only provides important theoretical explanations for the patient-level factors of in-clinic waiting time and the reasons for information technology (IT)-enabled appointment scheduling by time slot (ITASS) to shorten patient waiting time and improve patient experience but also provides potential solutions for further exploration of measures to reduce patient waiting time.
... Complicating outpatient appointment scheduling is the large variety of clinic characteristics that impact clinics operations, including: Multiple provider clinics (Cox et al., 1985;Liu & Liu, 1998;Rising et al., 1973;Schaak & Larson, 1986); Provider punctuality (Deceuninck et al., 2018;Klassen & Yoogalingam, 2013); Provider interruptions (Klassen & Yoogalingam, 2013; Patient punctuality (Cayirli et al., 2008;Vissers & Wijngaard, 1979;White & Pike, 1964); Patient no shows (Cayirli et al., 2008;Luo et al., 2019;Samorani & LaGanga, 2015;White & Pike, 1964) and Walk-in patients (Cayirli & Gunes, 2014;Kim & Giachetti, 2006;Klassen & Rohleder, 1996;Kortbeek et al., 2014;Qu et al., 2015;Rising et al., 1973). As we will discuss, our general formulation and SO approach are well equipped to accommodate these clinic characteristics. ...
Mixed registration type clinics accept both walk-in and scheduled patients. Such clinics provide patients with an additional option for how they access care while patient bookings help providers ensure a full workday. The model described in this paper determines how many patients to schedule (and when) in mixed registration type clinics. The methodology, simulation optimisation allows stochastic features found in such clinic to be modelled and provides optimisation techniques to identify solutions. A general simulation optimisation formulation for mixed registration type clinics is presented. Furthermore, the methodology is applied to a case study of a collaborative emergency centre in Nova Scotia, Canada. We demonstrate how the model can be used in clinics with multiple providers and multiple objectives. We compare the simulation optimisation generated schedule with existing schedules and show the advantages the collaborative emergency centre can expect when using schedules developed with the presented methods.
... However, patient unpunctuality, i.e., arriving either earlier or later than the appointment time, is prevalent all over the world. Empirical studies have reported that, while some patients would arrive 17 min ahead of the appointment on average, with a standard deviation of 30 min (Cox, Birchall, and Wong, 1985;Cayirli, Veral, and Rosen, 2006;Klassen and Yoogalingam, 2014), others would arrive 10 min late on average, with a maximum of 2 hours' delay (Zhu, Chen, Leung, and Liu, 2018). The unpunctual arrivals result in system congestion or provider idleness. ...
Patient unpunctuality causes perturbations in healthcare operations, compromising productivity and service quality. In this paper, we propose an approach that mitigates the negative impacts of unpunctuality using both appointment scheduling and real-time sequencing taking into account patient unpunctuality, no-shows, random service durations, and multiple providers. The objective is to minimize the total cost incurred by patient waiting and provider overtime. An optimal real-time sequencing strategy is established to serve the waiting patient with the smallest “LAR” index, which is defined as the Larger of Appointment time and Real arrival time for a patient. The optimal appointment schedule is determined by a simulation optimization approach with unbiased gradient estimators. Sample path discontinuities are smoothed by smoothed perturbation analysis. Properties of the optimal real-time sequencing strategies are used for the efficient sample path gradient estimation. Extensive experiments demonstrate the effectiveness of the proposed algorithm. Using real data, numerical experiments illustrate that the optimal appointment schedule depends on the system parameters and differs significantly from those of the existing literature. Specifically, the pattern of the appointment schedule is determined by the number of providers and the real-time sequencing strategy. The length of the appointment intervals is sensitive to the degree of unpunctuality and no-shows. Compared with the schedules in the previous studies, our schedule can achieve a significant cost reduction. Further, the optimal real-time sequencing strategy outperforms the commonly-used strategies in practice (e.g., appointment order, arrival order). Managerial insights are also provided for hospital managers to schedule unpunctual patients.
... On the other hand, on the basis of DES modeling, there are many researches on patient classification based on scheduling. Some scholars have proposed to divide patients into new patients which means they have not received treatments and return patients which means they return to secondary treatments (Cox et al. 1985), and others have proposed to classify according to the variability of treatment service time by doctors (Klassen & Rohleder, 1996). It has also been suggested to make a category according to the type of process (Vanden et al., 2000). ...
In recent years, the relationship between doctors and patients is becoming more and more tense. Many hospitals are paying more attention to the satisfaction of patients, because this is an important indicator to measure the quality of hospital services. In China, it is often a case that large-scale comprehensive hospitals such as the tertiary hospitals are always overcrowded and the waiting time for treatment is much higher than the time of treatment. The long waiting time will undoubtedly lead to lower patient satisfaction. Thus, how to improve patient satisfaction is focused on how to reduce patient waiting time. This study is based on the discrete event simulation (DES) method to construct an optimization model for the dental service process of a tertiary hospital in Changzhou. The data is collected through field research, and then we set the model parameters according to the existing service model. We suggest that adding pre-examination into the nursing triage process can improve the hospital’s service quality and enhance the resource utilization under limited resource conditions with reducing patient waiting time. In addition, we can inspire the hospital and other medical institutions to do some further improvements. After applying the proposed model, it can be seen that the effect is very significant that the average waiting time for treatment of the patient is reduced from 173 minutes to 45 minutes, and the length of stay (LOS) of the patient in the hospital is reduced from 209 minutes to 130 minutes.
... The t wo at a t ime rule was extensively studied with its original counterpart and its variations by Ho and Lau [8] and Cayirli, Veral, and Rosen [5], [6]. Multiple block/Fixed-interval with an in itial block rule -Co x, Birchall, et al. [14] investigated this rule with an initial b lock rule,introducing an initial b lock to the above rule studied by Soriano. ...
Extended waiting time for treatment in National hospitals is very common in S ri Lanka. This situation has created several problems to patients, doctors and even to other health workers. The quality of service leaves a lot to be desired and is costly to the economy. This study analyses different queues which create bottlenecks in the Out Patient Department at national eye hospital in S ri Lanka and critically evaluate several appointment scheduling rules with the help of a simulation model to come up with a solution which minimises the total patient waiting time. Our results shows that total patient waiting time can be reduced more than 60% using proper appointment scheduling system with process improvement.
... traffic jam. In the literature, most empirical studies indicate that patients arrive 17 minutes (min) early for appointments on average with a standard deviation of nearly 30 min (Fetter and Thompson 1966;Cox, Birchall, and Wong 1985;Cayirli, Veral, and Rosen 2006;Klassen and Yoogalingam 2014). Patients also arrive late to get the service. ...
Patient unpunctuality significantly disrupts the operations of healthcare facilities, reduces provider productivity, and increases healthcare costs. To alleviate the negative impact of unpunctual patients, this study addresses the appointment scheduling (AS) in the simultaneous presence of unpunctual patients, multiple servers, and no-shows. To determine the appointment schedule, we propose a two-stage stochastic mixed-integer programming model to minimise the total cost incurred by patient waiting and clinic overtime. It becomes challenging for a standard solver to solve this model due to the dynamic patient-to-server assignment decisions that are proactively anticipated in the determination of appointment times. To deal with this problem, a stochastic approximation algorithm is proposed under unbiased gradient estimators. The effectiveness and efficiency of this algorithm are validated in extensive numerical experiments that compare it with Benders decomposition and a heuristic algorithm. Further, the features of the optimal appointment schedule are analysed: (i) the shape of the appointment intervals relies on the number of servers; (ii) the length of intervals is sensitive to no-shows; (iii) the initial block size is greatly affected by patient unpunctuality. Managerial insights are also provided for hospital managers to schedule unpunctual patients in practice.
... One of the earliest appointment scheduling rules, known as Bailey's rule or 2ATBEG rule, scheduled two patients in the first slot and one patient in each of the remaining slots by fixing the slot duration to be constant and equal to the average service time of the patients ( Bailey, 1952 ). Similarly, many other rules, such as individual block/fixed interval (IBFI), multiple block/fixed interval (MBFI) and variable block/fixed interval (VBFI) were studied for the last five decades (e.g., Cox, Birchall, & Wong, 1985;Fetter & Thompson, 1966;Fries & Marathe, 1981;Rising, Baron, & Averill, 1973;Soriano, 1966 ). Meanwhile, Ho, Lau, and Li (1995) performed an extensive study by proposing different variable-interval appointment rules that minimized patient waiting time, without significantly increasing the clinic idle time. ...
In the US, the demand for outpatient services is expected to increase, while the supply of physicians to provide the care is projected to decrease. Besides, inefficiencies in the appointment system (AS) and patient no-shows (patients who do not arrive for scheduled appointments) reduce provider productivity, timely access to care, and cost the U.S. healthcare system more than $150 billion a year. To handle increasing demand and compensate for patient no-shows, outpatient clinics tend to overbook appointments. The current scheduling practice at most clinics and majority of the scheduling rules proposed in the literature assume all patients are equally likely to miss an appointment. Further, most scheduling rules in the literature do not leverage the available data, such as electronic health records, when scheduling patients. This paper proposes a prescriptive analytics framework to improve the performance of an AS with respect to patient satisfaction (measured using average patient waiting time and number of patients unable to get an appointment for the day under consideration) and resource utilization (measured using average resource idle time, overflow time and overtime). In the proposed framework, patient-related data from various sources are used to develop predictive models that identify the risk of a patient no-show. Different scheduling rules, that leverage the patient-specific no-show risk is then proposed. A case study, with real data from a Family Medicine Clinic in Pennsylvania, is used to show the feasibility of the proposed framework. The effectiveness of the proposed scheduling rules is evaluated by benchmarking it with three rules adapted from the literature. The results indicate that the proposed scheduling rules consistently outperform the benchmark rules for all the clinic settings tested. Further, the proposed framework is generic and can be adopted by any outpatient clinic characterized by occurrences of no-shows and appointment-based customer arrivals.
... Patient waiting time and physician idle time can now occur before each stage of service. In a single stage system, the waiting time of the patient is usually defined in terms of pre-service wait either from appointment time [9,32] or from arrival time when patient unpunctuality is modeled [3,8,22]. The idle time of the physician is defined as the time the physician has between appointments (e.g., if he finishes with one patient early and the next patient has not yet arrived). ...
Healthcare providers can benefit from adding less costly capacity to their existing resources in order to satisfy demand while maintaining the quality of patient care. The addition of mid-level service providers (MLSPs) such as physician assistants or nurse practitioners that carry out portions of patient care provides a viable alternative for adding physician capacity. This research considers the circumstances under which adding an MLSP to a single-physician outpatient office becomes the best strategy for the clinic, and determines how scheduling policies from the widely-researched single-stage environment should be adjusted for a multi-stage environment. Compared to a single-stage system where a physician completes all portions of the service, we show that adding an MLSP can reduce patient waiting time, patient flow time, and physician service time with patients. This, in turn, can enable the clinic to see more patients and/or free up physician time for other tasks. Appointment scheduling rules are developed for a multi-stage outpatient service system using a simulation optimization approach. Performance measures focus on the patient experience and clinic operation before and during each stage of service.
... In the second category, unpunctuality problems are studied using simulation methods. Some related studies [9,10,13,22] include unpunctual arrivals to enrich the environment and make it more closely match reality. Other studies concentrate more on how system performances vary and how to adjust scheduling rules for unpunctual patients, which is a more important focus because unpunctuality is considered to be a significant factor that influences the system. ...
Many papers on outpatient appointment scheduling assume that patients arrive on time. However, unpunctuality is a stochastic factor that is inevitable in practice, which leads to patients arriving out of order. A schedule may not be reasonable if a clinic neglects the influence of patient unpunctuality. This paper addresses the outpatient scheduling problem considering unpunctuality (OS-U) by developing a stochastic programming model. We compare the performance of the OS-U system with the strict-punctuality (OS-P) system. We illustrate that the model has an exact and unified formula for cases of patients arriving in the appointment order and arriving out of order. The OS-U problem is solved by using Benders decomposition combined with the sample average approximation (BD-SAA) technique to determine the global optimal set of appointment intervals with the goal of minimizing the weighted sum of all patient waiting times, doctor idle times, and overtime. Numerical experiments indicate that the appointment rule changes when considering unpunctuality, although the set of optimal appointment intervals still takes the shape of dome (interval width increases at first, then remains nearly constant and eventually decreases for the last patients). The OS-P system schedules the first two patients together at the start of a session, whereas the OS-U system schedules them with different appointment times and requires a longer slot between the first two patients if patients tend to arrive early rather than late. The variance of unpunctuality has little impact. The no-show probability has a greater influence on system performances in an OS-U system than those in an OS-P system.
... Currently, the Chinese domestic researches are mainly from the perspective of resource management, optimizing patient's waiting time and hospital service costs by optimizing allocation of outpatient resources and estimating the most reasonable number of outpatient doctors (Rising et al. 1973;Cox et al. 1985;chun PENG Y, bin DONG S, hu CHANG W, 2005). The existing outpatient appointment mechanism in Chinese hospitals complies with the "one-way appointment, one-way selection, first select first served" rule. ...
Currently specialists’ outpatient appointments in large hospitals in China are made by patients’ one-side choice of specialists, and most are “first select first served”. A specialist cannot choose a patient according to his specialty. Because of the “worship of famous doctors” and asymmetric information between specialists and patients, the appointments are often made with certain blindness, thus it is difficult for patients to get the best diagnosis and treatment from specialists. In this paper, we apply the two-sided matching theory, from the both views of patients and specialists, we design specialists-outpatients matching appointment system, in the system, we propose the process of the appointment and the one-to-many appointment matching algorithm. In order to provide fairness to both sides, we apply the theory of balance-matching, construct the algorithm of one-to-one and one-to-many two-sided balance matching. At last, through the computational examples we prove the model is effective in hospital specialists outpatient appointment.
... A decision maker can design a policy to assign patient categories to time blocks and appointment slots. This research stream suggests that adopting patient grouping approaches for new/return patients (Cox et al. 1985), inpatient/outpatient (Walter 1973), patient care procedure types (Bosch and Dietz 2000), and different service times (Cayirli et al. 2008, Qu et al. 2013) can substantially improve a clinic's schedule performance. ...
We study outpatient appointment block scheduling policies for single providers under conditions of patient heterogeneity in service times and patient no-shows. The objective is to find daily appointment schedules that minimize a weighted sum of patients’ waiting time, the physician's idle time, and the physician's overtime. We contribute by suggesting new effective sequential block scheduling procedures motivated by actual outpatient clinic practices across the globe and grounded in the successful Toyota Production System load smoothing approach. Our block scheduling policy first assigns a sequence of different patient types within a time block. The policy then allocates repetitive blocks across a planning horizon. We start our analysis by studying the case with zero probability of no-shows. Under the setting that the physician's idle time is zero, we propose a polynomial time optimal scheduling approach for two patient types, before demonstrating that the problem with at least three patient types is NP-Hard. Various extensions to incorporate practical outpatient clinic environment dimensions are considered. We then extend our scheduling approach to incorporate reasonable patient no-show probabilities. Finally, our block scheduling approach is adapted for scenarios where outpatient clinics use an open-access scheduling environment, where patients make same-day appointments. We compare our block scheduling policies against extant scheduling policy, finding our block scheduling policies surpass the benchmark method.
... To mitigate these limitations, we augmented the queueing analysis above with a discrete-event simulation analysis. Discrete-event simulation has been widely used in research on healthcare operations in general, and on outpatient clinic operations in particular (e.g., Cayirli et al. 2006, 2008, Cote 1999, Cox et al. 1985, Klassen and Yoogalingam 2009, Liu et al. 2010, Santib añez et al. 2009). It is appropriate here because it expands the generalizability of our results (so they are not limited to describing a single empirical environment) while accommodating the significant stochasticity commonly found in patient-care processes. ...
Capitalizing on the operational concept of division-of-labor, clinics often reduce physician service time by off-loading some of his/her clinical activities to lower-cost personnel. These personnel, such as nurse practitioners and physician assistants, are often collectively referred to as “mid-level care providers” (MLPs) and can perform many patient-consultation tasks. The common rationale is that using an MLP allows the physician to serve more patients, increase patients’ access to care, and, due to MLPs’ lower salaries, improve the clinic's financial performance. An MLP is typically integrated into the outpatient clinic process in one of two modes: as an “ice-breaker,” seeing each patient before the physician, or as a “standalone” provider, a substitute for the physician for the entirety of some patients’ visits. Despite both of these modes being widely used in practice, we find no research that identifies the circumstances under which either one is preferable. This study examines these two modes’ effects on operational performance, such as patient flow and throughput, as well as on financial measures. Using queueing and bottleneck analysis, discrete-event simulation, and profit modeling, we compare these two deployment modes and identify the optimal policies for deploying MLPs as either ice-breakers or as standalone providers. Interestingly, we also find there exists a range of scenarios where not hiring an MLP at all (i.e., the physician works alone) is likely to be most profitable for the clinic. Implications for practice are discussed. This article is protected by copyright. All rights reserved.
... Efforts to study the effects of patient punctuality in clinic operations have mostly relied on simulation models. [12][13][14] Also, most of the previous literature focuses on single clinics with one or a few doctors. 4 Late arrivals in pediatrics may be unique for a number of reasons, including more complex transportation arrangements, multiple people coming to the appointment, most appointments being during school hours, and the concentration of poverty among children. ...
We conducted a cross-sectional study to evaluate timeliness of patient arrival at a pediatric multispecialty clinic. Bivariate and ordered logistic regression analyses were conducted to determine the odds of late arrival by specified patient- and visit-level characteristics. A total of 64 856 visits were available for analysis, of which 6513 (10.0%) were late arrivals. The odds of late arrival were higher for patients who spoke English (odds ratio [OR] = 1.34, P < .001) compared with those who spoke Spanish, had Medicaid (OR = 1.54, P < .001) or no insurance (OR = 1.49, P < .001) compared with those with insurance other than Medicaid, and were late to their previous visit (OR = 2.46, P < .001). Visit-level variables associated with late arrival included appointment time earlier in the day (i.e. 8-10 am, OR = 2.77, P < .001 compared with 4-6 pm), earlier in the week (i.e. on Mondays, OR = 1.21, P < .001 compared with Wednesdays), and for certain subspecialty clinics (P < .001). Numerous variables are significantly associated with late arrival for pediatric clinic appointments.
... block size) and the length of appointment intervals (Cayirli, Veral, and Rosen 2006). Klassen and Yoogalingam (2014) show that a combination of variable-length intervals and block scheduling are better at mitigating the effects of patient unpunctuality The best performing appointment rules reported in the healthcare literature include: 1. the individualblock/fixed-interval rule (IBFI), used as a benchmark usually, which assigns patients individually to intervals of the same length equal to the mean service time of patients; 2. OFFSET rule (Ho and Lau 1992), where the initial patients are scheduled earlier and the rest are scheduled later than their appointment times by IBFI; 3. DOME rule (Wang 1997;Robinson and Chen 2003;Denton and Gupata 2003;Hassin and Mendel 2008;Cayirli, Yang, and Quek 2012), where appointment intervals are shorter at the beginning and the end of the day and longer in the middle of the day; 4. 2BEG rule (Bailey 1952, Ho and Lau 1992, Klassen and Rohleder 1996, which adopts a IBFI rule but assigns two patients at the beginning of the session; 5. the multi-block/fixed-interval rule (MBFI) (Soriano 1966;Cox, Birchall, and Wong 1985), which assigns two patients to one time slot, where the length of each time slot is twice the mean service time. The 2BGDM and MBDM rules are variations of 2BEG and MBFI with non-fixed appointment intervals that follow a "dome" pattern. ...
In this paper, we present an appointment scheduling problem faced by a medical imaging center in a major hospital in Macau. We developed an empirically calibrated simulation model to represent the appointment and medical diagnosis procedure as a multi-server queuing network with multiple patient classes. Four appointment overbooking schemes are proposed to compensate for patient no-shows and unpunctuality. The focus of this study is to integrate overbooking schemes with existing appointment rules to improve the operational efficiency of the center. Simulation results show that our proposed overbooking schemes significantly enhance the performance of the center. Compared with the current practice, the best performing overbooking scheme reduces the overtime by 58.32% and the idle time by 23.65%, increases the number of patients served by 15.9%, while still ensuring that patient waiting times remain acceptable.
... Several methods have been proposed to design appointment schedules [18][19][20][21]. Researchers tested the idea of scheduling multiple patients per block and found that it reduced patient wait time and doctors' idle time in some cases and increased in some other cases [22,23]. The variability in service times of providers, nature of treatment, and type of patients affect the performance of appointment systems [24]. ...
Abstract
Background: The Department of Obstetrics and Gynecology (OB/GYN) at the University of Arkansas for Medical
Sciences (UAMS) tested various, new system-restructuring ideas such as varying number of different types of nurses to reduce patient wait times for its outpatient clinic, often with little or no effect on waiting time. Witnessing little progress despite these time-intensive interventions, we sought an alternative way to intervene the clinic without affecting the normal clinic operations.
Aim: The aim is to identify the optimal (1) time duration between appointments and (2) number of nurses to reduce
wait time of patients in the clinic.
Methods: We developed a discrete-event computer simulation model for the OB/GYN clinic. By using the patient
tracker (PT) data, appropriate probability distributions of service times of staff were fitted to model different variability in staff service times. These distributions were used to fine-tune the simulation model. We then validated the model by comparing the simulated wait times with the actual wait times calculated from the PT data. The validated model was then used to carry out “what-if” analyses.
Results: The best scenario yielded 16 min between morning appointments, 19 min between afternoon
appointments, and addition of one medical assistant. Besides removing all peak wait times and bottlenecks around noon and late in the afternoon, the best scenario yielded 39.84 % (p < .001), 30.31 % (p < .001), and 15.12 % (p < .001) improvement in patients’ average wait times for providers in the exam rooms, average total wait time at various locations and average total spent time in the clinic, respectively. This is achieved without any compromise in the utilization of the staff and in serving all patients by 5pm.
Conclusions: A discrete-event simulation model is developed, validated, and used to carry out “what-if” scenarios to identify the optimal time between appointments and number of nurses. Using the model, we achieved a significant improvement in wait time of patients in the clinic, which the clinic management initially had difficulty achieving through manual interventions. The model provides a tool for the clinic management to test new ideas to improve the performance of other UAMS OB/GYN clinics.
Keywords: Outpatients, Patient types, Patient tracker data, Appointment template, Exam rooms, Optimization,
Utilization, Simulation
... Notable exceptions that do cover multi-node situations are the case study (backed by Monte Carlo simulation) presented by Rising et al. [16] and the visual simulation-based approach due to Swisher et al. [18]. An elementary queueing model, designed for a specific multistage application (i.e., an ear, nose and throat outpatient clinic), has been developed by Cox et al. [6]. While there is a variety of situations in which single-stage systems are a sufficiently accurate representation of the real system, one would ideally like to have appointment scheduling algorithms that can deal with more complex structures as well, such as the ones presented by Côté and Stein [5]. ...
... The t wo at a t ime rule was extensively studied with its original counterpart and its variations by Ho and Lau [8] and Cayirli, Veral, and Rosen [5], [6]. Multiple block/Fixed-interval with an in itial block rule -Co x, Birchall, et al. [14] investigated this rule with an initial b lock rule,introducing an initial b lock to the above rule studied by Soriano. ...
Extended waiting time for treatment in National hospitals is very common in Sri Lanka. This situation has created several problems to patients, doctors and even to other health workers. The quality of service leaves a lot to be desired and is costly to the economy. This study analyses different queues which create bottlenecks in the Out Patient Department at national eye hospital in Sri Lanka and critically evaluate several appointment scheduling rules with the help of a simulation model to come up with a solution which minimises the total patient waiting time. Our results shows that total patient waiting time can be reduced more than 60% using proper appointment scheduling system with process improvement.
... Based on these characteristics, patients can be classifi ed for scheduling purposes. Past studies in AS design have sequenced/prioritised patients, concentrating on three major patient classifi cations: new and return basis (Cox et al., 1985;Cayirli et al. 2006;Wijewickrama and Takakuwa, 2009), variability of consultation time (Wang, 1999;Klassen and Rohleder, 1996) and type of procedure (Bosch and Dietz, 2000). The study of Cayirli et al. (2006) concluded that sequencing decisions have a more pronounced impact on performance than the choice of an appointment. ...
Appointment system design based on patient characteristics has become a recent issue. This is investigated in a multi-facility system with the presence of second consultation using the discrete event simulation methodology. Different appointment systems are simulated, combining appointment rules and patient sequences with the adjustment of appointment intervals based on patient characteristics. The results show that the interval adjustment made on patient classifications is more successful than sequencing patients without making a time adjustment. The study identifies some efficient appointment systems for a given situation in relation to the trade-off between patient waiting time and physician idle time, while emphasising the importance of not excluding a second consultation in designing appointment systems.
... Patient visits are normally classified into two types: new patient and return visit patient (Cox et al., 1985). A patient classification scheme has also been developed based on patients' past appointment history or the procedure that were considered (Vanden et al., 2000). ...
Patient dissatisfaction has long been a recognised problem in current outpatient healthcare delivery systems especially with patient wait time. Many solutions have tried to improve the service quality from the view points of cost reduction and increasing utilisation of medical staff. However, the uncertainty of physician treatment time has been one of the primary concerns for effective scheduling. This paper demonstrates an analytical concept on improving quality of service for a clinic from the aspects of reducing costs and waiting by reclassifying patient visit groups in order to reduce the variability of physician service uncertainty. A case study from an orthopaedic surgery clinic is presented to illustrate the classification method by using a decision tree technique and how the redesign of scheduling better manages the variability of treatment times, helps alleviate the wait time for both patients and physicians, reduce overall costs of waiting and overtime, and consequently, improve the overall service quality.
... Two patients per block could better utilise the doctors' idle time and reduce patient waiting time. Cox et al. [52] found that calling multiple patients in an appointment slot worked best in two of the clinics that they modelled. However, this scheme was rated as inferior by Ho and Lau [47] because it fared poorly in time-cost efficiency for patient waiting time and doctors' idle time. ...
The increasing demand for outpatient services has led to overcrowded clinics, long waiting times for patients, and extended staff working hours in outpatient clinics. Simulation tools have been used to ameliorate deficiencies in the appointment system, resource allocation, and patient flow management that are the root causes of these problems. Integrated studies that considered these three factors together produced better results than attempts to resolve individual causes. While simulation has proved to be an effective problem-solving tool for outpatient clinic management, there is still room for improvement. This paper reviews studies over the past 50 years that have applied management simulation to resolve outpatient clinic problems.
... A number of previous studies take patient classification into account in the design of appointment systems. Cox et al. (1985) propose a series of methods to sequence new and return patients, resulting in a shorter queue length and higher utilization of physicians. Klassen and Rohleder (1996) point out that scheduling patients with a small variance in service time in the beginning of the session performs better than other approaches considered. ...
... In the literature, MBFI perfor-mance evaluations are varied. Blanco White and Pike (1964), Soriano (1966), and Cox et al. (1985) find that multiple-block rules perform better for the particular clinics they studied. Ho and Lau (1992) report that multiple-block rules perform worse than OFFSET and 2BEG rules for the operating environments investigated in their simulation experiments. ...
We propose a paradigm shift in how the performance of outpatient clinic appointment schedules is evaluated in practice and academia. Our research addresses the traditional dilemma between patients’ wait times and providers’ idle time and overtime, but with operational performance metrics that assess their respective probabilities of exceeding established thresholds, instead of optimizing a presumed cost function. Using a stochastic model, we introduce a new way of analyzing appointment schedules that is absent from the literature but appealing to practitioners. We take into account the variable nature of patient consultation times, known differences in the duration of diverse consults, and patients’ propensity to miss their appointments. Analysis shows that traditional scheduling systems have serious shortcomings in terms of providing consistent service levels, and we conclude that the managerial decision space so far investigated in the appointment scheduling literature is not adequate for exercising operational control over appointment system performance.
... Other suggestions for possible groupings include patient's age, physical mobility, and type of service. In a simulation model, Cox et al. (1985) investigate a number of different approaches to sequence new and return patients using real-life data from an ear, nose, and throat clinic. Implementation of the proposed systems results in improved patient flow times, queue lengths, and doctor utilization. ...
This study introduces a universal “Dome” appointment rule that can be parameterized through a planning constant for different clinics characterized by the environmental factors—no-shows, walk-ins, number of appointments per session, variability of service times, and cost of doctor's time to patients’ time. Simulation and nonlinear regression are used to derive an equation to predict the planning constant as a function of the environmental factors. We also introduce an adjustment procedure for appointment systems to explicitly minimize the disruptive effects of no-shows and walk-ins. The procedure adjusts the mean and standard deviation of service times based on the expected probabilities of no-shows and walk-ins for a given target number of patients to be served, and it is thus relevant for any appointment rule that uses the mean and standard deviation of service times to construct an appointment schedule. The results show that our Dome rule with the adjustment procedure performs better than the traditional rules in the literature, with a lower total system cost calculated as a weighted sum of patients’ waiting time, doctor's idle time, and doctor's overtime. An open-source decision-support tool is also provided so that healthcare managers can easily develop appointment schedules for their clinical environment.
... Finally, Jackson, Welch, and Fry (1964), Vissers and Wijngaard (1979), Rising, Baron, and Averill (1973), Cox, Birchall, and Wong (1985), O'Keefe (1985), Babes and Sarma (1991), Brahimi and Worthington (1991), and Bennett and Worthington (1998) provide more general and qualitative recommendations for appointment policy design. Most of them are based on the use of operations research to improve service quality in medical clinics. ...
In this paper we review the literature on appointment policies, specifically in terms of the objective function commonly used and the assumptions made about the behavior of demand. First, we provide an economic framework to analyze the problem. Based on this framework we make a critical analysis of the objective functions used in the literature. We also question the validity of the assumption made throughout the literature that demand is exogenous and independent of customers' waiting times. We conclude that the objective functions used in the literature are appropriate only in the case of a central planner facing a demand that is unresponsive to waiting time. For other scenarios, such as a private server facing a demand that does react to waiting time, these objective functions are only shortcuts for the real objective functions that must be used. A more general model is then proposed that fits these scenarios well. Finally, we determine the impact of using the literature's objective functions on optimal appointment policies. (SERVICE OPERATIONS; APPOINTMENT POLICIES; PRIVATE SERVER AND CENTRAL PLANNER)
... 2 Cox et al used a simulation study in order to optimize the running of an ear, nose, and throat outpatient clinic. 3 Brahimi and Worthington applied simulation models for an outpatient clinic department. 4 Hashimoto and Bell 5 investigated the behavior of an outpatient clinic to improve the performance of the clinic. ...
Background - In the interest of efficiently using limited resources, it is important to optimize the throughput of cardiac surgery patients. Accordingly, the present study was performed to estimate the bed occupancy rate and throughput of patients in cardiac surgery departments using simulation models. Methods - In this paper, the typical Heart Surgery Department of Freeman Hospital in Newcastle upon Tyne, England was considered, where there were some beds in the ward, theater, and intensive care unit (ICU). For a set of data, a computer program for Monte-Carlo simulation of the department using Fortran-77 software (Fortran Company, USA) was developed in order to observe the behavior of the department as a queuing system. Different number of beds in the ward and ICU were simulated in order to observe the bed occupancy rate in the ward and ICU and also the throughput of patients in the system. Results - Bed occupancy rates in the ward and ICU for the case of 2 beds in the ICU and 11 in the ward were 78% and 81%, respectively. In this case, the throughput of 500 patients in the system could take 513 days. For 3 beds in ICU and 16 in the ward the mean bed occupancy rate was 84% in the ward and 79% in ICU. The throughput of 500 patients in the system with 9 beds in ICU and 39 in the ward could take 130 days. Conclusion - To prevent disinvestment prior to building a hospital or a new ward, especially in developing countries, it is suggested to perform simulation studies to observe the behavior of system in advance.
... In another study [6] investigated the multiple-block/fixed-interval with an initial block rule, introducing an initial block to the above rule. The simulation model developed for the ear, nose, and throat (ENT) clinic was validated by comparing results with actual data. ...
Customers desire short waiting times whereas service providers want to maximize resources utilization. Long waiting time is not uncommon in many service organizations and it is familiar especially in outpatient departments. To make the study more realistic, some assumptions were removed and uses an animated simulation model for a mixed-patient type environment in an outpatient department. A special purpose data generator is designed to explore bottlenecks in consultation rooms. Four appointment scheduling rules and their possible combinations are evaluated in two steps. First, experimentation concentrates on appointed and non-appointed patients. Second, it considers new patients in addition to those two categories. It is revealed that the rule which records the lowest waiting time is not feasible due to the high portion of server idle time. The rule that shows the lowest server idle time is not viable due to increased waiting time. It is possible to find the best rule which lies between these two times in a mixed-patient type environment.
Appointment schedules, in essence, balance supply and demand and are often employed in settings where resources are scarce and thus a high utilization is realized (e.g., healthcare). Whereas most of the existing literature focuses on the single-server case, a framework is developed to study appointment scheduling in multiserver settings. Relying on phase-type approximations, general service-time distributions are modeled, which are fed into a recursive approach allowing evaluation and optimization of an objective function that balances expected waiting times and idle times. Studying optimized schedules for multiple servers reveals that the start and end of a session can deviate greatly from the dome-shaped pattern as established for the single-server case. Furthermore, a comparison of various multiserver setups shows that significant performance gains can be achieved when servers are pooled. This allows an explicit quantification of the cost of continuity of care. In addition, session overtime as well as early finish of servers can be incorporated in the approach; the benefits of the additional flexibility that a multiserver setting provides are summarized. For the stationary plateau of the dome, to which the optimal interarrival times converge, steady-state appointment schedules are obtained by exploiting the embedded Markov chain; these schedules are shown and argued to converge quickly to optimal solutions obtained in a heavy-traffic regime. In this regime, algebraic solutions are derived, which provide interesting managerial guidelines when the pooling of servers is considered in appointment scheduling.
This paper was accepted by Bariş Ata, stochastic models and simulation.
Background
Appointment scheduling in outpatient settings typically uses simple classification rules to assign patients to long or short appointment slots, based on the anticipated duration of the patient-physician consultation, i.e., the service time. For example, new patients are assigned longer appointment slots, and return patients are assigned shorter slots. While these rules are convenient, they fail to account for the significant variability in service time of outpatient visits.
Methods
We present a data-mining approach that allows practices to predict service time based on patient characteristics and several other clinical attributes. This approach provides a decision-support tool that helps practices determine the length of time to allocate to a patient’s appointment. Specifically, we use a neural network to accurately estimate service time for each patient based on his/her characteristics. The neural network is trained using eight years of real appointment data (2010 to 2018) from a local outpatient clinic. We compare the performance of the neural network predictions against commonly used classification rules, using a randomly sampled test dataset and a statistical test.
Results
Our results suggest that outpatient practices can refine their current practices by adopting a data-driven approach to determining slot lengths for appointments. The average absolute difference and the standard deviation of differences between the neural network predictions and the actual service times in practice (case study) are 5.7 min and 4.0 min, respectively. These two measures are significantly lower than the same comparison with the common classification rule (new patient versus return patient) at the clinic; i.e. average time and standard deviations are 14.3 min and 8.2 min, respectively.
Conclusion
Neural network modeling can capture the effect of processes in a medical facility and create individualized predictions of patient service time with more accuracy.
We study a stochastic outpatient appointment scheduling problem (SOASP) in which we need to design a schedule and an adaptive rescheduling (i.e., resequencing or declining) policy for a set of patients. Each patient has a known type and associated probability distributions of random service duration and random arrival time. Finding a provably optimal solution to this problem requires solving a multistage stochastic mixed‐integer program (MSMIP) with a schedule optimization problem solved at each stage, determining the optimal rescheduling policy over the various random service durations and arrival times. In recognition that this MSMIP is intractable, we first consider a two‐stage model (TSM) that relaxes the nonanticipativity constraints of MSMIP and so yields a lower bound. Second, we derive a set of valid inequalities to strengthen and improve the solvability of the TSM formulation. Third, we obtain an upper bound for the MSMIP by solving the TSM under the feasible (and easily implementable) appointment order (AO) policy, which requires that patients are served in the order of their scheduled appointments, independent of their actual arrival times. Fourth, we propose a Monte Carlo approach to evaluate the relative gap between the MSMIP upper and lower bounds. Finally, in a series of numerical experiments, we show that these two bounds are very close in a wide range of SOASP instances, demonstrating the near‐optimality of the AO policy. We also identify parameter settings that result in a large gap in between these two bounds. Accordingly, we propose an alternative policy based on neighbor‐swapping. We demonstrate that this alternative policy leads to a much tighter upper bound and significantly shrinks the gap.
Purpose
High lateness and no-show percentages pause great challenges on the patient scheduling process. Usually this addressed by optimizing the time between patients in the scheduling process and the percent of extra patients scheduled to account for absent patients. However, because the no-show and lateness is highly stochastic we might end up with many patients showing up on time which leads to crowded clinic and high waiting times. The clinic might end up as well with low utilization of the doctor time. This works aims to study the effect of scheduled overload percentages and the patient interval on: waiting time, overtime and the utilization.
Design/methodology/approach
Actual data collection and statistical modelling is used to model the distribution for common dentist procedures. Simulation and validation to used to model the treatment process. Then algorithm development is used to model and generate the patient arrival process. The simulation is run for various values of basic interval scheduled time between arrivals for the patients. Further 3d graphical illustration for the objectives is prepared for analysis.
Findings
This work initially reports a statistical distribution for the common procedures in a dentist clinics. This can be used for developing scheduling system and validating the scheduling algorithms developed. This work also suggest a model for generating patient arrivals in simulation. It was found that the overtime increases excessively when coupling both high basic interval and high overloading percentage. It was also found that: to obtain low overtime we must reduce the basic interval.Waiting time increases when reducing the basic scheduled appointment interval and increase the scheduled overload percentage. Also doctors utilization is increased when the basic interval is reduced.
Research limitations/implications
This work was done at a local clinic and this might limit the value of the modeled procedure times.
Practical implications
This work presents a statistical model for the various procedures and a detailed technique to model the operations of the clinics and patient arrival time which might assist researches and developers in developing their own model. This work present a procedure for troubleshooting scheduling problems in outpatient clinics. For example a clinic suffering from high patient waiting time is directly instructed to slightly increase their basic scheduled interval between patients or slightly reduce the overloading percentage.
Originality/value
This work presents a detailed modelling procedure for the outpatient clinics under high lateness and no-show and addresses the modelling procedure for the patient arrivals. This 3D graphical charting for the objectives includes a study of the multiple objectives that are of high concern to outpatient clinic scheduling interested partied in one paper.
A gestão da capacidade de atendimento na área de saúde desempenha um papel estratégico, no sentido de que fica cada vez mais clara a necessidade de um acompanhamento rigoroso na utilização de recursos, que além de escassos são de alto custo. Nesse cenário cresce a necessidade de ferramentas que capacitem a análise prévia e a quantificação dos impactos de possíveis mudanças. O objetivo desse trabalho é a apresentação de um modelo de simulação para gestão de capacidade de atendimento em hospitais. Sua abordagem é inovadora agregando conceitos da teoria das restrições na identificação e gerenciamento dos gargalos e de técnicas de simulação computacional para analisar as melhores alternativas para a utilização dos recursos humanos e da capacidade instalada no sentido de agilizar o acesso aos serviços de saúde.
The appointment system is widely used to facilitate customer access to service in many industries including healthcare and others. Because of its importance, much research has investigated how to build an effective appointment policy under various environments. However, most research has considered a single-server service system. The objective of this work is to evaluate several appointment policies in a two-stage service system in which multiple servers are available and build separate appointments at the second-stage. In such a system, we propose and evaluate the staggering appointment policy. Simulation experiments indicate that the proposed staggering appointment policy outperforms other traditional appointment policies in terms of customer waiting time, server idle time, and the number of customers who are later to scheduled appointments.
There has been a little attention given on to patient sequencing issues in appointment scheduling design. This is investigated in an outpatient system with and without adjusting appointment intervals using simulation methodology. Different appointment systems are simulated, combining appointment rules and patient sequences, including variability of consultation time, with the adjustment of appointment intervals based on patient groupings. The study identifies the most suitable appointment system and interval adjustment to be made for a given situation relation to the trade-off between patient waiting time and physician overtime and idle time.
Scheduling patients involves a trade-off between the productivity of the service provider and customer service. This study considers how outpatient medical facilities can improve their appointment scheduling by incorporating individual patient information in the scheduling process. Specifically, we obtain data on patient characteristics and examination durations from a health clinic, describe how that data can be used to predict patient examination durations in the clinic's appointment scheduling system, and evaluate the benefit of using individual patient characteristics over a conventional classification method. Computational results illustrate this method of patient scheduling reduces an overall cost function comprised of patient wait time, physician idle time, and over time by up to 24.2%, particularly when patients are sequenced with short duration patients being scheduled first. Several environmental characteristics are found to play critical roles in determining the magnitude of the benefit, including patient punctuality, no-show probability, the clinic duration, the appointment rule used for scheduling, and the ratio of the physician's idle time cost to the patient wait cost. We also detail and evaluate a practical procedure for using heterogeneous scheduling under a fixed schedule.
Patient wait time and access to care have long been a recognized problem in modern outpatient healthcare delivery systems. In spite of all the efforts to develop appointment rules and policies, the problem of long patient waits persists. Despite the reasons, the fact remains that there are few implemented models for effective scheduling that consider patient wait times, physician idle time, overtime, ancillary service time, as well as individual no-show rate, and are generalized sufficiently to accommodate a variety of outpatient clinic settings. The goal of this chapter is to improve the quality and efficiency of healthcare delivery by developing a physician schedule that meets the clinical policies without overbooking using an innovative wait ratio concept, a patient arrival schedule from the physician schedule accounting for ancillary services, an evidence-based predictive model of no-show probability for individual patient, and a model-supported dynamic overbooking policy to reduce the negative impact of no-shows.
Appointment policy design is complicated by patients who arrive earlier or later than their scheduled appointment time. This article considers the design of scheduling rules in the presence of patient unpunctuality and how they are impacted by various environmental factors. A simulation optimization framework is used to determine how to improve performance by adjusting the schedule of appointments. Prior studies (that did not include patient unpunctuality) have found that a scheduling policy with relatively consistent appointment interval lengths in the form of a dome or plateau dome rule to perform well in a variety of clinic environments. These rules still perform reasonably well here, but it is shown that a combination of variable-length intervals and block scheduling are better at mitigating the effects of patient unpunctuality. In addition, performance improves if the use of this policy increases toward the end of the scheduling session. Survey and observational data collected at multiple outpatient clinics are used to add realism to the input parameters and develop practical guidelines for appointment policy decision making.
The paper aims to provide a simulation optimization solution to improve patient scheduling that accounts for varying ancillary service time such as x-ray to minimize patient wait time.
The two-step approach is to: identify patients' needs for ancillary services while scheduling appointments; and propose an algorithm to determine ancillary service time via simulation optimization. The main aim is to provide sufficient time between arrival at the clinic and the actual examination time for a patient to complete pre-visit activities without contributing significantly to patient wait time. Two case studies are included to demonstrate the approach.
Triaging at the appointment-scheduling time saves an average 17 minutes for physician's first consultation in a clinic day, and a 7 percent reduction on current average patient wait time for case 1. Case 2 results in a 9 percent reduction on average patient wait time. The scheduled ancillary service time depends on the frequency and the ancillary service time, and appointment slot design.
One limitation is the impact of modeling error on the account of ancillary service times and the modeling assumptions.
The proposed approach provides a studying method for clinic staff to account for ancillary services prior to physicians' visits for a better patient care. Two case studies demonstrated the practicability and promising results on reducing patient waiting.
This article presents a unique approach to considering the required ancillary services in outpatient scheduling system that minimizes patient wait times. The approach will strengthen the existing scheduling methods to allow the time for ancillary services.
We undertook a study to improve the running of hospital outpatient clinics that were regularly overbooked, overrun, and had excessive patient waiting times. The methodology adopted entailed a mixture of qualitative and quantitative approaches, but was problem-driven and so only emerged as the project developed. We generated a number of proposals for the improved running of the clinics during the project, some implemented and some not. For future studies we would recommend that a flexible and open-minded approach is adopted. This may well involve an initial, mainly qualitative, study followed by the application of a series of modest models-occasionally more sophisticated modeling may be appropriate. We would also recommend that the benefits of such studies are not judged solely in terms of one-off implementation leading to measurable improvements in performance. They should also be seen as part of an overall process of improving health care practices.
Previous outpatient services have focused on patient waiting times in-clinic, for which the Patients' Charter sets a 30 minute limit. But the Patients' Charter also puts limits on the time a patient waits for first outpatient appointment after referral A computer simulation program has been developed which can model the new referral waiting list of any ambulatory care facility. The package has been applied in a case-study clinic for the purpose of predicting the impact of various scenarios on new referral waiting time.
Some recent research on queueing models is successfully applied to the problem of designing an appropriate appointment system for the out-patient department at the Royal Lancaster Infirmary. Although it is acknowledged that improving appointment systems is not simply a modelling problem, it is nevertheless argued that the model used here could be an effective tool in local studies.
One of the principal causes of waiting time in outpatient departments is the lack of well-designed appointment systems. A conceptual framework is given for dealing with existing appointment systems and to explain their working. The variables that play a role with respect to the appointment system are discussed. All different appointment systems can be compared according to their effect on the patients' waiting time and the physician's idle time, when the systems are expressed in terms of a new variable called "prepunctuality." Prepunctuality means the difference between the time of a patient's arrival at the clinic and the expected time of treatment, and is caused by the patient's own earliness, physician's lateness and the earliness induced by the appointment system chosen. The relationship between prepunctuality and both waiting and idle time was investigated by means of a computer simulation model. In this way, the consequences of using different appointment systems have been clarified, expressed in mean waiting time for the patient and total idle time for the physician. Given certain standards for waiting and idle time, the calculated results can be used to determine an appropriate appointment system and the corresponding waiting and idle time for the range of most common clinic situations. Examples are given to illustrate how these results can be used.
A discussion is presented of a generalized model of an outpatient clinic which duplicates many real-life complexities, e. g. different facilities, the patient routes through the clinic, number of observers in each facility, etc. The validation tests proved that the output generates distributions which are not statistically different from the observed distributions for The Pennsylvania State Outpatient Clinic. The model is relatively fast and efficient, and one typical day can be simulated in less than one second of the computer processing time on IBM System 370/168. With slight modifications, it is capable of being transferred to many different types of health care delivery systems, e. g. hospitals, health maintenance organizations and to prehospital emergency care systems. A description is give of some basic measures of effectiveness for outpatient clinics, and using these measures evaluates various operating procedures and policies.
Patients' waiting time and doctors idle time in the outpatient sening Selecting a suitable appointment system in an outpatient setting
- R B Fetter
- J D Thoiipson
FETTER, R.B. & THOIIPSON, J.D. (1966) Patients' waiting time and doctors idle time in the outpatient sening, Health Services Research, 1, pp. 6690. VISSERS, J.M.H. (1979) Selecting a suitable appointment system in an outpatient setting, Medical Care, 17, pp. 1207-1220.