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Scheduling rules to achieve lead-time targets in outpatient appointment systems

Authors:
Thuba T. Nguyen at Cranfield University
Thuba T. Nguyen
Appa Iyer Sivakumar at Nanyang Technological University
Appa Iyer Sivakumar
Stephen C. Graves at Massachusetts Institute of Technology
Stephen C. Graves
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This paper considers how to schedule appointments for outpatients, for a clinic that is subject to appointment lead-time targets for both new and returning patients. We develop heuristic rules, which are the exact and relaxed appointment scheduling rules, to schedule each new patient appointment (only) in light of uncertainty about future arrivals. The scheduling rules entail two decisions. First, the rules need to determine whether or not a patient's request can be accepted; then, if the request is not rejected, the rules prescribe how to assign the patient to an available slot. The intent of the scheduling rules is to maximize the utilization of the planned resource (i.e., the physician staff), or equivalently to maximize the number of patients that are admitted, while maintaining the service targets on the median, the 95th percentile, and the maximum appointment lead-times. We test the proposed scheduling rules with numerical experiments using real data from the chosen clinic of Tan Tock Seng hospital in Singapore. The results show the efficiency and the efficacy of the scheduling rules, in terms of the service-target satisfaction and the resource utilization. From the sensitivity analysis, we find that the performance of the proposed scheduling rules is fairly robust to the specification of the established lead-time targets.
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... The appointment scheduling problem is another approach for resource allocation. This problem has been studied extensively in the literature; Cayirli and Veral (2003) provided a review of the literature and some recent published papers include Green, Savin, and Wang (2006), Creemers, Belien, & Lambrecht (2012), LaGang and Lawrence (2012), Balasubramanian, Biehl, Dai, and Muriel (2014), Kemper, Klaassen, and Mandjes (2014), Kuiper and Mandjes (2015), Mak, Rong, and Zhang (2016), Patrick, Puterman, and Queyranne (2016) , and Nguyen, Sivakumar, and Graves (2016) . The research examines the trade-offs between patient waiting time, and physician idle-time and/or physician over-time. ...
... The research examines the trade-offs between patient waiting time, and physician idle-time and/or physician over-time. These studies, however, do not explicitly consider the achievement of the appointment lead-time targets, with the exception of Nguyen et al. (2016) . However, Nguyen et al. (2016) do not determine how many physicians are needed to achieve the established targets. ...
... These studies, however, do not explicitly consider the achievement of the appointment lead-time targets, with the exception of Nguyen et al. (2016) . However, Nguyen et al. (2016) do not determine how many physicians are needed to achieve the established targets. ...
Capacity Planning With Demand Uncertainty For Outpatient Clinics
Article
  • Nov 2017
  • EUR J OPER RES
In this study, we develop a capacity planning model to determine the required number of physicians for an outpatient system with patient reentry. First-visit (FV) patients are assumed to arrive randomly to the system. After their first appointment, the FV patient may require additional appointments, and will then become a re-visit (RV) patient; after each appointment an RV patient will require subsequent visits with a given probability. The system must achieve a set of targets on the appointment lead-times for both FV and RV patients. Furthermore, the system must have sufficient capacity to assure that a given percentile of FV patients is admitted. We develop a deterministic model that finds the required capacity over a finite horizon. We establish the tractability of the deterministic model and show that it provides a reasonable approximation to the stochastic model. We also demonstrate the value from knowing the demands in terms of the required resources. These conclusions are numerically illustrated using real data from the Urology outpatient clinic of the studied hospital.
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... One group is focused on Bdirect^waiting time, and the other, focused on Bindirect^waiting time; the former uses different operational levers (e.g., block size, consultation time)to reduce direct PWT and the latter employs scheduling window to decrease indirect PWT. To date, to our best knowledge, most studies have focused on the reduction of BdirectP WT and very few on Bindirect^PWT [11,[16][17][18][19][20][21][22].Our study belongs to the latter, i.e., finding an optimal scheduling window to minimize outpatient indirect PWT, patient rejection and physician idle time in an environment with patient noshows. ...
... Then they developed a dynamic model and proposed a heuristic solution procedure to search for feasible solutions. Nguyen et al. [21] developed heuristic rules to schedule appointments for both new and returning patients. Their objective was to maximize the utilization of the resource while maintaining the service targets with the maximum leadtime. ...
... The sensitivity analysis showed that the performance of the proposed scheduling rules is fairly robust to the specification of established lead-time targets. Note that the above studies [18,19,21,22] were aimed at developing efficient outpatient scheduling systems, but did not explicitly using the term Bscheduling window,^which essentially is their research focus. This may explain why the most-recent research review by Almadi-Javid et al. [16] identified only one paper focused on Bscheduling windows^for outpatient appointment. ...
An optimization model to determine appointment scheduling window for an outpatient clinic with patient no-shows
Article
Full-text available
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  • Health Care Manag Sci
This paper investigates appointment scheduling for an outpatient department in West China Hospital (WCH), one of the largest single point of access hospitals in the world. Our pilot data analysis shows that the appointment system at WCH can be improved through leveraging the scheduling window (i.e., the number of days in advance a patient makes an appointment for future services). To gain full insight into this strategy, our study considers two cases, based on if patients are willing to wait for scheduled appointments or not. We developed a stylized single server queueing model to find optimal scheduling windows. Results show that, when patients are less sensitive to time delay (i.e., patients will wait for scheduled services), levering scheduling windows is not effective to minimize the total cost per day of the appointment system. In contrast, when patients are sensitive to time delay (i.e., patients may find services elsewhere), then our model considers the potential cost of physician idle time. The modeling results indicate that the total cost per day is relatively sensitive to the magnitude of scheduling window. Thus, adopting a proper scheduling window is very important. In addition, our study proves that the cost functions of both cases are quasi-concave, which are also validated by actual data drawn from the Healthcare Information System at WCH. A comparison of numerical results between two cases is made to draw further managerial insights into scheduling policies for WCH. Discussion of our findings and research limitations are also provided.
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... Denton et al. (2010) proposed stochastic and robust optimization models for the assignment of surgeries to operating rooms on a given day of surgery considering uncertain surgery duration. After that, Guo et al. (2021) considered cancellation cost and unscheduled cost into the total cost to find an assignment of surgeries to ORs. Nguyen et al. (2017) developed scheduling rules for outpatient appointment problems. Berg and Denton (2017) presented a new stochastic model for dynamically allocating patients to rooms in outpatient centers considering service duration uncertainty. ...
Integration of text-mining and telemedicine appointment optimization
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  • Nov 2023
  • ANN OPER RES
Nowadays, many countries view profitable telemedicine as a viable strategy for meeting healthcare needs, especially during the pandemic. Existing appointment models are based on patients’ structured data. We study the value of incorporating textual patient data into telemedicine appointment optimization. Our research contributes to the healthcare operations management literature by developing a new framework showing (1) the value of the text in the telemedicine appointment problem, (2) the value of incorporating the textual and structured data in the problem. In particular, in the first phase of the framework, a text-driven classification model is developed to classify patients into normal and prolonged service time classes. In the second phase, we integrate the classification model into two existing decision-making policies. We analyze the performance of our proposed policy in the presence of existing methods on a data set from the National Telemedicine Center of China (NTCC). We first show that our classifier can achieve 90.4% AUC in a binary task based on textual data. We next show that our method outperforms the stochastic model available in the literature. In particular, with a slight change of actual distribution from historical data to a normal distribution, we observe that our policy improves the average profit of the policy obtained from the stochastic model by 42% and obtains lower relative regret (18%) from full information than the stochastic model (148%). Furthermore, our policy provides a promising trade-off between the cancellation and postponement rates of patients, resulting in a higher profit and a better schedule strategy for the telemedicine center.
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... Capacity planning for outpatient appointment systems has been a challenging and interesting field for many researchers [6]. Previous research has taken different approaches, some studies focus on resource allocation [7,8,9], and appointment scheduling problems [10,11,12] while others attempt to determine the required capacity [13,14,15,16] to achieve performance targets. In most of these works, performance (patient satisfaction) is generally measured through direct waiting time (i.e., the time spent in the facility) and indirect waiting time (i.e., the time between the patient's call for an appointment and the scheduled appointment time). ...
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  • Sep 2023
In this study, we investigate the required capacity of the ambulatory surgery units in a network of hospitals considering different outpatient surgeries within various specialties. The objective is to find the minimum cost capacity decisions that satisfy the increasing outpatient demand and keep the ‘waiting times to surgery’ below the specified thresholds. We also explore the potential improvement of a collaborative network to increase the resilience of day surgery services and prepare the territories for the expected increase in outpatient demand. For this, we propose integer programming optimization models for non-collaborative and collaborative networks. We demonstrate the benefits of potential collaboration between hospitals through a numerical study.
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... Berg et al. studied the use of constraint optimization modeling to balance doctors' work schedules in specialized outpatient clinics, minimizing the variability of timetables, improving work efficiency, and thus reducing the maximum number of doctors making visits [27]. Nguyen et al. proposed precise and relaxing appointment scheduling rules to arrange the appointment of each new patient according to the uncertainty of future arrival [28]. Its scheduling rules are designed to maximize the use of program resources (i.e., physician staff ) or, equivalently, to maximize the number of patients admitted. ...
Research on outpatient capacity planning combining lean thinking and integer linear programming
Article
Full-text available
  • Feb 2023
  • BMC MED INFORM DECIS
Background The size and cost of outpatient capacity directly affect the operational efficiency of a whole hospital. Many scholars have faced the study of outpatient capacity planning from an operations management perspective. Objective The outpatient service is refined, and the quantity allocation problem of each type of outpatient service is modeled as an integer linear programming problem. Thus, doctors’ work efficiency can be improved, patients’ waiting time can be effectively reduced, and patients can be provided with more satisfactory medical services. Methods Outpatient service is divided into examination and diagnosis service according to lean thinking. CPLEX is used to solve the integer linear programming problem of outpatient service allocation, and the maximum working time is minimized by constraint solution. Results A variety of values are taken for the relevant parameters of the outpatient service, using CPLEX to obtain the minimum and maximum working time corresponding to each situation. Compared with no refinement stratification, the work efficiency of senior doctors has increased by an average of 25%. In comparison, the patient flow of associate senior doctors has increased by an average of 50%. Conclusion In this paper, the method of outpatient capacity planning improves the work efficiency of senior doctors and provides outpatient services for more patients in need; At the same time, it indirectly reduces the waiting time of patients receiving outpatient services from senior doctors. And the patient flow of the associate senior doctors is improved, which helps to improve doctors’ technical level and solve the problem of shortage of medical resources.
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... Patients who can make appointments, know the clinic's noshow policy, and arrive on time, had less emergency room usage (Tzeng et al., 2019). Failure to adhere to healthcare facility policies regarding appointment scheduling could result in overcrowding, increased wait times, and limited time for patient-healthcare staff interaction, which further affects quality of healthcare delivery and treatment outcomes (Ahmadi-Javid et al., 2017;Ansell et al., 2017;Dantas et al., 2018;Deceuninck et al., 2018;Lu et al., 2018;Nguyen et al., 2017). ...
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... Choi and Banerjee (2016) attempted to minimize the total expected cost of delay and idle time between blocks by proposing two heuristic approaches. Nguyen et al. (2017) addressed an outpatient scheduling problem for a clinic, and they developed heuristic rules to obtain lead-time targets for new and returning patients. Their aim was to maximize the utilization of resources and the number of admitted patients considering some conditions. ...
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Solving bin Packing Problem with a Hybrid Genetic Algorithm for VM Placement in Cloud
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A network flow approach for tactical resource planning in outpatient clinics
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Full-text available
  • Jun 2015
This paper introduces a deterministic model to plan the physician requirements for outpatient clinics to achieve service targets for the appointment lead-times of patients. The Ministry of Health of Singapore has established targets for the median, 95th percentile, and 100th percentile of appointment lead-times for patients, since long appointment postponements are regarded as being unacceptable for health care services. The study is to match the capacity of the healthcare providers to the patient demand for a re-entry system, subject to restrictions on the appointment lead-times for patients. We propose a mixed-integer programming model for planning capacity with the minimization of the maximum required capacity as its objective. In the model we assume a finite planning horizon, deterministic arrivals, multiple types of patients, identical physicians, and dependent demand between types of patients. We solve this model with a Branch and Cut algorithm. We test the model with numerical experiments using real data from the chosen specialty at the outpatient clinic of the studied hospital. The results show the value of the proposed model via a systematic push-pull mechanism in scheduling patients’ requests to minimize the objective. The clinic should use one of the appointment lead-time targets to determine the patients’ appointment dates. Finally, from the sensitivity analyses we demonstrate that the objective is negatively correlated with first-visit patients’ appointment lead-time targets, the discharge rates, and the re-visit patients’ mean appointment lead-time; we find a positive correlation between the first-visit patients’ mean appointment lead-time and the appointment lead-time targets.
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Scheduling and Sequencing Arrivals to an Appointment System
Article
Full-text available
  • Aug 2001
  • J SERV RES-US
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Article
  • Jun 1996
  • J OPER MANAG
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Minimizing expected waiting in a medical appointment system
Article
  • Sep 2000
An appointment policy is established for a specific outpatient system, with the goal of reducing a combination of patients' expected waiting times and doctor's expected overtime. Service times are stochastic, and patients are assumed to be punctual if they show for their appointments. Substantial reductions in waiting times can be obtained over traditional scheduling practices, and the procedure is easily implemented by a naive scheduler once the optimal policy is established.
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A Study of Queues and Appointment Systems in Hospital Out-Patient Departments, with Special Reference to Waiting-Times
Article
  • Jul 1952
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Article
  • Apr 2015
  • EUR J OPER RES
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  • OMEGA-INT J MANAGE S
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Appointment Systems in Out-patients?? Clinics and the Effect of Patients?? Unpunctuality
Article
  • Jul 1964
  • MED CARE
The present level of unpunctuality by patients need not prevent the use of a simple appointment scheme, giving a reasonable balance between waiting by the doctor and the patients. Waiting-times when patients art punctual or unpunctual are compared, and are shown not to differ greatly. When clinics are small or consultation-times very variable, even with punctual patients, waiting-times may be long, and the effects of these factors may exceed that due to patients' unpunctuality. It is recommended that, when possible, patients should be sorted or doctor-sessions combined, in this type of clinic.
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