Outpatient appointment scheduling given individual day-dependent no-show predictions

This paper examines the combined use of predictive analytics, optimization, and overbooking to schedule outpatient appointments in the presence of no-shows. We tackle the problem of optimally overbooking appointments given no-show predictions that depend on the individual appointment characteristics and on the appointment day. The goal is maximizing the number of patients seen while minimizing waiting time and overtime. Our analysis leads to the definition of a near-optimal and simple heuristic which consists of giving same-day appointments to likely shows and future-day appointments to likely no-shows. We validate our findings by performing extensive simulation tests based on an empirical data set of nearly fifty thousand appointments from a real outpatient clinic. The results suggest that our heuristic can lead to a substantial increase in performance and that it should be preferred to open access under most parameter configurations. Our paper will be of great interest to practitioners who want to improve their clinic performance by using individual no-show predictions to guide appointment scheduling.     

Block appointment systems for outpatient clinics with multiple doctors

Studies of appointment systems have to some extent led to a wide acceptance of individual or block appointment schemes in private practice and outpatient clinics. Most of the studies assume there is one punctual doctor in a clinic, which is often not the case in reality. Motivated by observations of actual clinic operations, we develop a block appointment system for clinic operations with multiple random arriving doctors. Through extensive simulation studies, we identify properties shared by the best appointment schedules. With these properties we can design a scheme based on simulation search that provides the optimal schedule for a given scheduling environment in an acceptable computation time. A simple (suboptimal) appointment rule is also proposed.     

考虑存在取消预约情形的门诊预约能力分配策略

在现实的门诊预约问题中,已经预约的患者在接收医疗服务之前,有可能取消先前的预约,这会对医院的收益造成负面影响,如何在考虑患者存在取消预约的情形下,设计合理有效的能力分配策略来保证医院的收益,是一个值得研究的问题.本文针对具有提前预约和当天预约的门诊预约能力分配问题,在考虑提前预约患者可能存在取消预约行为的情形下,提出了一种提前预约患者和当天预约患者的最优能力分配策略。文中首先以医院的期望收益最大作为决策目标,建立了存在取消预约患者的医疗预约问题的马尔科夫过程模型,并给出了该模型的相关性质;基于所建立模型的特征,证明了对于任意的提前预约时段,存在提前预约患者的最佳数量,进而给出了提前预约患者和当天预约患者的最优能力分配策略以及确定该策略的精确算法;最后,通过数值试验说明了本文所提出的能力分配策略的适用性和有效性。     

A simulation study of scheduling clinic appointments in surgical care: individual surgeon <Emphasis Type="Italic">versus</Emphasis> pooled lists

The purpose of this paper is to compare two methods of scheduling outpatient clinic appointments in the setting where the availability of surgeons for appointments depends on other clinical activities. We used discrete-event simulation to evaluate the likely impact of the scheduling methods on the number of patients waiting for appointments, and the times to appointment and to surgery. The progression of individual patients in a surgical service was modelled as a series of updates in patient records in reaction to events generated by care delivery processes in an asynchronous fashion. We used the Statecharts visual formalism to define states and transitions within each care delivery process, based on detailed functional and behavioural specifications. Our results suggest that pooling referrals, so that clinic appointments are scheduled with the first available surgeon, has a differential impact on different segments of patient flow and across surgical priority groups.     

Benefits of a truck appointment system on the service quality of inland transport modes at a multimodal container terminal

Container terminals pay more and more attention to the service quality of inland transport modes such as tucks, trains and barges. Truck appointment systems are a common approach to reduce truck turnaround times. This paper provides a tool to use the truck appointment system to increase not only the service quality of trucks, but also of trains, barges and vessels. We propose a mixed integer linear programming model to determine the number of appointments to offer with regard to the overall workload and the available handling capacity. The model is based on a network flow representation of the terminal and aims to minimize overall delays at the terminal. It simultaneously determines the number of truck appointments to offer and allocates straddle carriers to different transport modes. Numerical experiments, conducted on actual data, quantify the benefits of this combined solution approach. Discrete-event simulation validates the results obtained by the optimization model in a stochastic environment.     

基于满意度的预约门诊排队策略研究

为了推进预约挂号服务在医院有效的应用,本文结合实际情形,提出了病人满意度度量的新指标——加权病人等待时间,建立了以最大化病人满意度为目标的排队模型,并分析了医院目前常用的两种预约排队策略:不同优先级预约排队策略与时间段优先型预约排队策略。通过两种预约策略的比较,得到后者优于前者;通过预约与非预约策略的比较,得到预约策略优于非预约策略。在此基础上,对两种预约策略进行优化分析,求解出两种预约策略分别对应的最佳预约与非预约病人比例。最后,通过数值分析说明了应用预约策略对改善病人等待满意度的合理性及有效性,并对应用预约策略达到更好的满意度提出了可行建议。     

Optimized appointment scheduling

In service systems, in order to balance the server’s idle times and the customers’ waiting times, one may fix the arrival times of the customers beforehand in an appointment schedule. We propose a procedure for determining appointment schedules in such a D/G/1-type of system by sequentially minimizing the per-customer expected loss. Our approach provides schedules for any convex loss function; for the practically relevant cases of the quadratic and absolute value loss functions appealing closed-form results are derived. Importantly, our approach does not impose any conditions on the service time distribution; it is even allowed that the customers’ service times have different distributions.     

A stochastic appointment scheduling system on multiple resources with dynamic call-in sequence and patient no-shows for an outpatient clinic

This research focuses on the stochastic assignment system motivated by outpatient clinics, especially the physical therapy in rehabilitation service. The aim of this research is to develop a stochastic overbooking model to enhance the service quality as well as to increase the utilization of multiple resources, like therapy equipment in a physical therapy room, with the consideration of patients’ call-in sequence. The schedule for a single-service period includes a fixed number of blocks of equal length. When patients call, they are assigned to an appointment time for that block, and an existing appointment is not allowed to be changed. In each visit, a patient might require more than one resource and a probability of no-show. Two estimation methods were proposed for the expected waiting and overtime cost with multiple resources: Convolution Estimation Method and Joint Cumulative Estimation Method for the upper and lower bound value; respectively. A numerical example based on a physical therapy room was used to show that this stochastic model was able to schedule patients for better profitability compared with traditional appointment systems based on four prioritization rules. The workload in each appointment slot was more balanced albeit more patients were assigned to the first slot to fill up the empty room.     

Two-day appointment scheduling with patient preferences and geometric arrivals

We consider an appointment system where the patients have preferences about the appointment days. A patient may be scheduled on one of the days that is acceptable to her, or be denied appointment. The patient may or may not show up at the appointed time. The net cost is a convex function of the actual number of patients served on a given day. We study the optimal scheduling policy that minimizes the long-run average cost and study its structural properties. We advocate an index policy, which is easy to implement, performs well in comparison with other heuristic policies, and is close to the optimal policy.     

Improving appointment scheduling for medical screening

We investigate the optimization of appointment scheduling forbreast cancer screening, using the fact that a woman's attendanceprobability can be predicted. The methodology used applies tomedical screening in general. The results of the mathematical investigation presented in thispaper include a new formula for the cost of a screening session,a probabilistic model of rebooking appointments, a model ofattendance probability as a function of previous performance,and a heuristic cost optimization procedure. Breast Test Wales have improved efficiency by introducing heavilyoverbooked sessions for patients who are unlikely to attend.We use simulation modelling and insights from probability theoryto confirm the gain achieved by the Wales procedure and to assessthe further gain achievable by optimization of appointment scheduling.It is found that a gain in throughput of at least 10% can beobtained by optimizing appointment scheduling for screeningsessions, in particular by inviting patients in decreasing orderof attendance probability, and by overbooking near the end ofthe session. This avoids the need to set up dedicated sessionsfor poor attenders. Another possibility is to book patientswho change their appointment time, and who are therefore verylikely to attend, into dedicated sessions. The provision of appointment scheduling software with a built-insimulation and optimization module along the lines describedin this paper could enable radiographers to tailor appointmentscheduling for each area and so to schedule appointments veryefficiently.     

Queueing Models for Out-Patient Appointment Systems — a Case Study

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.     

Numerical multi-block grids in coastal ocean circulation modeling

In coastal ocean modeling, one desires to capture the evolution and interaction of multi-scales of physical phenomena in a complicated physical domain. With limited computer resources, an appropriate choice of the numerical grid has a key role in determining the quality of the solution of a numerical coastal ocean model. Traditionally, single-block rectangular grids have been most commonly used in coastal ocean modeling for their simplicity. An effective coastal ocean model represents the dynamics of the coastal ocean flow on a numerical grid, including the effects of complicated features such as coastlines, bottom topography (submarine canyons, seamounts, narrow straits), and multi-scale physical phenomena. These problems require a model grid system more efficient than a traditional single-block rectangular grid. The model grids must give better resolution of coastlines and boundary conditions, multi-scale physical phenomenon, and save computer resources. These grids can also easily increase horizontal resolution in a subregion of the model domain without increasing computer expense with high resolution over the entire domain. The multi-block numerical generation grid technique is used in developing a coastal ocean system applied to the Mediterranean Sea (MED) with complicated coastlines, bottom topography and multi-scale physical features. The MED coastal ocean system consists of the MED model based on the Princeton Ocean Model, numerical grid generation routines, and a grid package which allows the model to be coupled with model grids. The traditional, nine-block orthogonal grid, and eight-block curvilinear nearly orthogonal coastline-following grid are used in the study. The numerical solutions with the three grids are compared in term of effectiveness. The numerical simulations show some MED basic physical features.     

Dynamic multi-priority,multi-class patient scheduling with stochastic service times

Efficient patient scheduling has significant operational, clinical and economical benefits on health care systems by not only increasing the timely access of patients to care but also reducing costs. However, patient scheduling is complex due to, among other aspects, the existence of multiple priority levels, the presence of multiple service requirements, and its stochastic nature. Patient appointment (allocation) scheduling refers to the assignment of specific appointment start times to a set of patients scheduled for a particular day while advance patient scheduling refers to the assignment of future appointment days to patients. These two problems have generally been addressed separately despite each being highly dependent on the form of the other. This paper develops a framework that incorporates stochastic service times into the advance scheduling problem as a first step towards bridging these two problems. In this way, we not only take into account the waiting time until the day of service but also the idle time/overtime of medical resources on the day of service. We first extend the current literature by providing theoretical and numerical results for the case with multi-class, multi-priority patients and deterministic service times. We then adapt the model to incorporate stochastic service times and perform a comprehensive numerical analysis on a number of scenarios, including a practical application. Results suggest that the advance scheduling policies based on deterministic service times cannot be easily improved upon by incorporating stochastic service times, a finding that has important implications for practice and future research on the combined problem.     

Staffing a service system with appointment-based customer arrivals

Appointment systems are widely used to facilitate customers’ access to services in many industries such as healthcare. A number of studies have taken a queueing approach to analyse service systems and facilitate managerial decisions on staffing requirements by assuming independent and stationary customer arrivals. This paper is motivated by the observation that the queueing-based method shows relatively poor performance when customers arrive according to their appointment times. Because customer arrivals are dependent on their appointment times, this study, unlike queueing-based methods, conducts a detailed analysis of appointment-based customer arrivals instead of making steady-state assumptions. We develop a new model that captures the characteristics of appointment-based customer arrivals and computes the probability of transient system states. Through the use of this model, which relaxes stationary and independent assumptions, we propose a heuristic algorithm that determines staffing requirements with aims to minimizing staff-hours while satisfying a target service level. The simulation results show that the proposed method outperforms the queueing-based method.     

Recovery management for a dial-a-ride system with real-time disruptions

The problem considered in this work stems from a non-profit organization in charge of door-to-door passenger transportation for medical appointments. Patients are picked up at home by a driver and are then dropped at their appointment location. They may also be driven back home at the end of their appointment. Some patients have specific requirements, e.g., they may require an accompanying person or a wheelchair. Planning such activities gives rise to a so-called dial-a-ride problem. In the present work, it is assumed that the requests assigned to the drivers have been selected, and the transportation plan has been established for the next day. However, in practice, appointment durations may vary due to unforeseen circumstances, and some transportation requests may be modified, delayed or canceled during the day. The aim of this work is to propose a reactive algorithm which can adapt the initial plan in order to manage the disruptions and to take care of as many patients as possible in real-time. The plan should be modified quickly when a perturbation is observed, without resorting to major changes which may confuse the drivers and the patients. Several recourse procedures are defined for this purpose. They allow the dispatcher to temporarily delete a request, to insert a previously deleted request, or to permanently cancel a request. Simulation techniques are used to test the approach on randomly generated scenarios. Several key performance indicators are introduced in order to measure the impact of the disruptions and the quality of the solutions.     

Queueing models for appointment-driven systems

Many service systems are appointment-driven. In such systems, customers make an appointment and join an external queue (also referred to as the “waiting list”). At the appointed date, the customer arrives at the service facility, joins an internal queue and receives service during a service session. After service, the customer leaves the system. Important measures of interest include the size of the waiting list, the waiting time at the service facility and server overtime. These performance measures may support strategic decision making concerning server capacity (e.g. how often, when and for how long should a server be online). We develop a new model to assess these performance measures. The model is a combination of a vacation queueing system and an appointment system.     

A queueing network analysis of a health center

This paper shows how a queueing network model helped to uncover the causes of delay in a health center appointment clinic. Patients, clerks, technicians, doctors and nurses agreed that the clerical registration area was the major bottleneck in the system. Our first reaction was to simulate the system with special attention on the complex registration procedure. Time constraints on data collection and program development led us to a queueing network model and QNA, a software tool for analyzing queueing networks developed by Whitt. The queueing analysis showed the registration area was not the bottleneck and we conjectured that delays were due to scheduling problems. A preliminary trial in the clinic of a modified appointment system showed promise with a 20 minute reduction in average time in the system (based on a small sample). Although there were significant differences between features of the real system and assumptions in the queueing network model, the queueing network model yielded insight into the operation of the appointment clinic.     

Computationally efficient evaluation of appointment schedules in health care

We consider the problem of evaluating and constructing appointment schedules for patients in a health care facility where a single physician treats patients in a consecutive manner, as is common for general practitioners, clinics and for outpatients in hospitals. Specifically, given a fixed-length session during which a physician sees K patients, each patient has to be given an appointment time during this session in advance. Optimising a schedule with respect to patient waiting times, physician idle times, session overtime, etc. usually requires a heuristic search method involving a huge number of repeated schedule evaluations. Hence, our aim is to obtain accurate predictions at very low computational cost. This is achieved by (1) using Lindley’s recursion to allow for explicit expressions and (2) choosing a discrete-time (slotted) setting to make those expressions easy to compute. We assume general, possibly distinct, distributions for the patients’ consultation times, which allows to account for multiple treatment types, emergencies and patient no-shows. The moments of waiting and idle times are obtained and the computational complexity of the algorithm is discussed. Additionally, we calculate the schedule’s performance in between appointments in order to assist a sequential scheduling strategy.     

Effect of global FCFS and relative load distribution in two-class queues with dedicated servers

In this paper, we investigate multi-class multi-server queueing systems with global FCFS policy, i.e., where customers requiring different types of service—provided by distinct servers—are accommodated in one common FCFS queue. In such scenarios, customers of one class (i.e., requiring a given type of service) may be hindered by customers of other classes. The purpose of this paper is twofold: to gain (qualitative and quantitative) insight into the impact of (i) the global FCFS policy and (ii) the relative distribution of the load amongst the customer classes, on the system performance. We therefore develop and analyze an appropriate discrete-time queueing model with general independent arrivals, two (independent) customer classes and two class-specific servers. We study the stability of the system and derive the system-content distribution at random slot boundaries; we also obtain mean values of the system content and the customer delay, both globally and for each class individually. We then extensively compare these results with those obtained for an analogous system without global FCFS policy (i.e., with individual queues for the two servers). We demonstrate that global FCFS, as well as the relative distribution of the load over the two customer classes, may have a major impact on the system performance.     

On a dual hybrid queueing system

This article deals with a hybrid system, in which a single server processes two different queues of units, one called primary and the other one — secondary. The queueing process in the primary system is formed by a Poisson flow of groups of units, while the secondary system is closed. The server’s primary appointment (in hybrid mode I) is to process units in batches until the buffer content drops significantly. In this case, the server takes over a queue in the secondary system (activating hybrid mode II), and he is to complete some minimum amount of jobs (rendered in groups of random sizes during random times). When he is done with this work, he returns to the primary system. If the queue there is not long enough, he waits, thereby activating hybrid mode III. The authors first apply and embellish some techniques from fluctuation theory to find the exit times from respective hybrid modes and queue levels in both systems in terms of their joint functionals. The results are then utilized for the subsequent (semi-regenerative) analysis of the evolution of queueing processes. The authors obtain explicit formulas for the limiting distribution of the queueing process and the mean number of units processed in the secondary system.