Clinic scheduling models with overbooking for patients with heterogeneous no-show probabilities

Clinical overbooking is intended to reduce the negative impact of patient no-shows on clinic operations and performance. In this paper, we study the clinical scheduling problem with overbooking for heterogeneous patients, i.e. patients who have different no-show probabilities. We consider the objective of maximizing expected profit, which includes revenue from patients and costs associated with patient waiting times and physician overtime. We show that the objective function with homogeneous patients, i.e. patients with the same no-show probability, is multimodular. We also show that this property does not hold when patients are heterogeneous. We identify properties of an optimal schedule with heterogeneous patients and propose a local search algorithm to find local optimal schedules. Then, we extend our results to sequential scheduling and propose two sequential scheduling procedures. Finally, we perform a set of numerical experiments and provide managerial insights for health care practitioners.     

Dynamic overbooking scheduling system to improve patient access

Patient no-show has long been a recognized problem in modern outpatient health-care delivery systems. The common impacts are reduced clinic efficiency and provider productivity, wasted medical resources, increased health-care cost and limited patient access to care. The main goal of this research is to develop an effective dynamic overbooking policy into any scheduling system that accounts for the predictive probability of no-shows for any given patient. This policy increases the quality of patient care in terms of wait time and access to care while minimizing the clinic's costs. This proposed model is also illustrated to be more cost-effective than overbooking patients evenly throughout a clinic session. This paper also suggests that overbooking should be performed at better patient flow and higher no-show rate so that the costs are minimized. Consequently, this research improves the outpatient experience for both patients and medical providers.     

Effective cancellation policy to reduce the negative impact of patient no-show

The problem of patient no-show in outpatient delivery systems has been a long recognized issue. The negative impacts include underutilized medical resources, increased healthcare costs, decreased access to care, and reduced clinic efficiency and provider productivity. Many clinics have cancellation policies of asking their patients to cancel 24 or 48?h in advance. However, there is no logical or mathematical basis for such a policy. The objective is to develop an effective cancellation policy that accounts for current no-show rates, the clinic's flow, and its fill rates to minimize the cost of patient wait time, physician idle time, and overtime. A simulation approach is presented to determine the hours required for patients to call in advance for cancelling appointments. The findings indicate that when fill rates are low and no-show probabilities are high, the time required for patients to cancel appointments needs to increase in order to achieve the goal of being cost-effective.     

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.     

A cost-effective urgent care policy to improve patient access in a dynamic scheduled clinic setting

Patient no-show in outpatient clinics has been a long recognized issue, which negatively impacts clinic operational efficiency in terms of costs and patient access to care. One way to reduce these negative impacts is to allow urgent walk-ins during a clinic day. Some clinics allow random walk-ins and some purposely leave open time slots to accommodate them. The objective of this paper is to develop a cost-effective urgent care policy that is added on top of a full schedule and takes into account scheduled patients’ no-show rates to improve patient access to care in a dynamic clinic environment. The findings indicate that the proposed approach outperforms the current random and urgent slot approaches. This paper demonstrates a dynamic approach for accommodating urgent patients into a patient scheduling system, based on the prediction of an individual patient's no-show probability and the maximum number of urgent patients allowed.     

Heuristic algorithms for a vehicle routing problem with simultaneous delivery and pickup and time windows in home health care

This paper addresses a vehicle scheduling problem encountered in home health care logistics. It concerns the delivery of drugs and medical devices from the home care company’s pharmacy to patients’ homes, delivery of special drugs from a hospital to patients, pickup of bio samples and unused drugs and medical devices from patients. The problem can be considered as a special vehicle routing problem with simultaneous delivery and pickup and time windows, with four types of demands: delivery from depot to patient, delivery from a hospital to patient, pickup from a patient to depot and pickup from a patient to a medical lab. Each patient is visited by one vehicle and each vehicle visits each node at most once. Patients are associated with time windows and vehicles with capacity. Two mixed-integer programming models are proposed. We then propose a Genetic Algorithm (GA) and a Tabu Search (TS) method. The GA is based on a permutation chromosome, a split procedure and local search. The TS is based on route assignment attributes of patients, an augmented cost function, route re-optimization, and attribute-based aspiration levels. These approaches are tested on test instances derived from existing VRPTW benchmarks.     

Matching daily healthcare provider capacity to demand in advanced access scheduling systems

Advanced access scheduling, introduced in the early 1990s, is reported to significantly improve the performance of outpatient clinics. The successful implementation of advanced access scheduling requires the match of daily healthcare provider capacity with patient demand. In this paper, for the first time a closed-form approach is presented to determine the optimal percentage of open-access appointments to match daily provider capacity to demand. This paper introduces the conditions for the optimal percentage of open-access appointments and the procedure to find the optimal percentage. Furthermore, the sensitivity of the optimal percentage of open-access appointments to provider capacity, no-show rates, and demand distribution is investigated. Our results demonstrate that the optimal percentage of open-access appointments mainly depends on the ratio of the average demand for open-access appointments to provider capacity and the ratio of the show-up rates for prescheduled and open-access appointments.     

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.     

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.     

Determination of optimal variable-sized multiple-block appointment systems

The single-block appointment system is the most common method of scheduling ambulatory care clinics today. Several studies have examined various appointment systems ranging from single-block appointments on one extreme to individual appointments on the other, and including mixtures of these such as multiple-block (m-at-a-time) and block/individual systems. In this paper we analyze a general single-server multiple-block system, one permitting blocks of variable size. In the analysis we use a dynamic programming approach, with some modifications to compensate for the non-Markov nature of the problem. Analytical results and approximations which significantly reduce the computational requirements for a solution are obtained. Examples demonstrate that under certain weightings of the criteria of waiting, idle, and overtime, the generality of the system considered here allows performance superior to that of other commonly used systems.     

Master surgery scheduling with consideration of multiple downstream units

We consider a master surgery scheduling (MSS) problem in which block operating room (OR) time is assigned to different surgical specialties. While many MSS approaches in the literature consider only the impact of the MSS on operating theater and operating staff, we enlarge the scope to downstream resources, such as the intensive care unit (ICU) and the general wards required by the patients once they leave the OR. We first propose a stochastic analytical approach, which calculates for a given MSS the exact demand distribution for the downstream resources. We then discuss measures to define downstream costs resulting from the MSS and propose exact and heuristic algorithms to minimize these costs.     

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。     

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.     

Surgical case scheduling as a generalized job shop scheduling problem

Surgical case scheduling allocates hospital resources to individual surgical cases and decides on the time to perform the surgeries. This task plays a decisive role in utilizing hospital resources efficiently while ensuring quality of care for patients. This paper proposes a new surgical case scheduling approach which uses a novel extension of the Job Shop scheduling problem called multi-mode blocking job shop (MMBJS). It formulates the MMBJS as a mixed integer linear programming (MILP) problem and discusses the use of the MMBJS model for scheduling elective and add-on cases. The model is illustrated by a detailed example, and preliminary computational experiments with the CPLEX solver on practical-sized instances are reported.     

Suitability and managerial implications of a Master Surgical Scheduling approach

Operating room (OR) planning and scheduling is a popular and challenging subject within the operational research applied to health services research (ORAHS). However, the impact in practice is very limited. The organization and culture of a hospital and the inherent characteristics of its processes impose specific implementation issues that affect the success of planning approaches. Current tactical OR planning approaches often fail to account for these issues. Master surgical scheduling (MSS) is a promising approach for hospitals to optimize resource utilization and patient flows. We discuss the pros and cons of MSS and compare MSS with centralized and decentralized planning approaches. Finally, we address various implementation issues of MSS and discuss its suitability for hospitals with different organizational foci and culture.     

Literature review on multi-appointment scheduling problems in hospitals

This paper presents a review of the literature on multi-appointment scheduling problems in hospitals. In these problems, patients need to sequentially visit multiple resource types in a hospital setting so they can receive treatment or be diagnosed. Therefore, each patient is assigned a specific path over a subset of the considered resources and each step needs to be scheduled. The main aim of these problems is to let each patient visit the resources in his or her subset within the allotted time to receive timely care. This is important because a delayed diagnosis or treatment may result in adverse health effects. Additionally, with multi-appointment scheduling, hospitals have the opportunity to augment patient satisfaction, allowing the patient to visit the hospital less frequently. To structure the growing body of literature in this field and aid researchers in the field, a classification scheme is proposed and used to classify the scientific work on multi-appointment scheduling in hospitals published before the end of 2017. The results show that multi-appointment scheduling problems are becoming increasingly popular. In fact, multi-appointment scheduling problems in hospitals are currently gaining progressively more momentum in the academic literature.     

Optimization models for radiotherapy patient scheduling

The efficient radiotherapy patient scheduling, within oncology departments, plays a crucial role in order to ensure the delivery of the right treatment at the right time. In this context, generating a high quality solution is a challenging task, since different goals (i.e., all the activities are scheduled as soon as possible, the patient waiting time is minimized, the device utilization is maximized) could be achieved and a large set of constraints (i.e., every device can be used by only one patient at time, the treatments have to be performed in an exact time order) should be taken into account. We propose novel optimization models dealing with the efficient outpatient scheduling within a radiotherapy department defined in such a way to represent different real-life situations. The effectiveness of the proposed models is evaluated on randomly generated problems and on a real case situation. The results are very encouraging since the developed optimization models allow to overcome the performance of human experts (i.e., the number of patients that begin the radiotherapy treatment is maximized).      

A Markovian queueing model for ambulance offload delays

Ambulance offload delays are a growing concern for health care providers in many countries. Offload delays occur when ambulance paramedics arriving at a hospital Emergency Department (ED) cannot transfer patient care to staff in the ED immediately. This is typically caused by overcrowding in the ED. Using queueing theory, we model the interface between a regional Emergency Medical Services (EMS) provider and multiple EDs that serve both ambulance and walk-in patients. We introduce Markov chain models for the system and solve for the steady state probability distributions of queue lengths and waiting times using matrix-analytic methods. We develop several algorithms for computing performance measures for the system, particularly the offload delays for ambulance patients. Using these algorithms, we analyze several three-hospital systems and assess the impact of system resources on offload delays. In addition, simulation is used to validate model assumptions.     

Sequencing and scheduling N customers for a stochastic server

In this paper, we study the problem of sequencing and scheduling N customers for a single-server system. The goal is to balance the expected customer flow times and the expected system completion time. Customers are scheduled to enter the system by appointments only and the service times are exponentially distributed with different rates. The optimization of such a system involves determining the customer service order (sequencing) and the interarrival times (scheduling). We show that the service order depends upon the order of service rates and the optimal schedule can be obtained by solving a set of nonlinear equations. Numerical examples are used to illustrate the method.     

Stochastic radiotherapy appointment scheduling

Central European Journal of Operations Research - When scheduling the starting times for treatment appointments of patients in hospitals or outpatient clinics such as radiotherapy centers,...