Dynamic scheduling with due dates and time windows: an application to chemotherapy patient appointment booking

Intraday dynamic rescheduling under patient no-shows

Patient no-shows are a major source of uncertainty for outpatient clinics. A common approach to hedge against the effect of no-shows is to overbook. The trade-off between patient's waiting costs and provider idling/overtime costs determines the optimal level of overbooking. Existing work on appointment scheduling assumes that appointment times cannot be updated once they have been assigned. However, advances in communication technology and the adoption of online (as opposed to in-person) appointments make it possible for appointments to be flexible. In this paper, we describe an intraday dynamic rescheduling model that adjusts upcoming appointments based on observed no-shows. We formulate the problem as a Markov Decision Process in order to compute the optimal pre-day schedule and the optimal policy to update the schedule for every scenario of no-shows. We also propose an alternative formulation based on the idea of 'atomic' actions that allows us to apply a shortest path algorithm to solve for the optimal policy more efficiently. Based on a numerical study using parameter estimates from existing literature, we find that intraday dynamic rescheduling can reduce expected cost by 15% compared to static scheduling.

Online scheduling using a fixed template: the case of outpatient chemotherapy drug administration

In this paper, we use a fixed template of slots for the online scheduling of appointments. The template is a link between planning the service capacity at a tactical level and online scheduling at an operational level. We develop a detailed heuristic for the case of drug administration appointments in outpatient chemotherapy. However, the approach can be applied to online scheduling in other application areas as well. The desired scheduling principles are incorporated into the cost coefficients of the objective function of a binary integer program for booking appointments in the template, as requests arrive. The day and time of appointments are decided simultaneously, rather than sequentially, where optimal solutions may be eliminated from the search. The service that we consider in this paper is an example to show the versatility of a fixed template online scheduling model. It requires two types of resource, one of which is exclusively assigned for the whole appointment duration, and the other is shared among multiple appointments after setting up the service. There is high heterogeneity among appointments on a day of this service. The appointments may range from fifteen minutes to more than eight hours. A fixed template gives a pattern for the scheduling of possibly required steps before the service. Instead of maximizing the fill-rate of the template, the objective of our heuristic is to have high performance in multiple indicators pertaining to various stakeholders (patients, nurses, and the clinic). By simulation, we illustrate the performance of the fixed template model for the key indicators.

Clustering and Stochastic Simulation Optimization for Outpatient Chemotherapy Appointment Planning and Scheduling

Outpatient Chemotherapy Appointment (OCA) planning and scheduling is a process of distributing appointments to available days and times to be handled by various resources through a multi-stage process. Proper OCAs planning and scheduling results in minimizing the length of stay of patients and staff overtime. The integrated consideration of the available capacity, resources planning, scheduling policy, drug preparation requirements, and resources-to-patients assignment can improve the Outpatient Chemotherapy Process's (OCP's) overall performance due to interdependencies. However, developing a comprehensive and stochastic decision support system in the OCP environment is complex. Thus, the multi-stages of OCP, stochastic durations, probability of uncertain events occurrence, patterns of patient arrivals, acuity levels of nurses, demand variety, and complex patient pathways are rarely addressed together. Therefore, this paper proposes a clustering and stochastic optimization methodology to handle the various challenges of OCA planning and scheduling. A Stochastic Discrete Simulation-Based Multi-Objective Optimization (SDSMO) model is developed and linked to clustering algorithms using an iterative sequential approach. The experimental results indicate the positive effect of clustering similar appointments on the performance measures and the computational time. The developed cluster-based stochastic optimization approaches showed superior performance compared with baseline and sequencing heuristics using data from a real Outpatient Chemotherapy Center (OCC).

Appointment Scheduling Problem in Complexity Systems of the Healthcare Services: A Comprehensive Review

This paper provides a comprehensive review of Appointment Scheduling (AS) in healthcare service while we propose appointment scheduling problems and various applications and solution approaches in healthcare systems. For this purpose, more than 150 scientific papers are critically reviewed. The literature and the articles are categorized based on several problem specifications, i.e., the flow of patients, patient preferences, and random arrival time and service. Several methods have been proposed to shorten the patient waiting time resulting in the shortest idle times in healthcare centers. Among existing modeling such as simulation models, mathematical optimization techniques, Markov chain, and artificial intelligence are the most practical approaches to optimizing or improving patient satisfaction in healthcare centers. In this study, various criteria are selected for structuring the recent literature dealing with outpatient scheduling problems at the strategic, tactical, or operational levels. Based on the review papers, some new overviews, problem settings, and hybrid modeling approaches are highlighted.

Bibliometric analysis of cancer care operations management: current status, developments, and future directions

Around the world, cancer care services are facing many operational challenges. Operations management research can provide important solutions to these challenges, from screening and diagnosis to treatment. In recent years, the growth in the number of papers published on cancer care operations management (CCOM) indicates that development has been fast. Within this context, the objective of this research was to understand the evolution of CCOM through a comprehensive study and an up-to-date bibliometric analysis of the literature. To achieve this aim, the Web of Science Core Collection database was used as the source of bibliographic records. The data-mining and quantitative tools in the software Biblioshiny were used to analyze CCOM articles published from 2010 to 2021. First, a historical analysis described CCOM research, the sources, and the subfields. Second, an analysis of keywords highlighted the significant developments in this field. Third, an analysis of research themes identified three main directions for future research in CCOM, which has 11 evolutionary paths. Finally, this paper discussed the gaps in CCOM research and the areas that require further investigation and development.

Dynamic multistage scheduling for patient-centered care plans

We investigate the scheduling practices of multistage outpatient health programs that offer care plans customized to the needs of their patients. We formulate the scheduling problem as a Markov decision process (MDP) where patients can reschedule their appointment, may fail to show up, and may become ineligible. The MDP has an exponentially large state space and thus, we introduce a linear approximation to the value function. We then formulate an approximate dynamic program (ADP) and implement a dual variable aggregation procedure. This reduces the size of the ADP while still producing dual cost estimates that can be used to identify favorable scheduling actions. We use our scheduling model to study the effectiveness of customized-care plans for a heterogeneous patient population and find that system performance is better than clinics that do not offer such plans. We also demonstrate that our scheduling approach improves clinic profitability, increases throughput, and decreases practitioner idleness as compared to a policy that mimics human schedulers and a policy derived from a deep neural network. Finally, we show that our approach is fairly robust to errors introduced when practitioners inadvertently assign patients to the wrong care plan.

Real-time prediction of COVID-19 patients health situations using Artificial Neural Networks and Fuzzy Interval Mathematical modeling

At the end of 2019, the SARS-CoV-2 virus caused an outbreak of COVID-19 disease. The spread of this once-in-a-century pathogen increases demand for appropriate medical care, which strains the capacity and resources of hospitals in a critical way. Given the limited time available to prepare for the required demand, health care administrators fear they will not be ready to face patient’s influx. To aid health managers with the Prioritization and Scheduling COVID-19 Patients problem, a tool based on Artificial Intelligence (AI) through the Artificial Neural Networks (ANN) method, and Operations Research (OR) through a Fuzzy Interval Mathematical model was developed. The results indicated that combining both models provides an effective assessment under scarce initial information to select a suitable list of patients for a set of hospitals. The proposed approach allows to achieve a key goal: minimizing death rates under each hospital constraints of available resources. Furthermore, there is a serious concern regarding the resurgence of the COVID-19 virus which could cause a more severe pandemic. Thus, the main outcome of this study is the application of the above-mentioned approaches, especially when combining them, as efficient tools serving health establishments to manage critical resources.

Managing admission and discharge processes in intensive care units

The intensive care unit (ICU) is one of the most crucial and expensive resources in a health care system. While high fixed costs usually lead to tight capacities, shortages have severe consequences. Thus, various challenging issues exist: When should an ICU admit or reject arriving patients in general? Should ICUs always be able to admit critical patients or rather focus on high utilization? On an operational level, both admission control of arriving patients and demand-driven early discharge of currently residing patients are decision variables and should be considered simultaneously. This paper discusses the trade-off between medical and monetary goals when managing intensive care units by modeling the problem as a Markov decision process. Intuitive, myopic rule mimicking decision-making in practice is applied as a benchmark. In a numerical study based on real-world data, we demonstrate that the medical results deteriorate dramatically when focusing on monetary goals only, and vice versa. Using our model, we illustrate the trade-off along an efficiency frontier that accounts for all combinations of medical and monetary goals. Coming from a solution that optimizes monetary costs, a significant reduction of expected mortality can be achieved at little additional monetary cost.

Access Planning and Resource Coordination for Clinical Research Operations

This research creates an operations engineering and management methodology to optimize a complex operational planning and coordination challenge faced by sites that perform clinical research trials. The time-sensitive and resource-specific treatment sequences for each of the many trial protocols conducted at a site make it very difficult to capture the dynamics of this unusually complex system. Existing approaches for site planning and participant scheduling exhibit both excessively long and highly variable Time to First Available Visit (TFAV) waiting times and high staff overtime costs. We have created a new method, termed CApacity Planning Tool And INformatics (CAPTAIN) that provides decision support to identify the most valuable set of research trials to conduct within available resources and a plan for how to book their participants. Constraints include (i) the staff overtime costs, and/or (ii) the TFAV by trial. To estimate the site's metrics via a Mixed Integer Program, CAPTAIN combines a participant trajectory forecasting with an efficient visit booking reservation plan to allocate the date for the first visit of every participant's treatment sequence. It also plans a daily nursing staff schedule that is optimized together with the booking reservation plan to optimize each nurse's shift assignments in consideration of participants' requirements/needs.

Chemotherapy scheduling template development using an optimization approach

PURPOSE

The purpose of this paper is to develop a chemotherapy scheduling template that accounts for nurse resource availability and patient treatment needs to alleviate the mid-day patient load and provide quality services for patients.

DESIGN/METHODOLOGY/APPROACH

Owing to treatment complexity in chemotherapy administration, nurses are required at the beginning, end and during treatment. When nurses are not available to continue treatment, the service is compromised, and the resource constraint is violated, which leads to inevitable delay that risks service quality. Consequently, an optimization method is used to create a scheduling template that minimizes the violation between resource assignment and treatment requirements, while leveling patient load throughout a day. A case study from a typical clinic day is presented to understand current scheduling issues, describe nursing resource constraints, and develop a constraint-based optimization model and leveling algorithm for the final template.

FINDINGS

The approach is expected to reduce the variation in the system by 24 percent and result in five fewer chemo chairs used during peak hours. Adjusting staffing levels could further reduce resource constraint violations and more savings on chair occupancy. The actual implementation results indicate a 33 percent reduction on resource constraint violations and positive feedback from nursing staff for workload.

RESEARCH LIMITATIONS/IMPLICATIONS

Other delays, including laboratory test, physician visit and treatment assignment, are potential research areas.

ORIGINALITY/VALUE

The study demonstrates significant improvement in mid-day patient load and meeting treatment needs using optimization with a unique objective.

Chemotherapy appointment scheduling and daily outpatient-nurse assignment

Chemotherapy planning and patient-nurse assignment problems are complex multiobjective decision problems. Schedulers must make upstream decisions that affect daily operations. To improve productivity, we propose a two-stage procedure to schedule treatments for new patients, to plan nurse requirements, and to assign the daily patient mix to available nurses. We develop a mathematical formulation that uses a waiting list to take advantage of last-minute cancellations. In the first stage, we assign appointments to the new patients at the end of each day, we estimate the daily requirement for nurses, and we generate the waiting list. The second stage assigns patients to nurses while minimizing the number of nurses required. We test the procedure on realistically sized problems to demonstrate the impact on the cost effectiveness of the clinic.

Characterization of the flow of patients in a hospital from complex networks

We study the efficiency of operations management in a hospital from the dynamics of the flow of patients. Our principal aim is to characterize strategic departments and seasonal patterns in a hospital from a complex networks approach. Process mining techniques are developed to track out-patients' pathways along different departments for the purpose of building weekly networks. In these networks, departments act as nodes with multiple out/in-going arrows connecting other departments. Strategic departments are classified into target and critical departments. On the one hand, target departments, which in this study belong to the oncology area, correspond to those affected by new management policies whose impact is to be assessed. On the other hand, critical departments correspond to the most active departments, the hubs of the networks. Using suitable networks parameters, strategic departments are shown to be highly efficient regardless of the season, which naturally translates into a high level of service offered to patients. In addition, our results show conformance with the new objectives concerning target departments. The methodology presented is shown to be successful in evaluating the efficiency of hospital services in order to enhance process performances, and moreover, it is suitable to be implemented in healthcare management systems at a greater scale and the service industry whenever the flow of clients or customers are involved.

A Capacity Allocation Planning Model for Integrated Care and Access Management

The prevailing first-come-first-served approach to outpatient appointment scheduling ignores differing urgency levels, leading to unnecessarily long waits for urgent patients. In data from a partner healthcare organization, we found in some departments that urgent patients were inadvertently waiting longer for an appointment than non-urgent patients. This paper develops a capacity allocation optimization methodology that reserves appointment slots based on urgency in a complicated, integrated care environment where multiple specialties serve multiple types of patients. This optimization reallocates network capacity to limit access delays (indirect waiting times) for initial and downstream appointments differentiated by urgency. We formulate this problem as a queueing network optimization and approximate it via deterministic linear optimization to simultaneously smooth workloads and guarantee access delay targets. In a case study of our industry partner we demonstrate the ability to (1) reduce urgent patient mean access delay by 27% with only a 7% increase in mean access delay for non-urgent patients, and (2) increase throughput by 31% with the same service levels and overtime.

Optimizing Daily Service Scheduling for Medical Diagnostic Equipment Considering Patient Satisfaction and Hospital Revenue

Under the background of the unbalanced supply and demand of medical diagnostic equipment and rising health care costs, this study aims to optimize the service scheduling for medical diagnostic equipment so as to improve patient satisfaction by ensuring the equipment utilization rate and hospital revenue. The finite horizon Markov Decision Process (MDP) was adopted to solve this problem. On the basis of field research, we divided patients into four categories: emergency patients, inpatients, appointed outpatients, and the randomly arrived outpatients according to the severity of illness and appointment situations. In the construction of the MDP model, we considered the possibility of cancellation (no-show patients) in scheduling optimization. Combined with the benefits and costs related to patient satisfaction, based on the value iteration algorithm, we took patient satisfaction and hospital revenue as the objective functions. Results indicated that, compared with the current scheduling strategy, the integrated strategy proposed in this study has a better performance, which could maintain the sustainable usage rate of large medical resources and patient satisfaction.

Alternative Outpatient Chemotherapy Scheduling Method to Improve Patient Service Quality and Nurse Satisfaction

INTRODUCTION

Optimal scheduling and calendar management in an outpatient chemotherapy unit is a complex process that is driven by a need to focus on safety while accommodating a high degree of variability. Primary constraints are infusion times, staffing resources, chair availability, and unit hours.

METHODS

We undertook a process to analyze our existing management models across multiple practice settings in our health care system, then developed a model to optimize safety and efficiency. The model was tested in one of the community chemotherapy units. We assessed staffing violations as measured by nurse-to-patient ratios throughout the workday and at key points during treatment. Staffing violations were tracked before and after the implementation of the new model.

RESULTS

The new model reduced staffing violations by nearly 50% and required fewer chairs to treat the same number of patients for the selected clinic day. Actual implementation results indicated that the new model leveled the distribution of patients across the workday with an 18% reduction in maximum chair utilization and a 27% reduction in staffing violations. Subsequently, a positive impact on peak pharmacy workload reduced delays by as much as 35 minutes. Nursing staff satisfaction with the new model was positive.

CONCLUSION

We conclude that the proposed optimization approach with regard to nursing resource assignment and workload balance throughout a day effectively improves patient service quality and staff satisfaction.

Population-level intervention and information collection in dynamic healthcare policy

We develop a general framework for optimal health policy design in a dynamic setting. We consider a hypothetical medical intervention for a cohort of patients where one parameter varies across cohorts with imperfectly observable linear dynamics. We seek to identify the optimal time to change the current health intervention policy and the optimal time to collect decision-relevant information. We formulate this problem as a discrete-time, infinite-horizon Markov decision process and we establish structural properties in terms of first and second-order monotonicity. We demonstrate that it is generally optimal to delay information acquisition until an effect on decisions is sufficiently likely. We apply this framework to the evaluation of hepatitis C virus (HCV) screening in the general population determining which birth cohorts to screen for HCV and when to collect information about HCV prevalence.

Simulation-based approximate policy iteration for dynamic patient scheduling for radiation therapy

We study radiation therapy scheduling problem where dynamically and stochastically arriving patients of different types are scheduled to future days. Unlike similar models in the literature, we consider cancellation of treatments. We formulate this dynamic multi-appointment patient scheduling problem as a Markov Decision Process (MDP). Since the MDP is intractable due to large state and action spaces, we employ a simulation-based approximate dynamic programming (ADP) approach to approximately solve our model. In particular, we develop Least-square based approximate policy iteration for solving our model. The performance of the ADP approach is compared with that of a myopic heuristic decision rule.

Appointment Lead Time Policy Development to Improve Patient Access to Care

BACKGROUND

Patient access to care has been a known and continuing struggle for many health care providers. In spite of appointment lead time policies set by government or clinics, the problem persists. Justification for how lead time policies are determined is lacking.

OBJECTIVES

This paper proposed a data-driven approach for how to best set feasible appointment target lead times given a clinic's capacity and appointment requests.

METHODS

The proposed approach reallocates patient visits to minimize the deviation between actual appointment lead time and a feasible target lead time. A step-by-step algorithm was presented and demonstrated for return visit (RV) and new patient (NP) types from a Pediatric clinic excluding planned visits such as well-child exam and the same day urgent appointments. The steps are: 1. Obtain appointment requests; 2. Initialize a target lead time; 3. Set up an initial schedule; 4. Check the feasibility based on appointment availability; 5. Adjust schedule backward to fill appointment slots earlier than the target; 6. Adjust schedule forward for appointments not able to be scheduled earlier or on target to the later slots; 7. Trial different target lead times until the difference between earlier and later lead time is minimized.

RESULTS

The results indicated a 59% lead time reduction for RVs and a 45% reduction for NPs. The lead time variation was reduced by 75% for both patient types. Additionally, the opportunity for the participating clinic to achieve their organization's goal of a two-week lead time for RVs and a two-day lead time for NPs is discussed by adjusting capacity to increase one slot for NP and reduce one slot for RV.

CONCLUSIONS

The proposed approach and study findings may help clinics identify feasible appointment lead times.

Chemotherapy appointment scheduling under uncertainty using mean-risk stochastic integer programming

Oncology clinics are often burdened with scheduling large volumes of cancer patients for chemotherapy treatments under limited resources such as the number of nurses and chairs. These cancer patients require a series of appointments over several weeks or months and the timing of these appointments is critical to the treatment's effectiveness. Additionally, the appointment duration, the acuity levels of each appointment, and the availability of clinic nurses are uncertain. The timing constraints, stochastic parameters, rising treatment costs, and increased demand of outpatient oncology clinic services motivate the need for efficient appointment schedules and clinic operations. In this paper, we develop three mean-risk stochastic integer programming (SIP) models, referred to as SIP-CHEMO, for the problem of scheduling individual chemotherapy patient appointments and resources. These mean-risk models are presented and an algorithm is devised to improve computational speed. Computational results were conducted using a simulation model and results indicate that the risk-averse SIP-CHEMO model with the expected excess mean-risk measure can decrease patient waiting times and nurse overtime when compared to deterministic scheduling algorithms by 42 % and 27 %, respectively.

Operations research methods improve chemotherapy patient appointment scheduling

BACKGROUND

Clinical complexity, scheduling restrictions, and outdated manual booking processes resulted in frequent clerical rework, long waitlists for treatment, and late appointment notification for patients at a chemotherapy clinic in a large cancer center in British Columbia, Canada. A 17-month study was conducted to address booking, scheduling and workload issues and to develop, implement, and evaluate solutions.

METHODS

A review of scheduling practices included process observation and mapping, analysis of historical appointment data, creation of a new performance metric (final appointment notification lead time), and a baseline patient satisfaction survey. Process improvement involved discrete event simulation to evaluate alternative booking practice scenarios, development of an optimization-based scheduling tool to improve scheduling efficiency, and change management for implementation of process changes. Results were evaluated through analysis of appointment data, a follow-up patient survey, and staff surveys.

RESULTS

Process review revealed a two-stage scheduling process. Long waitlists and late notification resulted from an inflexible first-stage process. The second-stage process was time consuming and tedious. After a revised, more flexible first-stage process and an automated second-stage process were implemented, the median percentage of appointments exceeding the final appointment notification lead time target of one week was reduced by 57% and median waitlist size decreased by 83%. Patient surveys confirmed increased satisfaction while staff feedback reported reduced stress levels.

CONCLUSION

Significant operational improvements can be achieved through process redesign combined with operations research methods.