Radiotherapy treatment scheduling: Implementing operations research into clinical practice.

BACKGROUND: Every week, radiotherapy centers face the complex task of scheduling hundreds of treatment sessions amongst the available linear accelerators. With the increase in cancer patient numbers, manually creating a feasible and efficient schedule has shown to be a difficult, time-consuming task. Although operations research models have been increasingly reported upon to optimize patient care logistics, there is almost no scientific evidence of implementation in practice. METHODS: A mathematical operations research model was adapted to generate radiotherapy treatment schedules in two Dutch centers. The model was iteratively adjusted to fulfill the technical and medical constraints of each center until a valid model was attained. Patient data was collected for the planning horizon of one week, and the feasibility of the obtained schedules was verified by the staff of each center. The resulting optimized solutions are compared with the ones manually developed in practice. RESULTS: The weekly schedule was improved in both centers by decreasing the average standard deviation between sessions' starting times from 103.0 to 50.4 minutes (51%) in one center, and the number of gaps in the schedule from 18 to 5 (72%) in the other. The number of patients requiring linac switching between sessions has also decreased from 71 to 0 patients in one center, and from 43 to 2 in the other. The automated process required 5 minutes and 1.5 hours of computation time to find an optimal weekly patient schedule, respectively, as opposed to approximately 1.5 days when performed manually for both centers. CONCLUSIONS: The practical application of a theoretical operations research model for radiotherapy treatment scheduling has provided radiotherapy planners a feasible, high-quality schedule in an automated way. Iterative model adaptations performed in small steps, early engagement of stakeholders, and constant communication proved to facilitate the implementation of operations research models into clinical practice.

Radiotherapy treatment scheduling considering time window preferences.

External-beam radiotherapy treatments are delivered by a linear accelerator (linac) in a series of high-energy radiation sessions over multiple days. With the increase in the incidence of cancer and the use of radiotherapy (RT), the problem of automatically scheduling RT sessions while satisfying patient preferences regarding the time of their appointments becomes increasingly relevant. While most literature focuses on timeliness of treatments, several Dutch RT centers have expressed their need to include patient preferences when scheduling appointments for irradiation sessions. In this study, we propose a mixed-integer linear programming (MILP) model that solves the problem of scheduling and sequencing RT sessions considering time window preferences given by patients. The MILP model alone is able to solve the problem to optimality, scheduling all sessions within the desired window, in reasonable time for small size instances up to 66 patients and 2 linacs per week. For larger centers, we propose a heuristic method that pre-assigns patients to linacs to decompose the problem in subproblems (clusters of linacs) before using the MILP model to solve the subproblems to optimality in a sequential manner. We test our methodology using real-world data from a large Dutch RT center (8 linacs). Results show that, combining the heuristic with the MILP model, the problem can be solved in reasonable computation time with as few as 2.8% of the sessions being scheduled outside the desired time window.

Improving workflow control in radiotherapy using discrete-event simulation.

BACKGROUND: In radiotherapy, minimizing the time between referral and start of treatment (waiting time) is important to possibly mitigate tumor growth and avoid psychological distress in cancer patients. Radiotherapy pre-treatment workflow is driven by the scheduling of the first irradiation session, which is usually set right after consultation (pull strategy) or can alternatively be set after the pre-treatment workflow has been completed (push strategy). The objective of this study is to assess the impact of using pull and push strategies and explore alternative interventions for improving timeliness in radiotherapy. METHODS: Discrete-event simulation is used to model the patient flow of a large radiotherapy department of a Dutch hospital. A staff survey, interviews with managers, and historical data from 2017 are used to generate model inputs, in which fluctuations in patient inflow and resource availability are considered. RESULTS: A hybrid (40% pull / 60% push) strategy representing the current practice (baseline case) leads to 12% lower average waiting times and 48% fewer first appointment rebooks when compared to a full pull strategy, which in turn leads to 41% fewer patients breaching the waiting time targets. An additional scenario analysis performed on the baseline case showed that spreading consultation slots evenly throughout the week can provide a 21% reduction in waiting times. CONCLUSIONS: A 100% pull strategy allows for more patients starting treatment within the waiting time targets than a hybrid strategy, in spite of slightly longer waiting times and more first appointment rebooks. Our algorithm can be used by radiotherapy policy makers to identify the optimal balance between push and pull strategies to ensure timely treatments while providing patient-centered care adapted to their specific conditions.

Operations research for resource planning and -use in radiotherapy: a literature review.

BACKGROUND: The delivery of radiotherapy (RT) involves the use of rather expensive resources and multi-disciplinary staff. As the number of cancer patients receiving RT increases, timely delivery becomes increasingly difficult due to the complexities related to, among others, variable patient inflow, complex patient routing, and the joint planning of multiple resources. Operations research (OR) methods have been successfully applied to solve many logistics problems through the development of advanced analytical models for improved decision making. This paper presents the state of the art in the application of OR methods for logistics optimization in RT, at various managerial levels. METHODS: A literature search was performed in six databases covering several disciplines, from the medical to the technical field. Papers included in the review were published in peer-reviewed journals from 2000 to 2015. Data extraction includes the subject of research, the OR methods used in the study, the extent of implementation according to a six-stage model and the (potential) impact of the results in practice. RESULTS: From the 33 papers included in the review, 18 addressed problems related to patient scheduling (of which 12 focus on scheduling patients on linear accelerators), 8 focus on strategic decision making, 5 on resource capacity planning, and 2 on patient prioritization. Although calculating promising results, none of the papers reported a full implementation of the model with at least a thorough pre-post performance evaluation, indicating that, apart from possible reporting bias, implementation rates of OR models in RT are probably low. CONCLUSIONS: The literature on OR applications in RT covers a wide range of approaches from strategic capacity management to operational scheduling levels, and shows that considerable benefits in terms of both waiting times and resource utilization are likely to be achieved. Various fields can be further developed, for instance optimizing the coordination between the available capacity of different imaging devices or developing scheduling models that consider the RT chain of operations as a whole rather than the treatment machines alone.

A case study of cost-efficient staffing under annualized hours.

We propose a mathematical programming formulation that incorporates annualized hours and shows to be very flexible with regard to modeling various contract types. The objective of our model is to minimize salary cost, thereby covering workforce demand, and using annualized hours. Our model is able to address various business questions regarding tactical workforce planning problems, e.g., with regard to annualized hours, subcontracting, and vacation planning. In a case study for a Dutch hospital two of these business questions are addressed, and we demonstrate that applying annualized hours potentially saves up to 5.2% in personnel wages annually.

Tactical resource allocation and elective patient admission planning in care processes.

Tactical planning of resources in hospitals concerns elective patient admission planning and the intermediate term allocation of resource capacities. Its main objectives are to achieve equitable access for patients, to meet production targets/to serve the strategically agreed number of patients, and to use resources efficiently. This paper proposes a method to develop a tactical resource allocation and elective patient admission plan. These tactical plans allocate available resources to various care processes and determine the selection of patients to be served that are at a particular stage of their care process. Our method is developed in a Mixed Integer Linear Programming (MILP) framework and copes with multiple resources, multiple time periods and multiple patient groups with various uncertain treatment paths through the hospital, thereby integrating decision making for a chain of hospital resources. Computational results indicate that our method leads to a more equitable distribution of resources and provides control of patient access times, the number of patients served and the fraction of allocated resource capacity. Our approach is generic, as the base MILP and the solution approach allow for including various extensions to both the objective criteria and the constraints. Consequently, the proposed method is applicable in various settings of tactical hospital management.

Reducing the throughput time of the diagnostic track involving CT scanning with computer simulation.

INTRODUCTION: To examine the use of computer simulation to reduce the time between the CT request and the consult in which the CT report is discussed (diagnostic track) while restricting idle time and overtime. METHODS: After a pre implementation analysis in our case study hospital, by computer simulation three scenarios were evaluated on access time, overtime and idle time of the CT; after implementation these same aspects were evaluated again. Effects on throughput time were measured for outpatient short-term and urgent requests only. CONCLUSION: The pre implementation analysis showed an average CT access time of 9.8 operating days and an average diagnostic track of 14.5 operating days. Based on the outcomes of the simulation, management changed the capacity for the different patient groups to facilitate a diagnostic track of 10 operating days, with a CT access time of 7 days. After the implementation of changes, the average diagnostic track duration was 12.6 days with an average CT access time of 7.3 days. The fraction of patients with a total throughput time within 10 days increased from 29% to 44% while the utilization remained equal with 82%, the idle time increased by 11% and the overtime decreased by 82%. The fraction of patients that completed the diagnostic track within 10 days improved with 52%. Computer simulation proved useful for studying the effects of proposed scenarios in radiology management. Besides the tangible effects, the simulation increased the awareness that optimizing capacity allocation can reduce access times.

ORchestra: an online reference database of OR/MS literature in health care.

We introduce the categorized reference database ORchestra, which is available online at http://www.utwente.nl/choir/orchestra/.

Accounting for inpatient wards when developing master surgical schedules.

BACKGROUND: As the demand for health care services increases, the need to improve patient flow between departments has likewise increased. Understanding how the master surgical schedule (MSS) affects the inpatient wards and exploiting this relationship can lead to a decrease in surgery cancellations, a more balanced workload, and an improvement in resource utilization. We modeled this relationship and used the model to evaluate and select a new MSS for a hospital. METHODS: An operational research model was used in combination with staff input to develop a new MSS. A series of MSSs were proposed by staff, evaluated by the model, and then scrutinized by staff. Through iterative modifications of the MSS proposals (i.e., the assigned operating time of specialties), insight is obtained into the number, type, and timing of ward admissions, and how these affect ward occupancy. RESULTS: After evaluating and discussing a number of proposals, a new MSS was chosen that was acceptable to operating room staff and that balanced the ward occupancy. After implementing the new MSS, a review of the bed-use statistics showed it was achieving a balanced ward occupancy. The model described in this article gave the hospital the ability to quantify the concerns of multiple departments, thereby providing a platform from which a new MSS could be negotiated. CONCLUSION: The model, used in combination with staff input, supported an otherwise subjective discussion with quantitative analysis. The work in this article, and in particular the model, is readily repeatable in other hospitals and relies only on readily available data.

A simulation model for determining the optimal size of emergency teams on call in the operating room at night.

BACKGROUND: Hospitals that perform emergency surgery during the night (e.g., from 11:00 pm to 7:30 am) face decisions on optimal operating room (OR) staffing. Emergency patients need to be operated on within a predefined safety window to decrease morbidity and improve their chances of full recovery. We developed a process to determine the optimal OR team composition during the night, such that staffing costs are minimized, while providing adequate resources to start surgery within the safety interval. METHODS: A discrete event simulation in combination with modeling of safety intervals was applied. Emergency surgery was allowed to be postponed safely. The model was tested using data from the main OR of Erasmus University Medical Center (Erasmus MC). Two outcome measures were calculated: violation of safety intervals and frequency with which OR and anesthesia nurses were called in from home. We used the following input data from Erasmus MC to estimate distributions of all relevant parameters in our model: arrival times of emergency patients, durations of surgical cases, length of stay in the postanesthesia care unit, and transportation times. In addition, surgeons and OR staff of Erasmus MC specified safety intervals. RESULTS: Reducing in-house team members from 9 to 5 increased the fraction of patients treated too late by 2.5% as compared to the baseline scenario. Substantially more OR and anesthesia nurses were called in from home when needed. CONCLUSION: The use of safety intervals benefits OR management during nights. Modeling of safety intervals substantially influences the number of emergency patients treated on time. Our case study showed that by modeling safety intervals and applying computer simulation, an OR can reduce its staff on call without jeopardizing patient safety.

Closing emergency operating rooms improves efficiency.

Long waiting times for emergency operations increase a patient's risk of postoperative complications and morbidity. Reserving Operating Room (OR) capacity is a common technique to maximize the responsiveness of an OR in case of arrival of an emergency patient. This study determines the best way to reserve OR time for emergency surgery. In this study two approaches of reserving capacity were compared: (1) concentrating all reserved OR capacity in dedicated emergency ORs, and (2) evenly reserving capacity in all elective ORs. By using a discrete event simulation model the real situation was modelled. Main outcome measures were: (1) waiting time, (2) staff overtime, and (3) OR utilisation were evaluated for the two approaches. Results indicated that the policy of reserving capacity for emergency surgery in all elective ORs led to an improvement in waiting times for emergency surgery from 74 (+/-4.4) minutes to 8 (+/-0.5) min. Working in overtime was reduced by 20%, and overall OR utilisation can increase by around 3%. Emergency patients are operated upon more efficiently on elective Operating Rooms instead of a dedicated Emergency OR. The results of this study led to closing of the Emergency OR in the Erasmus MC (Rotterdam, The Netherlands).

A norm utilisation for scarce hospital resources: evidence from operating rooms in a Dutch university hospital.

BACKGROUND: Utilisation of operating rooms is high on the agenda of hospital managers and researchers. Many efforts in the area of maximising the utilisation have been focussed on finding the holy grail of 100% utilisation. The utilisation that can be realised, however, depends on the patient mix and the willingness to accept the risk of working in overtime. MATERIALS AND METHODS: This is a mathematical modelling study that investigates the association between the utilisation and the patient mix that is served and the risk of working in overtime. Prospectively, consecutively, and routinely collected data of an operating room department in a Dutch university hospital are used. Basic statistical principles are used to establish the relation between realistic utilisation rates, patient mixes, and accepted risk of overtime. RESULTS: Accepting a low risk of overtime combined with a complex patient mix results a low utilisation rate. If the accepted risk of overtime is higher and the patient mix is less complex, the utilisation rate that can be reached is closer to 100%. CONCLUSION: Because of the inherent variability of healthcare processes, the holy grail of 100% utilisation is unlikely to be found. The method proposed in this paper calculates a realistic benchmark utilisation that incorporates the patient mix characteristics and the willingness to accept risk of overtime.

Improving operating room efficiency by applying bin-packing and portfolio techniques to surgical case scheduling.

BACKGROUND: An operating room (OR) department has adopted an efficient business model and subsequently investigated how efficiency could be further improved. The aim of this study is to show the efficiency improvement of lowering organizational barriers and applying advanced mathematical techniques. METHODS: We applied advanced mathematical algorithms in combination with scenarios that model relaxation of various organizational barriers using prospectively collected data. The setting is the main inpatient OR department of a university hospital, which sets its surgical case schedules 2 wk in advance using a block planning method. The main outcome measures are the number of freed OR blocks and OR utilization. RESULTS: Lowering organizational barriers and applying mathematical algorithms can yield a 4.5% point increase in OR utilization (95% confidence interval 4.0%-5.0%). This is obtained by reducing the total required OR time. CONCLUSIONS: Efficient OR departments can further improve their efficiency. The paper shows that a radical cultural change that comprises the use of mathematical algorithms and lowering organizational barriers improves OR utilization.

Applying the variety reduction principle to management of ancillary services.

BACKGROUND: As central diagnostic facilities, computer tomography (CT) scans appear to be bottlenecks in many patient-care processes. This study describes a case study concerning redesign of a CT scan department in the Academic Medical Center in Amsterdam, the Netherlands. PURPOSES: The aim was to decrease access time for the CT-scan and simultaneously increase utilization level. METHODOLOGY/APPROACH: An important cause of relatively low-capacity utilization is variability in the time needed for the scanning process. We performed a qualitative and quantitative analysis of current processes; identified bottlenecks and selected interventions with the greatest expected reduction of variability in flow time. FINDINGS: The most promising and most feasible opportunity appeared to be to reallocate the insertion of intravenous access lines to a preparation room. The time needed for this activity was very hard to predict and needed a lot of slack in the lead time for appointments. By removing it from the CT room, lead time could be reduced by 5 minutes. The intervention resulted in a decrease of access time from 21 days to less than 5 days, and an increase of the utilization rate from 44% to 51%. This contributed directly to patient service and indirectly to cost reduction. PRACTICE IMPLICATIONS: Our strategy is applicable in every appointment-based hospital facility with variation in the length of time of the process. It allows to simultaneously reduce costs and improve service for the patient.

Influence of cardiac risk factors and medication on length of hospitalization in patients undergoing major vascular surgery.

Major vascular surgery is associated with a long in-hospital length of stay (LOS). Cardiac risk factors identify patients with an increased risk. Recent studies have associated statin, aspirin, and beta-blocker therapies with improved postoperative outcome. However, the effect of all these factors on LOS has not been defined. Our aims were to determine the effect of cardiac risk factors and (preventive) statin, aspirin, and beta-blocker therapy on LOS and to deduce from these factors a model that predicts LOS. In total, 2,374 patients from 1990 to 2004 were enrolled. Mean LOS was 18 +/- 9 days. Cardiac risk factors that were significantly associated with LOS in the multivariable analysis were age, previous heart failure, hypertension, diabetes mellitus, renal failure, and chronic obstructive pulmonary disease. Statin and aspirin use was associated with a shorter LOS. Beta blockers shortened LOS only in patients with underlying coronary artery disease. Together, these factors explained 14.1% of the variance in LOS. In conclusion, in-hospital LOS in patients who undergo major vascular surgery can be predicted more accurately by clinical cardiac risk factors. A significant decrease in in-hospital LOS was achieved with statin, aspirin, and beta-blocker therapies.