Patient mix optimisation and stochastic resource requirements: a case study in cardiothoracic surgery planning

Improving Resource Utilization for Arthroplasty Care by Leveraging Machine Learning and Optimization: A Systematic Review

Background

There is a growing demand for total joint arthroplasty (TJA) surgery. The applications of machine learning (ML), mathematical optimization, and computer simulation have the potential to improve efficiency of TJA care delivery through outcome prediction and surgical scheduling optimization, easing the burden on health-care systems. The purpose of this study was to evaluate strategies using advances in analytics and computational modeling that may improve planning and the overall efficiency of TJA care.

Methods

A systematic review including MEDLINE, Embase, and IEEE Xplore databases was completed from inception to October 3, 2022, for identification of studies generating ML models for TJA length of stay, duration of surgery, and hospital readmission prediction. A scoping review of optimization strategies in elective surgical scheduling was also conducted.

Results

Twenty studies were included for evaluating ML predictions and 17 in the scoping review of scheduling optimization. Among studies generating linear or logistic control models alongside ML models, only 1 found a control model to outperform its ML counterpart. Furthermore, neural networks performed superior to or at the same level as conventional ML models in all but 1 study. Implementation of mathematical and simulation strategies improved the optimization efficiency when compared to traditional scheduling methods at the operational level.

Conclusions

High-performing predictive ML-based models have been developed for TJA, as have mathematical strategies for elective surgical scheduling optimization. By leveraging artificial intelligence for outcome prediction and surgical optimization, there exist greater opportunities for improved resource utilization and cost-savings in TJA than when using traditional modeling and scheduling methods.

Case-Mix Moderation of the Relationship Between OR Performance Metrics and Utilization

We investigated the impact of the case-mix ratio of inpatients to outpatients on the relationships between OR utilization and late starts, turnover time, delays, cancellations, and idle time at an academic medical center in the southeastern United States. After extracting 55 months of data from the surgical repository, we used simple and multiple linear regression models to analyze the data and determine the strength and direction of the relationships among the variables. We compared models comprising proportionally more inpatients to models comprising proportionally more outpatients for each metric to ascertain the effects of case mix on OR utilization. Idle time had the greatest effect on OR utilization, followed by late starts and turnover time. Case mix moderated the relationship between OR utilization and the metrics of cancellations and turnover time. Perioperative leaders may enhance OR utilization by monitoring and addressing idle time and late starts and scheduling an appropriate mix of inpatients and outpatients.

Balancing control and autonomy in master surgery scheduling: Benefits of ICU quotas for recovery units

When scheduling surgeries in the operating theater, not only the resources within the operating theater have to be considered but also those in downstream units, e.g., the intensive care unit and regular bed wards of each medical specialty. We present an extension to the master surgery schedule, where the capacity for surgeries on ICU patients is controlled by introducing downstream-dependent block types – one for both ICU and ward patients and one where surgeries on ICU patients must not be performed. The goal is to provide better control over post-surgery patient flows through the hospital while preserving each medical specialty’s autonomy over its operational surgery scheduling. We propose a mixed-integer program to determine the allocation of the new block types within either a given or a new master surgery schedule to minimize the maximum workload in downstream units. Using a simulation model supported by seven years of data from the University Hospital Augsburg, we show that the maximum workload in the intensive care unit can be reduced by up to 11.22% with our approach while maintaining the existing master surgery schedule. We also show that our approach can achieve up to 79.85% of the maximum workload reduction in the intensive care unit that would result from a fully centralized approach. We analyze various hospital setting instances to show the generalizability of our results. Furthermore, we provide insights and data analysis from the implementation of a quota system at the University Hospital Augsburg.

Patient Mix Optimization in Admission Planning under Multitype Patients and Priority Constraints

Hospital beds are one of the most critical medical resources. Large hospitals in China have caused bed utilization rates to exceed 100% due to long-term extra beds. To alleviate the contradiction between the supply of high-quality medical resources and the demand for hospitalization, in this paper, we address the decision of choosing a case mix for a respiratory medicine department. We aim to generate an optimal admission plan of elective patients with the stochastic length of stay and different resource consumption. We assume that we can classify elective patients according to their registration information before admission. We formulated a general integer programming model considering heterogeneous patients and introducing patient priority constraints. The mathematical model is used to generate a scientific and reasonable admission planning, determining the best admission mix for multitype patients in a period. Compared with model II that does not consider priority constraints, model I proposed in this paper is better in terms of admissions and revenue. The proposed model I can adjust the priority parameters to meet the optimal output under different goals and scenarios. The daily admission planning for each type of patient obtained by model I can be used to assist the patient admission management in large general hospitals.

A hybrid analytical model for an entire hospital resource optimisation

Given the escalating healthcare costs around the world (more than 10% of the world's GDP) and increasing demand hospitals are under constant scrutiny in terms of managing services with limited resources and tighter budgets. Hospitals endeavour to find sustainable solutions for a variety of challenges ranging from productivity enhancements to resource allocation. For instance, in the UK, evidence suggests that hospitals are struggling due to increased delayed transfers of care, bed-occupancy rates well above the recommended levels of 85% and unmet A&E performance targets. In this paper, we present a hybrid forecasting-simulation-optimisation model for an NHS Foundation Trust in the UK. Using the Hospital Episode Statistics dataset for A&E, outpatient and inpatient services, we estimate the future patient demands for each speciality and model how it behaves with the forecasted activity in the future. Discrete event simulation is used to capture the entire hospital within a simulation environment, where the outputs is used as inputs into a multi-period integer linear programming (MILP) model to predict three vital resource requirements (on a monthly basis over a 1-year period), namely beds, physicians and nurses. We further carry out a sensitivity analysis to establish the robustness of solutions to changes in parameters, such as nurse-to-bed ratio. This type of modelling framework is developed for the first time to better plan the needs of hospitals now and into the future.

Surgery scheduling heuristic considering OR downstream and upstream facilities and resources

BACKGROUND

Surgical theater (ST) operations planning is a key subject in the healthcare management literature, particularly the scheduling of procedures in operating rooms (ORs). The OR scheduling problem is usually approached using mathematical modeling and made available to ST managers through dedicated software. Regardless of the large body of knowledge on the subject, OR scheduling models rarely consider the integration of OR downstream and upstream facilities and resources or validate their propositions in real life, rather using simulated scenarios. We propose a heuristic to sequence surgeries that considers both upstream and downstream resources required to perform them, such as surgical kits, post anesthesia care unit (PACU) beds, and surgical teams (surgeons, nurses and anesthetists).

METHODS

Using hybrid flow shop (HFS) techniques and the break-in-moment (BIM) concept, the goal is to find a sequence that maximizes the number of procedures assigned to the ORs while minimizing the variance of intervals between surgeries' completions, smoothing the demand for downstream resources such as PACU beds and OR sanitizing teams. There are five steps to the proposed heuristic: listing of priorities, local scheduling, global scheduling, feasibility check and identification of best scheduling.

RESULTS

Our propositions were validated in a high complexity tertiary University hospital in two ways: first, applying the heuristic to historical data from five typical ST days and comparing the performance of our proposed sequences to the ones actually implemented; second, pilot testing the heuristic during ten days in the ORs, allowing a full rotation of surgical specialties. Results displayed an average increase of 37.2% in OR occupancy, allowing an average increase of 4.5 in the number of surgeries performed daily, and reducing the variance of intervals between surgeries' completions by 55.5%. A more uniform distribution of patients' arrivals at the PACU was also observed.

CONCLUSIONS

Our proposed heuristic is particularly useful to plan the operation of STs in which resources are constrained, a situation that is common in hospital from developing countries. Our propositions were validated through a pilot implementation in a large hospital, contributing to the scarce literature on actual OR scheduling implementation.

Integrated Scheduling and Capacity Planning with Considerations for Patients' Length-of-Stays

Motivated by the shortcoming of current hospital scheduling and capacity planning methods which often model different units in isolation, we introduce the first dynamic multi-day scheduling model that integrates information about capacity usage at more than one location in a hospital. In particular, we analyze the first dynamic model that accounts for patients' length-of-stay and downstream census in scheduling decisions. Via a simple and innovative variable transformation, we show that the optimal number of patients to be allowed in the system is increasing in the state of the system and in the downstream capacity. Moreover, the total system cost exhibits decreasing marginal returns as the capacity increases at any location independently of another location. Through numerical experiments on realistic data, we show that there is substantial value in making integrated scheduling decisions. In contrast, localized decision rules that only focus on a single location of a hospital can result in up to 60% higher expenses.

Multi-objective admission planning problem: a two-stage stochastic approach

Effective admission planning can improve inpatient throughput and waiting times, resulting in better quality of service. The uncertainty in the patient arrival and the availability of resources makes the patient's allocation difficult to manage. Thus, in the admission process hospitals aim to accomplish targets of resource utilization and to lower the cost of service. Both objectives are related and in conflict. In this paper, we present a bi-objective stochastic optimization model to study the trade-off between the resource utilization and the cost of service, taking into account demand and capacity uncertainties. Real data from the surgery and medical areas of a Chilean public hospital are used to illustrate the approach. The results show that the solutions of our approach outperform the actual practice in the Chilean hospital.

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.

Application of Operational Research Techniques in Operating Room Scheduling Problems: Literature Overview

Increased healthcare costs are pushing hospitals to reduce costs and increase the quality of care. Operating rooms are the most important source of income and expense for hospitals. Therefore, the hospital management focuses on the effectiveness of schedules and plans. This study includes analyses of recent research on operating room scheduling and planning. Most studies in the literature, from 2000 to the present day, were evaluated according to patient characteristics, performance measures, solution techniques used in the research, the uncertainty of the problem, applicability of the research, and the planning strategy to be dealt within the solution. One hundred seventy studies were examined in detail, after scanning the Emerald, Science Direct, JSTOR, Springer, Taylor and Francis, and Google Scholar databases. To facilitate the identification of these studies, they are grouped according to the different criteria of concern and then, a detailed overview is presented.

Case mix planning in hospitals: a review and future agenda

The case mix planning problem deals with choosing the ideal composition and volume of patients in a hospital. With many countries having recently changed to systems where hospitals are reimbursed for patients according to their diagnosis, case mix planning has become an important tool in strategic and tactical hospital planning. Selecting patients in such a payment system can have a significant impact on a hospital's revenue. The contribution of this article is to provide the first literature review focusing on the case mix planning problem. We describe the problem, distinguish it from similar planning problems, and evaluate the existing literature with regard to problem structure and managerial impact. Further, we identify gaps in the literature. We hope to foster research in the field of case mix planning, which only lately has received growing attention despite its fundamental economic impact on hospitals.

Simulation-Based Optimization for Surgery Scheduling in Operation Theatre Management Using Response Surface Method

Operation theatre is one of the most significant assets in a hospital as the greatest source of revenue as well as the largest cost unit. This paper focuses on surgery scheduling optimization, which is one of the most crucial tasks in operation theatre management. A combined scheduling policy composed of three simple scheduling rules is proposed to optimize the performance of scheduling operation theatre. Based on the real-life scenarios, a simulation-based model about surgery scheduling system is built. With two optimization objectives, the response surface method is adopted to search for the optimal weight of simple rules in a combined scheduling policy in the model. Moreover, the weights configuration can be revised to cope with dispatching dynamics according to real-time change at the operation theatre. Finally, performance comparison between the proposed combined scheduling policy and tabu search algorithm indicates that the combined scheduling policy is capable of sequencing surgery appointments more efficiently.

Scheduling elective surgeries: the tradeoff among bed capacity, waiting patients and operating room utilization using goal programming

Scheduling of surgeries in the operating rooms under limited competing resources such as surgical and nursing staff, anesthesiologist, medical equipment, and recovery beds in surgical wards is a complicated process. A well-designed schedule should be concerned with the welfare of the entire system by allocating the available resources in an efficient and effective manner. In this paper, we develop an integer linear programming model in a manner useful for multiple goals for optimally scheduling elective surgeries based on the availability of surgeons and operating rooms over a time horizon. In particular, the model is concerned with the minimization of the following important goals: (1) the anticipated number of patients waiting for service; (2) the underutilization of operating room time; (3) the maximum expected number of patients in the recovery unit; and (4) the expected range (the difference between maximum and minimum expected number) of patients in the recovery unit. We develop two goal programming (GP) models: lexicographic GP model and weighted GP model. The lexicographic GP model schedules operating rooms when various preemptive priority levels are given to these four goals. A numerical study is conducted to illustrate the optimal master-surgery schedule obtained from the models. The numerical results demonstrate that when the available number of surgeons and operating rooms is known without error over the planning horizon, the proposed models can produce good schedules and priority levels and preference weights of four goals affect the resulting schedules. The results quantify the tradeoffs that must take place as the preemptive-weights of the four goals are changed.

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.

Scheduling admissions and reducing variability in bed demand

Variability in admissions and lengths of stay inherently leads to variability in bed occupancy. The aim of this paper is to analyse the impact of these sources of variability on the required amount of capacity and to determine admission quota for scheduled admissions to regulate the occupancy pattern. For the impact of variability on the required number of beds, we use a heavy-traffic limit theorem for the G/G/∞ queue yielding an intuitively appealing approximation in case the arrival process is not Poisson. Also, given a structural weekly admission pattern, we apply a time-dependent analysis to determine the mean offered load per day. This time-dependent analysis is combined with a Quadratic Programming model to determine the optimal number of elective admissions per day, such that an average desired daily occupancy is achieved. From the mathematical results, practical scenarios and guidelines are derived that can be used by hospital managers and support the method of quota scheduling. In practice, the results can be implemented by providing admission quota prescribing the target number of admissions for each patient group.

Redesigning intensive care unit flow using variability management to improve access and safety

BACKGROUND

Poor flow of patients into and out of the ICU can result in gridlock and bottlenecks that disrupt care and have a detrimental effect on patient safety and satisfaction, hospital efficiency, staff stress and morale, and revenue. Beginning in 2006, Cincinnati Children's Hospital Medical Center implemented a series of interventions to "smooth" patient flow through the system.

METHODS

Key activities included patient flow models based on surgical providers' predicted need for intensive care and predicted length of stay; scheduling the case and an ICU bed at the same time; capping and simulation models to identify the appropriate number of elective surgical cases to maximize occupancy without cancelling elective cases; and a morning huddle by the chief of staff, manager of patient services, and representatives from the operating room, pediatric ICUS, and anesthesia to confirm that day's plan and anticipate the next day's needs.

RESULTS

New elective surgical admissions to the pediatric ICU were restricted to a maximum of five cases per day. Diversion of patients to the cardiac ICU, keeping patients in the postanesthesia care unit longer than expected, and delaying or canceling cases are now rare events. Since implementation of the operations management interventions, there have been no cases when beds in the pediatric ICU were not available when needed for urgent medical or surgical use.

DISCUSSION

A system for smoothing flow, based on an advanced predictive model for need, occupancy, and length of stay, coupled with an active daily strategy for demand/capacity matching of resources and needs, allowed much better early planning, predictions, and capacity management, thereby ensuring that all patients are in suitable ICU environments.