A time predefined variable depth search for nurse rostering

This paper presents a variable depth search for the nurse rostering problem. The algorithm works by chaining together single neighbourhood swaps into more effective compound moves. It achieves this by using heuristics to decide whether to continue extending a chain and which candidates to examine as the next potential link in the chain. Because end users vary in how long they are willing to wait for solutions, a particular goal of this research was to create an algorithm that accepts a user specified computational time limit and uses it effectively. When compared against previously published approaches the results show that the algorithm is very competitive

The falling tide algorithm: A new multi-objective approach for complex workforce scheduling

We present a hybrid approach of goal programming and meta-heuristic search to find compromise solutions for a difficult employee scheduling problem, i.e. nurse rostering with many hard and soft constraints. By employing a goal programming model with different parameter settings in its objective function, we can easily obtain a coarse solution where only the system constraints (i.e. hard constraints) are satisfied and an ideal objective-value vector where each single goal (i.e. each soft constraint) reaches its optimal value. The coarse solution is generally unusable in practise, but it can act as an initial point for the subsequent meta-heuristic search to speed up the convergence. Also, the ideal objective-value vector is, of course, usually unachievable, but it can help a multi-criteria search method (i.e. compromise programming) to evaluate the fitness of obtained solutions more efficiently. By incorporating three distance metrics with changing weight vectors, we propose a new time-predefined meta-heuristic approach, which we call the falling tide algorithm, and apply it under a multi-objective framework to find various compromise solutions. By this approach, not only can we achieve a trade off between the computational time and the solution quality, but also we can achieve a trade off between the conflicting objectives to enable better decision-making

Modeling the labor scheduling problem considering wellbeing for the clinic’s employees

Resumen El problema de la programación de turnos de trabajo, consiste en programar el horario de trabajo o los turnos de los distintos empleados buscando la minimización de los costos asociados al personal, el cual es un problema NP-hard. En este artículo se presenta un modelo de programación lineal entera mixta aplicado a un caso real, el cual tiene como objetivo minimizar el costo laboral, cumplir con los requerimientos de demanda y establecer condiciones laborales adecuadas para los empleados mediante la incorporación de restricciones que garanticen bienestar, para así generar una asignación óptima de los turnos de trabajo de los fisioterapeutas en las áreas de cuidados intensivos e intermedios de una Clínica. Para esto, se definieron diferentes escenarios variando tanto el número de fisioterapeutas como la estructura del modelo, resultando así que el número apropiado de fisioterapeutas a programar en la Clínica es de 32, ya que satisface todos los requerimientos de demanda, la legislación laboral, y las necesidades de la empresa y de los empleados. Abstract The Labor Scheduling Problem consists of planning the shifts for the employees, and minimizing costs associated to the workforce, which is a NP-hard problem.This paper presents a mixed integer linear programming modelapplied to a real case, which minimizes labor costs, satisfies the requirements of demand and establishes adequate working conditions for employees by incorporating constraints that ensure well-being to generate an optimal assignment of physiotherapist shifts in the intensive and intermediate care areas in a Clinic.For this, different scenarios were defined by varying both the number of physiotherapists and the structure of the model, the result that the appropriate number of physiotherapists in the clinic schedule is 32, since it satisfies the requirements of demand, employment law and the needs of the company and employees

Nursing workload balancing: Lean healthcare, analytics and optimization in two Latin American University Hospitals

91 páginasIn most Latin American hospitals, the workload assignment of healthcare workers is a crucial process. These strategies seek to improve the level of patient care and safety while avoiding incurring unnecessary costs by hiring and maintaining excessive staff. The distribution of activities falls to the chief nurses in the hospital, taking as criteria for allocation the number of patients rather than the complexity of care that each individual carries. Specifically for the inpatient area and for nursing professionals, it is complex to determine an adequate distribution of human resources, considering the diagnosis of the patients and the number of tasks that a nursing professional must carry out throughout the day. Therefore, this work proposes the development of a strategy and a load-balancing model based on lean healthcare theory, analytics, and mathematical optimization, so that working hours do not result in the generation of stress and the presence of burnout in nurses. Likewise, mathematical modelling maximizes the use of the nursing staff’s capacity, generating awareness based on the integration of continuous improvement theories so that the clinics can be updated to technological trends. Finally, this project is part of a macro-project for the development of technologies that support hospital nursing processes, carried out by the Universidad de La Sabana Clinic in Colombia and the Universidad de los Andes Clinic in Chile, so the results of this project impact two clinics in Latin America.En la mayoría de los hospitales latinoamericanos, la asignación de carga laboral al personal de la salud es un proceso de vital importancia. Estas estrategias buscan mejorar el nivel de atención al paciente y la seguridad, sin tener que incurrir en gastos innecesarios por la contratación y manutención de un personal excesivo. Esto conlleva a la distribución de las actividades recae en los jefes de las áreas en el hospital, tomando como criterios de asignación la cantidad de pacientes y no la complejidad del cuidado que acarrea cada individuo. Específicamente para el área de hospitalización y para los profesionales de enfermería, resulta complejo determinar una distribución adecuada del recurso humano teniendo en cuenta el diagnóstico de los pacientes y la cantidad de tareas que debe realizar un profesional de enfermería a lo largo de su jornada. Por ello, este trabajo propone el desarrollo de una estrategia y un modelo de balanceo de carga a partir de la teoría lean healthcare, analítica y optimización matemática, de tal forma que las jornadas laborales no resulten en la generación de estrés y la presencia de burnout en los enfermeros. Así mismo, se logra maximizar el aprovechamiento de la capacidad del personal de enfermería, generando bases de concientización sobre la integración de teorías de mejora continua para que las clínicas puedan actualizarse a las tendencias tecnológicas. Por último, este proyecto se enmarcó en un macroproyecto para el desarrollo de tecnologías que soporten los procesos hospitalarios de enfermería, llevado a cabo por la Clínica Universidad de La Sabana en Colombia y la Clínica Universidad de los Andes en Chile, por lo que los resultados de este proyecto impactan dos clínicas en Latinoamérica.Maestría en Diseño y Gestión de ProcesosMagíster en Diseño y Gestión de Proceso

A domain transformation approach for addressing staff scheduling problems

Staff scheduling is a complex combinatorial optimisation problem concerning allocation of staff to duty rosters in a wide range of industries and settings. This thesis presents a novel approach to solving staff scheduling problems, and in particular nurse scheduling, by simplifying the problem space through information granulation. The complexity of the problem is due to a large solution space and the many constraints that need to be satisfied. Published research indicates that methods based on random searches of the solution space did not produce good-quality results consistently. In this study, we have avoided random searching and proposed a systematic hierarchical method of granulation of the problem domain through pre-processing of constraints. The approach is general and can be applied to a wide range of staff scheduling problems. The novel approach proposed here involves a simplification of the original problem by a judicious grouping of shift types and a grouping of individual shifts into weekly sequences. The schedule construction is done systematically, while assuring its feasibility and minimising the cost of the solution in the reduced problem space of weekly sequences. Subsequently, the schedules from the reduced problem space are translated into the original problem space by taking into account the constraints that could not be represented in the reduced space. This two-stage approach to solving the scheduling problem is referred to here as a domain-transformation approach. The thesis reports computational results on both standard benchmark problems and a specific scheduling problem from Kajang Hospital in Malaysia. The results confirm that the proposed method delivers high-quality results consistently and is computationally efficient

Strategic Nurse Allocation Policies Under Dynamic Patient Demand

ABSTRACT STRATEGIC NURSE ALLOCATION POLICIES UNDER DYNAMIC PATIENT DEMAND by Osman T. Aydas The University of Wisconsin-Milwaukee, 2017 Under the Supervision of Professor Anthony D. Ross Several studies have shown a strong association between nurse staffing and patient outcomes. When a nursing unit is chronically short-staffed, nurses must maintain an intense pace to ensure that patients receive timely care. Over time this can result in nurse burnout, as well as dissatisfied patients and even medical errors. Improved accuracy in the allocation of nursing staff can mitigate these operational risks and improve patient outcomes. Nursing care is identified as the single biggest factor in both the cost of hospital care and patient satisfaction. Yet, there is widespread dissatisfaction with the current methods of determining nurse staffing levels, including the most common one of using minimum nurse-to-patient ratios. Nurse shortage implications go beyond healthcare quality, extending to health economics as well. In addition, implementation of mandatory nurse-to-patient ratios in some states creates a risk of under- or over-estimating required nurse resources. With this motivation, this dissertation aims to develop methodologies that generate feasible six-week nurse schedules and efficiently assign nurses from various profiles to these schedules while controlling staffing costs and understaffing ratios in the medical unit. First, we develop and test various medium-term staff allocation approaches using mixed-integer optimization and compare their performance with respect to a hypothetical full information scenario. Second, using stochastic integer programming approach, we develop a short-term staffing level adjustment model under a sizable list of patient admission scenarios. We begin by providing an overview of the organization of the dissertation. Chapter 1 presents the problem context and we provide research questions for this dissertation. Chapter 2 provides a review of the literature on nurse staffing and scheduling specifically from the Operations Management journals. We introduce the challenges of nursing care and nurse scheduling practices. We identify major research areas and solution approaches. This is followed by a discussion of the complexities associated with computing nursing requirements and creating rosters. Staffing requirements are the result of a complex interaction between care-unit sizes, nurse-to-patient ratios, bed census distributions, and quality-of-care requirements. Therefore, we review the literature on nursing workload measurement approaches because workloads depend highly on patient arrivals and lengths of stay, both of which can vary greatly. Thus, predicting these workloads and staffing nurses accordingly are essential to guaranteeing quality of care in a cost-effective manner. For completeness, a brief review of the literature on workforce planning and scheduling that is linked to the nurse staffing and scheduling problem is also provided. Chapter 3 develops a framework for estimating the daily number of nurses required in Intensive Care Units (ICUs). Many patient care units, including ICUs, find it difficult to accurately estimate the number of nurses needed. One factor contributing to this difficulty is not having a decision support tool to understand the distribution of admissions to healthcare facilities. We statistically evaluate the existing staff allocation system of an ICU using clinical operational data, then develop a predictive model for estimating the number of admissions to the unit. We analyze clinical operational data covering 44 months for three wards of a pediatric ICU. The existing staff allocation model does not accurately estimate the required number of nurses required. This is due in part to not understanding the pattern and frequency of admissions, particularly those which are not known 12 hours in advance. We show that these “unknown” admissions actually follow a Poisson distribution. Thus, we can more accurately estimate the number of admissions overall. Analytical predictive methods that complement intuition and experience can help to decrease unplanned requirements for nurses and recommend more efficient nurse allocations. The model developed here can be inferred to estimate admissions for other intensive care units, such as pediatric facilities. Chapter 4 examines an integrated nurse staffing and scheduling model for a Pediatric Intensive Care Unit (PICU). This model is targeted to recommend initial staffing plans and schedules for a six-week horizon given a variety of nurse groups and nursing shift assignment types in the PICU. Nurse rostering is an NP-hard combinatorial problem, which makes it extremely difficult to efficiently solve life-sized problems due to their complexity. Usually, real problem instances have complicated work rules related to safety and quality of service issues, as well as preferences of the personnel. To avoid the size and complexity limitations, we generate feasible nurse schedules for the full-time equivalent (FTE) nurses, using algorithms that will be employed in the mixed-integer programming models we develop. Pre-generated schedules eliminate the increased number of constraints, and reduce the number of decision variables of the integrated nurse staffing and scheduling model. We also include a novel methodology for estimating nurse workloads by considering the patient, and individual patient’s acuity, and activity in the unit. When the nursing administration prepares the medium-term nurse schedules for the next staffing cycle (six weeks in our study), one to two months before the actual patient demand realizations, it typically uses a general average staffing level for the nursing care needs in the medical units. Using our mixed-integer optimization model, we examine fixed vs. dynamic medium-term nurse staffing and scheduling policy options for the medical units. In the fixed staffing option, the medical unit is staffed by a fixed number of nurses throughout the staffing horizon. In the dynamic staffing policy, we propose, historical patient demand data enables us to suggest a non-stationary staffing scheme. We compare the performance of both nurse allocation policy options, in terms of cost savings and understaffing ratios, with the optimal staffing scheme reached by the actual patient data. As a part of our experimental design, we evaluate our optimization model for the three medical units of the PICU in the “as-is” state. In Chapter 5, we conduct two-stage short-term staffing adjustments for the upcoming nursing shift. Our proposed adjustments are first used at the beginning of each nursing shift for the upcoming 4-hour shift. Then, after observing actual patient demand for nursing at the start of the next shift, we make our final staffing adjustments to meet the patient demand for nursing. We model six different adjustment options for the two-stage stochastic programming model (five options available as first-stage decisions and one option available as the second-stage decision). Because the adjustment horizon is less than 12 hours, the current patient census, patient acuity, and the number of scheduled admissions/discharges in the current and upcoming shift are known to the unit nurse manager. We develop a two-stage stochastic integer programming model which will minimize total nurse staffing costs (and the cost of adjustments to the original schedules developed in the medium-term planning phase) while ensuring adequate coverage of nursing demand. Chapter 6 provides conclusions from the study and identify both limitations and future research directions

Personnel scheduling during Covid-19 pandemic

This paper addresses a real-life personnel scheduling problem in the context of Covid19 pandemic, arising in a large Italian pharmaceutical distribution warehouse. In this case study, the challenge is to determine a schedule that attempts to meet the contractual working time of the employees, considering the fact that they must be divided into mutually exclusive groups to reduce the risk of contagion. To solve the problem, we propose a mixed integer linear programming formulation (MILP). The solution obtained indicates that optimal schedule attained by our model is better than the one generated by the company. In addition, we performed tests on random instances of larger size to evaluate the scalability of the formulation. In most cases, the results found using an open-source MILP solver suggest that high quality solutions can be achieved within an acceptable CPU time. We also project that our findings can be of general interest for other personnel scheduling problems, especially during emergency scenarios such as those related to Covid-19 pandemic

Novel heuristic and metaheuristic approaches to the automated scheduling of healthcare personnel

This thesis is concerned with automated personnel scheduling in healthcare organisations; in particular, nurse rostering. Over the past forty years the nurse rostering problem has received a large amount of research. This can be mostly attributed to its practical applications and the scientific challenges of solving such a complex problem. The benefits of automating the rostering process include reducing the planner’s workload and associated costs and being able to create higher quality and more flexible schedules. This has become more important recently in order to retain nurses and attract more people into the profession. Better quality rosters also reduce fatigue and stress due to overwork and poor scheduling and help to maximise the use of leisure time by satisfying more requests. A more contented workforce will lead to higher productivity, increased quality of patient service and a better level of healthcare. Basically stated, the nurse rostering problem requires the assignment of shifts to personnel to ensure that sufficient employees are present to perform the duties required. There are usually a number of constraints such as working regulations and legal requirements and a number of objectives such as maximising the nurses working preferences. When formulated mathematically this problem can be shown to belong to a class of problems which are considered intractable. The work presented in this thesis expands upon the research that has already been conducted to try and provide higher quality solutions to these challenging problems in shorter computation times. The thesis is broadly structured into three sections. 1) An investigation into a nurse rostering problem provided by an industrial collaborator. 2) A framework to aid research in nurse rostering. 3) The development of a number of advanced algorithms for solving highly complex, real world problems

Operating room and surgical team members scheduling: A comprehensive review

Operating rooms (OR) are one of the most expensive parts of a hospital with complex processes, and the efficient use of resources is of utmost importance. Therefore, proper management and operation of operating rooms are extremely crucial. OR scheduling ensures that the surgeries are performed at the proper time, patients are treated effectively and safely, resources are used effectively, and staff is increased in work efficiency. Furthermore, accurately scheduled surgeries are safer for patients' healing processes. This is dependent on factors such as the availability of qualified personnel at the appropriate time, the readiness of surgical equipment, and the provision of proper sterilization and hygienic conditions. Surgical team scheduling ensures that surgeries begin on time, are completed effectively, and patients are treated safely. It is also critical to reduce employee fatigue and balance the workload. As a result, integrating surgical teams into operating room scheduling problems provides significant benefits. Accordingly, 29 research articles focusing on the problem of OR scheduling, within the scope of constraints on surgical team members, scheduling strategies, uncertainties, and solution methods, are thoroughly reviewed in this study