Application of Quantum Annealing to Nurse Scheduling Problem

Quantum annealing is a promising heuristic method to solve combinatorial optimization problems, and efforts to quantify performance on real-world problems provide insights into how this approach may be best used in practice. We investigate the empirical performance of quantum annealing to solve the Nurse Scheduling Problem (NSP) with hard constraints using the D-Wave 2000Q quantum annealing device. NSP seeks the optimal assignment for a set of nurses to shifts under an accompanying set of constraints on schedule and personnel. After reducing NSP to a novel Ising-type Hamiltonian, we evaluate the solution quality obtained from the D-Wave 2000Q against the constraint requirements as well as the diversity of solutions. For the test problems explored here, our results indicate that quantum annealing recovers satisfying solutions for NSP and suggests the heuristic method is sufficient for practical use. Moreover, we observe that solution quality can be greatly improved through the use of reverse annealing, in which it is possible to refine a returned results by using the annealing process a second time. We compare the performance NSP using both forward and reverse annealing methods and describe how these approach might be used in practice.Comment: 20 pages, 13 figure

Welcome to OR&S! Where students, academics and professionals come together

In this manuscript, an overview is given of the activities done at the Operations Research and Scheduling (OR&S) research group of the faculty of Economics and Business Administration of Ghent University. Unlike the book published by [1] that gives a summary of all academic and professional activities done in the field of Project Management in collaboration with the OR&S group, the focus of the current manuscript lies on academic publications and the integration of these published results in teaching activities. An overview is given of the publications from the very beginning till today, and some of the topics that have led to publications are discussed in somewhat more detail. Moreover, it is shown how the research results have been used in the classroom to actively involve students in our research activities

Three Essays on Data-Driven Optimization for Scheduling in Manufacturing and Healthcare

This dissertation consists of three essays on data-driven optimization for scheduling in manufacturing and healthcare. In Chapter 1, we briefly introduce the optimization problems tackled in these essays. The first of these essays deals with machine scheduling problems. In Chapter 2, we compare the effectiveness of direct positional variables against relative positional variables computationally in a variety of machine scheduling problems and we present our results. The second essay deals with a scheduling problem in healthcare: the team primary care practice. In Chapter 3, we build upon the two-stage stochastic integer programming model introduced by Alvarez Oh (2015) to solve this challenging scheduling problem of determining patient appointment times to minimize a weighted combination of patient wait and provider idle times for the team practice. To overcome the computational complexity associated with solving the problem under the large set of scenarios required to accurately capture uncertainty in this setting, our approach relies on a lower bounding technique based on solving an exhaustive and mutually exclusive group of scenario subsets. Our computational results identify the structure of optimal schedules and quantify the impact of nurse flexibility, patient crossovers and no-shows. We conclude with practical scheduling guidelines for team primary care practices. The third essay deals with another scheduling problem observed in a manufacturing setting similar to first essay, this time in aerospace industry. In Chapter 4, we propose mathematical models to optimize scheduling at a tactical and operational level in a job shop at an aerospace parts manufacturer and implement our methods using real-life data collected from this company. We generalize the Multi-Level Capacitated Lot-Sizing Problem (MLCLSP) from the literature and use novel computational techniques that depend on the data structure observed to reduce the size of the problem and solve realistically-sized instances in this chapter. We also provide a sensitivity analysis of different modeling techniques and objective functions using key performance indicators (KPIs) important for the manufacturer. Chapter 5 proposes extensions of models and techniques that are introduced in Chapters 2, 3 and 4 and outlines future research directions. Chapter 6 summarizes our findings and concludes the dissertation

Partnering Strategies for Fitness Evaluation in a Pyramidal Evolutionary Algorithm

This paper combines the idea of a hierarchical distributed genetic algorithm with different inter-agent partnering strategies. Cascading clusters of sub-populations are built from bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes for (sub-)fitness evaluation purposes are examined for two multiple-choice optimisation problems. It is shown that random partnering strategies perform best by providing better sampling and more diversity

'On the Application of Hierarchical Coevolutionary Genetic Algorithms: Recombination and Evaluation Partners'

This paper examines the use of a hierarchical coevolutionary genetic algorithm under different partnering strategies. Cascading clusters of sub-populations are built from the bottom up, with higher-level sub-populations optimising larger parts of the problem. Hence higher-level sub-populations potentially search a larger search space with a lower resolution whilst lower-level sub-populations search a smaller search space with a higher resolution. The effects of different partner selection schemes amongst the sub-populations on solution quality are examined for two constrained optimisation problems. We examine a number of recombination partnering strategies in the construction of higher-level individuals and a number of related schemes for evaluating sub-solutions. It is shown that partnering strategies that exploit problem-specific knowledge are superior and can counter inappropriate (sub-) fitness measurements

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