Integrated Nurse Staffing And Assignment Under Uncertainty
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One of the major problems in the United States health care system is a shortage of nurses. Baby boomers and an increasing elderly population are the main reasons for a rapidly growing demand for nurses. Besides the decline in enrollments in registered nurse degree programs, many nurses have suffered from work burnout. High workloads and undesirable schedules are two major issues that cause nurses' job dissatisfaction. As a result, nurses plan to leave their jobs causing low retention and low entering rates. One consequence of the shortage is that excessive workload on nurses decreases the quality of patient care. Many states have seriously considered taking actions to cope with the shortage to ensure patient safety, e.g., California has regulated mandatory nurse-to-patient ratios. To satisfy patient care demands, hospital administrations are obligated to employ other expensive staffing resources, such as part-time nurses, agency nurses, overtime nurses, etc. Since nurse staffing costs account for over 50% of hospital expenditures, health care costs are continuously increasing driven by an ongoing severe shortage of nurses. Consequently, the nursing shortage will become more severe and nurse staffing has become one of the most attractive research areas. We describe four phases of nurse planning, which are nurse budgeting, nurse scheduling, nurse staffing, and nurse assignment. The first part of this dissertation considers only the last phase of nurse planning, which makes daily decisions on assigning nurses to patients. With nurses from the nurse staffing phase, a charge nurse assigns nurses to patients at the beginning of a shift. To capture uncertainty in patient care, we develop a stochastic integer programming model for nurse assignment with an objective to minimize excess workload on nurses. The problem is solved using a Benders' decomposition approach, whose master problem assigns nurses to patients, and whose recourse subproblems penalize the assignment and determine excess workload on nurses. The recourse subproblems can be considered as network flow problems, in which we develop a new greedy algorithm to solve them. When hospital units have new hires, there is no sufficient data to consider them unique. A symmetry problem may arise when there are identical nurses, which leads us to construct sets of valid inequalities to strengthen the restricted master problem. We develop sets of valid inequalities to prevent symmetric assignments, which eventually reduce the computational effort. In addition, we develop a set of valid inequalities representing the nurse-to-patient ratio to ensure patient safety. These valid inequalities not only enhance the algorithmic performance, but also prevent illegal and impractical assignments. The second part of this dissertation focuses on an integration between the third and the last phases, which makes short-term decisions (90 minutes before a shift) on staffing and assigning nurses to patients. We present a stochastic integer programming model for integrated nurse staffing and assignment with uncertain patient care with an objective of minimizing excess workload on nurses. We present three decomposition approaches based on the L-shaped method for solving our model, which are (1) Benders' decomposition, (2) Lagrangian relaxation with Benders' decomposition, and (3) nested Benders' decomposition. The Lagrangian relaxation with Benders' decomposition approach can be viewed as a novel search method for bicriteria stochastic integer programs. Computational results are provided based upon data from two medical-surgical units at Northeast Texas hospital. The focus of this dissertation is to find good solutions within 30 minutes. Results suggest that the hospital can save up to 1588 hours of excess workload each year in each unit by using our stochastic programming for nurse assignment model. The greedy algorithm for the network primal subproblem is 30 times faster than the current commercial network simplex solver (CPLEX 9.1). Moreover, integrated nurse staffing and assignment results indicated the Lagrangian relaxation with Benders' decomposition approach provided the most promising results among three methods. The nurse staffs and assignments found by these methods can be used in a nurse staffing decision supporting system, which facilitates a nurse supervisor to select a nurse staff and assignment based on a tradeoff between staffing cost and excess workload on nurses. Moreover, a nurse supervisor can also use our model to evaluate a float assignment. Our model allows decision makers to play important roles in utilizing their judgments to comply the right staffing policy. Furthermore, topics of future research are discussed. Finally, a nurse assignment decision supporting tool based on our underlying model is provided in the appendix.