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Nursing costs account for over 50% of Health Service Organizations budgetary expenses. In a financially contracting Healthcare market that is amidst the focus of current National and International economic concerns and political agenda, here a counter-intuitive method to minimize exposure to rising nursing costs. Healthcare’s conundrum is marked by rising nursing costs, growing patient population, rising uninsured rates and decreasing insurance reimbursements. Participants traditionally focus on nurse staffing to minimize costs, but in its inextricable link to scheduling, budgets are often inaccurately projected as compared to actual staffing quantities and costs; this is largely due to front-line staffing policies and unpredictable nursing rates. This paper presents a nationwide experimental and empirical study of ten healthcare participants in a cross market “Hedging” application in Nursing Services as an approach to reduce exposure to rising nursing costs based on nursing rate volatility notwithstanding nursing quantity needs and day-to-day staffing decisions, and considering Options as a primary hedging approach to reduce budget disparity and yield nursing expense savings. Nursing monthly costs and demand were collected for all participants over varying range of time periods. A correlation analysis indicated that total nursing costs are highly correlated to nursing rate change, differing across participant types. Additionally, the data was analyzed for “asset” and “options” applicability, as well as tested for appropriateness of the Black-Scholes model for options pricing. The analysis concluded that nursing service qualifies as an underlying asset for options as a hedging technique and may be priced using the Black-Scholes model. The approach was tested on one of the participants, and indicated a savings of over 11% in nursing expenses and a decrease in budget disparity of approximately 14%. Hypothetical application across the non-tested participants alludes that the implementation results are likely to be sustainable across participant with dissimilar demographics.

As in many service organizations, hospitals use a variety of shift types when scheduling nurse resources. In general, the operational decisions of workforce planning can be divided into two interrelated problems: (1) midterm planning in terms of shift assignments for up to six weeks at a time, and (2) the short-term daily adjustment of schedules. Individual nurse profiles are a function of a unit's skill requirements, labor laws, and other qualifications, and are results of the long-term planning decision. At the midterm level, the goal is to match nurse resources with the expected workload over the planning horizon. Rosters are designed to maximize personnel preferences as well as minimize cost. To investigate this problem, a large-scale integer program model was developed and solved with two methodologies. The first is based on Lagrangian Relaxation based heuristic, which uses a combination of subgradient optimization and Bundle methods, with variable fixing strategy and IP-based heuristic. The second methodology is a branch-and-price algorithm that makes use of several new branching rules, an extremely effective rounding heuristic, a dual bound procedure, and specialized aggregation scheme. To extend the algorithms to solve different levels of nursing skills, a downgrading strategy is used by giving scheduling priorities to higher level of worker. The midterm schedules provide a blueprint for the monthly work assignments of the staff. Because of absenteeism and unpredicted demand fluctuations, though, a hospital-wide reallocation of resources is needed on a daily basis. While the overall goal is to ensure adequate coverage at minimize cost, a secondary goal is to minimize changes to the assigned rosters. Nevertheless, to allow more flexibility, nurses are permitted to work in several units during a shift rather than just their home unit. An IP-based column generation methodology was developed to solve this problem and applied within a rolling horizon framework. The idea is to consider 24 hours at a time, but implement the results for only the first 8 hours. All algorithms were tested on data obtained from a 400-bed US hospital. The results show an order-of-magnitude improvement over current approaches in terms of solution quality and computation times. / text

Integer programming can be used to provide solutionsto complex decision and planning problems occurring in a wide varietyof situations. Applying integer programming to a real life problembasically involves a first phase where a mathematical model isconstructed, and a second phase where the problem described by themodel is solved. While the nature of the challenges involved in therespective two phases differ, the strong relationship between theproperties of models, and which methods that are appropriate for theirsolution, links the two phases. This thesis constitutes of threepapers, of which the third one considers the modeling phase, while thefirst and second one consider the solution phase.   Many applications of column generation yield master problems of setpartitioning type, and the first and second papers presentmethodologies for solving such problems. The characteristics of themethodologies presented are that all successively found solutions arefeasible and integral, where the retention of integrality is a majordistinction from other column generation methods presented in theliterature.   The third paper concerns nurse scheduling and describes the results ofa pilot implementation of a scheduling tool at a Swedish nursing ward.This paper focuses on the practical aspects of modeling and thechallenges of providing a solution to a complex real life problem.

<p>Integer programming can be used to provide solutionsto complex decision and planning problems occurring in a wide varietyof situations. Applying integer programming to a real life problembasically involves a first phase where a mathematical model isconstructed, and a second phase where the problem described by themodel is solved. While the nature of the challenges involved in therespective two phases differ, the strong relationship between theproperties of models, and which methods that are appropriate for theirsolution, links the two phases. This thesis constitutes of threepapers, of which the third one considers the modeling phase, while thefirst and second one consider the solution phase.</p><p> </p><p>Many applications of column generation yield master problems of setpartitioning type, and the first and second papers presentmethodologies for solving such problems. The characteristics of themethodologies presented are that all successively found solutions arefeasible and integral, where the retention of integrality is a majordistinction from other column generation methods presented in theliterature.</p><p> </p><p>The third paper concerns nurse scheduling and describes the results ofa pilot implementation of a scheduling tool at a Swedish nursing ward.This paper focuses on the practical aspects of modeling and thechallenges of providing a solution to a complex real life problem.</p>

Session ID: TH-E1-4 / SCIS & ISIS 2010, Joint 5th International Conference on Soft Computing and Intelligent Systems and 11th International Symposium on Advanced Intelligent Systems. December 8-12, 2010, Okayama Convention Center, Okayama, Japan

A hybrid methodology of game theory and Monte Carlo Tree Search was developed and the hybrid methodology was tested with various case studies through the nurse scheduling problem to show that it was able to form Pareto front dominance solutions, finding feasible solutions that were optimal and finding feasible partial solutions in over-constrained problems. The performance comparison was carried out with the Genetic Algorithm on the Resident Physician Scheduling problem and showed that the hybrid methodology was able to produce better quality solutions compared to the state of the art approach.

Numerous studies have been done in the area of nurse scheduling, since this is a complex area with a lot of aspects that has to be taken into account. An interesting but little studied subject is how the requirements for the scheduling affect the possibility to construct a feasible schedule, or how the requirements affect the quality of the schedule. Of special interest is the effect of the composition of the workforce and of the change in scheduling rules. What is missing is results showing which composition and changes that are possible, and if so what is needed to be able to follow through with them. The changes tested in our simulation study are changes that is up for discussion at many wards in Sweden today, with topics such as split shifts and high part-time work percentages within the staff. In order to simulate various scheduling requirements and changes, an integer linear model for creating nurse schedules is developed. The results provide some insight into the dependence between scheduling requirements and the resulting schedules. In particular our simulation results indicate that there is an inherent conflict between high part-time work percentages and split or long work shifts. Our results can be used as a basis for future research on these topics in the area of nurse scheduling.

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This thesis develops quantitative methods which incorporate transportation modeling for tactical and operational home health logistics planning problems. We define home health nurse routing and scheduling (HHNRS) problems, which are dynamic periodic routing and scheduling problems with fixed appointment times, where a set of patients must be visited by a home health nurse according to a prescribed weekly frequency for a prescribed number of consecutive weeks during a planning horizon, and each patient visit must be assigned an appointment time belonging to an allowable menu of equally-spaced times. Patient requests are revealed incrementally, and appointment time selections must be made without knowledge of future requests. First, a static problem variant is studied to understand the impact of fixed appointment times on routing and scheduling decisions, independent of other complicating factors in the HHNRS problem. The costs of offering fixed appointment times are quantified, and purely distance-based heuristics are shown to have potential limitations for appointment time problems unless proposed arc cost transformations are used. Building on this result, a new rolling horizon capacity-based heuristic is developed for HHNRS problems. The heuristic considers interactions between travel times, service times, and the fixed appointment time menu when inserting appointments for currently revealed patient requests into partial nurse schedules. The heuristic is shown to outperform a distance-based heuristic on metrics which emphasize meeting as much patient demand as possible. The home health nurse districting (HHND) problem is a tactical planning problem which influences HHNRS problem solution quality. A set of geographic zones must be partitioned into districts to be served by home health nurses, such that workload is balanced across districts and nurse travel is minimized. A set partitioning model for HHND is formulated and a column generation heuristic is developed which integrates ideas from optimization and local search. Methods for estimating district travel and workload are developed and implemented within the heuristic, which outperforms local search on test instances.