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A generalized linear programming model for nurse scheduling

A generalized linear programming model for nurse scheduling,10.1016/S0377-2217(97)00330-5,European Journal of Operational Research,Brigitte Jaumard,Fr

A generalized linear programming model for nurse scheduling   (Citations: 92)
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This paper presents a 0–1 column generation model with a resource constrained shortest path auxiliary problem for nurse scheduling. The master problem finds a configuration of individual schedules to satisfy the demand coverage constraints while minimizing salary costs and maximizing both employee preferences and team balance. A feasible solution of the auxiliary problem is an acceptable schedule for a given nurse, with respect to collective agreement requirements such as seniority, workload, rotations and days off. We define a new resource structure in the auxiliary problem in order to take into account the complex collective agreement rules specific to the nurse scheduling problem. This model generalizes further the previous formulations discussed in the literature and can be viewed as a general scheme for complex personnel scheduling problems, especially in the context of organizations which operate around the clock. Solution methods and preliminary test results are discussed.
Journal: European Journal of Operational Research - EJOR , vol. 107, no. 1, pp. 1-18, 1998
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    • ...In essence, the approaches range from mathematical programming methods (Warner and Prawda 1972; Beaumont 1997; Jaumard et al. 1998; Bard and Purnomo 2005) to special purpose heuristic methods (Isken and Hancock 1990; Randhawa and Sitompul 1993; Bard and Purnomo 2007; Beddoe and Petrovic 2007)...

    Edmund K. Burkeet al. A Pareto-based search methodology for multi-objective nurse scheduling

    • ...[13] utilized linear programming to obtain the solution that can simultaneously minimize the total payment, satisfy the staff preference, and level the nurse workforce...

    Jihene Jlassiet al. A combined AHP-GP model for nurse scheduling

    • ...Similarly, Jaumard et al. [20] use an exact branch-and-price algorithm for the midterm nurse scheduling problem...

    Jens O. Brunneret al. Long term staff scheduling of physicians with different experience lev...

    • ...In order to overcome these difficulties, several authors have solved personnel scheduling problems using column generation and closely connected resulting branch-and-price approaches (e.g., Bard and Purnomo, 2005a, 2005b ;B eliën and Demeulemeester, 2005, 2006; Caprara et al. 2003; Jaumard et al. 1998; Mehrotra et al. 2000; Gamache et al. 1999)...
    • ...Jaumard et al. (1998) were the first to present a basic 0–1 column generation model with a dedicated resource constrained shortest path auxiliary problem for the scheduling of nursing personnel...
    • ...This pricing problem, i.e., the identified subproblem, is a resource constrained shortest path problem (Jaumard et al. 1998), which defines the generated paths to be feasible with respect to different resource constraints and the path structural constraints...
    • ...Beliën and Demeulemeester (2005 )r ely on a dynamic programming approach whereas Jaumard et al. (1998) propose a dedicated pseudo-polynomial two-phase algorithm to solve the resource constrained shortest path problem...
    • ...–T hefirst possible strategy (i.e., 0/1 branching) determines the obligate assignment of a nurse to a particular shift requiring a specific skill competency on a particular day (ximj k = 1) or explicitly prohibits the specific assignment (ximj k = 0). This branching strategy is often applied in personnel scheduling literature (e.g., Jaumard et al. 1998; Mehrotra et al. 2000; Beliën and Demeulemeester, 2005, 2006)...

    Broos Maenhoutet al. Branching strategies in a branch-and-price approach for a multiple obj...

    • ...Jaumard et al. (1998) were the first to propose an exact B&P algorithm to solve the midterm scheduling problem for nurses...

    Jens O. Brunneret al. Midterm scheduling of physicians with flexible shifts using branch and...

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