T Vovor

A generalized linear programming model for nurse scheduling

Abstract 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.

Erratum to Comparison of column generation models for channel assignment in cellular networks [Discrete Appl. Math. 112 (2001) 217-240]

Abstract We study several formulations of the channel assignment problem in an FDMA network as a linear integer 0–1 program. We consider the objective of minimizing the unsatisfied channel demand while satisfying the co-channel, the adjacent channel and the antenna channel spacing constraints. We compare the formulations according to two criteria: the ease with which their linear programming relaxations can be solved, and the quality of the bounds provided by these relaxations. We show that the best lower bound is provided by one of the set covering formulations, while the other two formulations provide the same lower bound. We present computational results that support the theoretical comparison of the models.

Paths with minimum range and ratio of arc lengths

Two new path problems in graphs are studied: MINRANGE, i.e., find a path from a vertex s to a vertex t with the smallest possible range of arc lengths, and MINRATIO, i.e., find such a path for which the ratio of the largest to the smallest arc length is minimum. Several bicriterion extensions of these problems are also considered.