Author:

Keywords:

itec, iMinds

Abstract:

This work studies a Markov manpower planning problem concerned with fulfilling the long term personnel need. Two criteria are considered for evaluating a personnel structure, i.e. the degree of attainability and the degree of desirability. The degree of attainability is an extension of the concept attainability described by Bartholomew et al. (1991) to overcome the crisp division of the set of the attainable and the set of the unattainable personnel structures. The degree of attainability represents the similarity of a personnel structure and the set of personnel structures that are attainable (Guerry, 1999). The degree of desirability is the degree in which the personnel structure corresponds with the long term objectives defined by the top management. The degree of desirability reflects the degree of similarity of a personnel structure and the desired personnel structure. In previous work, both criteria have been defined based on fuzzy set theory. Current state of the art has combined these two criteria and presented a model under several assumptions (De Feyter & Guerry, 2009). One of the assumptions is that the personnel structure has a fixed value for the total size, i.e. the total number of personnel. At present no optimization method has been presented for finding a personnel structure with a high value for the degree of attainability as well as for the degree of desirability. We extend the previous model and propose two new models that provide more flexibility. The new models are flexible in terms of providing generalizations by, for example, allowing fixed total size constraint relaxation. Moreover, the new models can accommodate additional constraints, such as a required ratio between the number of personnel in one subgroup to another, etc. The two models are formulated using different membership functions. The first model uses a reciprocal function to formulate the degree of attainability and the degree of desirability whereas the second model employs a triangular function to define them. The first model can be formulated as a linear program. However, the second model can only be formulated as a mixed integer nonlinear program. Two different algorithms are proposed to address the second model, i.e. piecewise linear approximation(PLA) and particle swarm optimization PSO). Extensive experiments have been performed to instances derived from existing nurse rostering data sets, in order to assess the algorithms. It is shown that each of the proposed algorithms can be used to effectively solve its respective model.