The extended roster quality staffing problem: addressing roster quality variation within a staffing planning period

Staffing and rostering are two interdependent optimization problems related to personnel planning. Where staffing concerns an organization’s personnel composition, personnel rostering aims to assign that staff to shifts while respecting a set of constraints. Staffing decisions therefore impact on the extent to which personnel rostering objectives can be accomplished. Previous research has suggested that it may prove beneficial to address both problems simultaneously and has introduced the roster quality staffing (RQS) problem to this effect. The RQS aims to assess the appropriateness of a given personnel structure based on the quality of its corresponding roster. The RQS problem is, however, limited by the fact that it only considers one rostering period and thus neglects that staffing and rostering span different time horizons. One staffing period usually consists of multiple rostering periods, during which the rostering objectives and constraints may vary. This difference between rostering periods causes roster quality variation within the same staffing period. This paper remedies this issue by introducing a generalization of the RQS problem: the Extended RQS problem. This generalization considers the impact of a personnel structure upon possible roster quality over the entire staffing period. There currently exist no suitable algorithms for solving the extended roster quality staffing problem, and therefore, two local search-based approaches have been developed and assessed by means of publicly available personnel rostering instances. Experimental results demonstrate both algorithms’ optimization potential. In addition, the accuracy of the new model is assessed with respect to both staffing decisions and overall roster quality.