An automatic constructive matheuristic for the shift minimization personnel task scheduling problem

The shift minimization personnel task scheduling problem is an NP-complete optimization problem that concerns the assignment of tasks to multi-skilled employees with a view to minimize the total number of assigned employees. Recent literature indicates that hybrid methods which combine exact and heuristic techniques such as matheuristics are efficient as regards to generating high quality solutions. The present work employs a constructive matheuristic (CMH): a decomposition-based method where sub-problems are solved to optimality using exact techniques. The optimal solutions of sub-problems are subsequently utilized to construct a feasible solution for the entire problem. Based on the study, a time-based CMH has been developed which, for the first time, solves all the difficult instances introduced by Smet et al. (Omega 46:64–73, 2014) to optimality. In addition, an automated CMH algorithm that utilizes instance-specific problem features has also been developed that produces high quality solutions over all current benchmark instances.