A matheuristic based on Lagrangian relaxation for the multi-activity shift scheduling problem.

•We propose a matheuristic for the multi-activity shift scheduling problem.•The matheuristic is based on a Lagrangian relaxation and context-free grammars.•Context-free grammars are used to model the feasible shifts for each employee.•The matheuristic reports better solutions than the best known in the literature.•The matheuristic provides dual bounds, which are used to estimate the optimality gap.