An implicit model for multi-activity shift scheduling problems

We consider a multi-activity shift scheduling problem where the objective is to construct anonymous multi-activity shifts that respect union rules, satisfy the demand and minimize workforce costs. An implicit approach using adapted forward and backward constraints is proposed that integrates both the shift construction and the activity assignment problems. Our computational study shows that using the branch-and-bound procedure of CPLEX 12.6 on the proposed implicit model yields optimal solutions in relatively short times for environments including up to 2970 millions of explicit shifts. Our implicit model is compared to the grammar-based implicit model proposed by Côté et al. (Manag Sci 57(1):151–163, 2011b) on a large set of instances. The results prove that both implicit models have their strengths and weaknesses and are more or less efficient depending on the scheduling environment.