Solving an integrated employee timetabling and production scheduling problem via hybrid branch-and-bound

We propose exact hybrid methods based on integer linear programming and constraint programming for an integrated employee timetabling and production scheduling problem. Each method we investigate uses a constraint programming (CP) formulation associated with a linear programming (LP) relaxation. Under a CP framework, the LP-relaxation is integrated into a global constraint using in addition reduced cost-based filtering techniques. We propose two CP formulations of the problem yielding two different LP relaxations. The first formulation is based on a direct representation of the problem. The second formulation is based on a decomposition in intervals of the set of possible operation start time values. We show the theoretical interest of the decomposition-based representation compared the direct representation through the analysis of dominant schedules. Computational experiments on a set of randomly generated instances confirms the superiority of the decomposition-based representation. In both cases, the hybrid methods outperforms pure constraint programming for employee cost minimization while it is not the case for makespan minimization.