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On hierarchical planning and scheduling in a parallel machine environment

In this paper we propose a branch-and-cut algorithm for solving an integrated production planning and scheduling problem in a parallel machine environment. The planning problem consists of assigning each job to a week over the planning horizon, whereas in the scheduling problem those jobs assigned to a given week have to be scheduled on the parallel machines such that all jobs are finished within the week. We solve this problem in two ways: (1) as a monolithic mathematical program, and (2) using a hierarchical decomposition approach in which only the planning decisions are modeled explicitly, and the existence of a feasible schedule for each week is verified by using cutting planes. Our computational results show that the hierarchical decomposition approach outperforms the monolithic model for this problem.