Solving a multiprocessor problem by column generation and branch-and-price

This work presents an algorithm for solving exactly a scheduling problem with identical parallel machines and malleable tasks, subject to arbitrary release dates and due dates. The objective is to minimize a function of late work and setup costs. A task is malleable if we can freely change the set of machines assigned to its processing over the time horizon. We present an integer programming model, a Dantzig-Wolfe decomposition reformulation and its solution by column generation. We also developed an equivalent network flow model, used for the branching phase. Finally, we carried out extensive computational tests to verify the algorithm’s efficiency and to determine the model’s sensitivity to instance size parameters: the number of machines, the number of tasks and the size of the planning horizon