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We study a production planning problem known as the Discrete Lot-sizing and Scheduling problem with sequence-dependent changeover costs. We consider here the case where there are several identical parallel resources available for production and we propose solving the resulting optimization problem as a mixed-integer program (MIP) using a commercial solver. This is achieved thanks to the extension of an existing tight MIP formulation for the case of a single resource to the case of parallel resources. The results of our computational experiments show that using the proposed solution approach, we are able to provide guaranteed optimal solutions for instances of medium size with a reasonable computational effort.