This work presents a new mathematical programming formulation for the problem of scheduling cutting operations on multiple parallel slitting machines. A Mixed-Integer Linear Programming (MILD) model is proposed, solved to optimality using standard techniques. A continuous time representation is used to avoid unnecessary time intervals and to limit the number of variables in the formulation. One important feature of the model is the explicit treatment of change-over times as an important part of a multiple objective cost function, which may be adapted to minimizing makespan, or total flow time, or any weighted combination of the two. An industrial case study from the paper-converting industry is presented to illustrate the applicability and efficiency of the proposed model.