Mixed-time mixed-integer linear programming scheduling model

This paper presents a novel mixed-time mixed-integer linear programming (MILP) scheduling model for industrial problems where intermediate storage handling is of particular concern. The proposed model is a crossbreed between a continuous-time and a discrete-time model where a continuous-time representation is incorporated in a discrete-time grid. The mixed-time formulation is useful in the modeling of multi-stage multi-product production processes using intermediate storages with nonlinear optimal storage profiles. The model is combining useful features from continuous-time models, flexibility, and solution efficiency, with the functional reference grid for the time representation, included in discrete-time representations. The model is able to handle both short-term and periodic problems. The main purpose of the presented model is not to challenge existing models on solution efficiency or quality on theoretical problems but to present a model that is very useful in the modeling of industrial scheduling problems where intermediate storage handling is of importance. The proposed model is able to solve industrial problems which, according to our knowledge, have not previously been solvable by existing models. The novelty with the proposed model is that an entirely continuous-time representation is incorporated in a uniform time grid. In practice this means that despite the continuous-time representation, aging profiles or highly nonlinear storage inventory profiles may, for example, be addressed with the proposed model.