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 p...