An MILP model for the optimal scheduling of a lube oil and paraffin production plant is presented. The plant is composed of processing units that operate in continuous and discontinuous modes, and some are also duplicated. The raw materials for the process are stored in dedicated tanks, and the plant presents finite intermediate storage. The mathematical formulation was developed under a continuous time representation and compared to a discrete-time and other continuous-time MILP models. Results with significant reduction of the computational time are generated and allow the model application for realistic time horizons with a significant level of scheduling detail.