This paper presents MILP models for the optimal scheduling of a lube oil and paraffin production plant. The plant is composed of processing units that operate in continuous and discontinuous modes, and some also may execute the same task. There is finite storage capacity and most of the tanks are dedicated to a specified product, except for the basic lube oils that can be stored in any available tank. There are upper bounds for campaign changes in the units as well as shutdowns of the discontinuous units. Two mathematical formulations were developed under a discrete and continuous-time representation and compared to each other as well as to other continuous-time MILP models. Results with significant reduction in the computational time are generated with the continuous-time proposed model and allow the model application for real-world time horizons with a significant level of scheduling detail. © 2005 Elsevier Ltd. All rights reserved.