This research paper presents an offline and online user defined priority driven multi-objective optimal control study of a bioprocess in a fed-batch reactor. Productivity and the amount of substrates used in the process are considered as the two control objectives in that order of priority for this purpose. The priorities in the objective functions are realized using the lexicographic approach by sequentially solving multiple objectives to arrive at a Pareto solution point. This approach is not sensitive to the tuning of weighting parameters as compared to the scalarized objective, practiced conventionally. The weighting factors tuning issue is demonstrated with an offline optimal control. The lexicographic optimization approach is then implemented to overcome this thing issue. Subsequently, the online optimal control problem is solved using economic model predictive control (EMPC) owing to the economic nature of the control objectives. Often, the Pareto curve is such that marginally relaxing one objective results into a significant improvement in the other objective. This can easily be implemented with the lexicographic approach and is demonstrated using EMPC. Moreover, unlike the continuous processes, the batch processes operate for a specific batch time. Hence, the shrinking horizon approach along with the EMPC framework is employed in the fed-batch bioreactor for online control with extended Kalman filter (EKF). (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.