Mathematical programming approaches for downstream processing optimisation of biopharmaceuticals

• We address integrated optimal chromatography sequencing & column sizing decisions.
• A novel MILFP model is proposed for continuous column bed heights.
• Two efficient hierarchical approaches are developed for discrete column bed heights.
• These approaches are applied to an industrially relevant example for demonstration.
• The hierarchical approaches save CPU time by over two orders of magnitude.

This work addresses the optimal downstream chromatography sequencing and column sizing strategies in the manufacturing processes of monoclonal antibodies (mAbs). A mixed integer linear fractional programming (MILFP) model is developed to achieve continuous bed height values. In addition, to ease the computational expense of the literature MILFP model for discrete bed height values, two efficient hierarchical solution approaches are developed involving the two MILFP models, in which, based on its optimal solution of the newly developed MILFP model, the reduced MILFP model is solved with smaller decision region to find the final solution. A Dinkelbach-based algorithm is used as the solution approach of the MILFP models. Finally, a case study with different upstream processing (USP) and downstream processing (DSP) ratios are investigated, and the results show that all proposed approaches have high computational efficiency to satisfy different needs of the decision makers.