Capacity Planning under Clinical Trials Uncertainty in Continuous Pharmaceutical Manufacturing, 2: Solution Method

In Part 1 of this paper, we presented a scenario-based multiperiod mixed-integer linear programming (MILP) formulation for a capacity planning problem in continuous pharmaceutical manufacturing under clinical trials uncertainty. The number of scenarios and, thus, the formulation size grows exponentially with the number of products. The model size easily becomes intractable for conventional algorithms for more than 8 products. However, industrial-scale problems often involve 10 or more products, and thus a scalable solution algorithm is essential to solve such large-scale problems in reasonable times. In this part of the paper, we develop a rigorous decomposition strategy that exploits the underlying problem structure. We demonstrate the effectiveness of the proposed algorithm using several examples containing up to 16 potential products and over 65 000 scenarios. With the proposed decomposition algorithm, the solution time scales linearly with the number of scenarios, whereby a 16-product example with over 65 million binary variables, nearly 240 million continuous variables, and over 250 million constraints was solved in less than 6 h of solver time.