Optimal scheduling and open-loop control of network batch processes under variable processing times using Generalized Benders Decomposition

This work addresses the discrete-time simultaneous scheduling and open-loop control (SSOC) of network batch processes with variable processing times through a tailored Generalized Benders Decomposition (GBD) framework. This SSOC problem is a challenging mixed-integer nonlinear programming (MINLP) problem because variable processing times introduce more binary variables to a discrete-time scheduling formulation and may generate new infeasibilities if those variables are poorly selected. Variable processing times are key in SSOC since they affect both the flexibility of the schedule, and the dynamic performance of batch systems. The key novelty of the proposed GBD approach is the addition of initial and auxiliary feasibility cuts to facilitate the handling of infeasibilities generated by variable processing times. The performance of the proposed GBD framework is tested using a case study adapted from the literature. A GBD methodology that implements traditional feasibility cuts is used as a benchmark. While the conventional GBD method was unable to converge to a feasible solution, the proposed GBD framework found a feasible solution within the first two interactions and then converged by closing the absolute MINLP gap. Therefore, the proposed GBD framework is a promising strategy to solve SSOC problems involving batch processes often found in the pharmaceutical, energy, and food industries.