Optimal scheduling for multi-product batch processes under consideration of non-zero transfer times and set-up times

Simple recurrence relations for calculating completion times of various storage polices (unlimited, intermediate storages(FIS), finite intermediate storages(FIS), no intermediate storage(NIS), zero wait(ZW) for serial multi-product multi-unit processes are suggested. Not only processing times but also transfer times, set-up (clean-up) times of units and set-up times of storages are considered. Optimal scheduling strategies with zero transfer times and zero set-up times had been developed as a mixed integer linear programniing(MILP) formulation for several intermediate storage policies. In this paper those with non-zero transfer times, non-zero set-up times of units and set-up times of storages are newly proposed as a mixed integer nonlinear programming(MINLP) formulation for various storage polices (UIS, NIS, FIS, and ZW). Several examples are tested to evaluate the robustness of this strategy and reasonable computation times.