Capacitated Lot Sizing Problem with Family-based Setup and Downstream-process-based Demand

We propose two formulations for the capacitated lot sizing problem with family-based setup and downstream-process-based demand (CLSP-FSDPD), one is the aggregate formulation (AGG) and the other one is the facility-location-based disaggregate formulation (FDG). We compare two formulations and extensive computational experiments show that FDG formulation outperforms AGG formulation in terms of solution quality when the planning horizon is relatively short, and AGG formulation consistently takes shorter CPU computation time that FDG formulation to solve in most cases. We show some of the differences in the performance of these various formulations arise from their different use of variables to represent production, setup or inventory states.