The Production Scheduling Problem in a High-mix, Low-volume Production Setting with Non-identical Parallel Machines

Abstract

In this study, we address the production scheduling problem in a high-mix, low-volume production setting with non-identical parallel machines. Our two objectives are to minimize production costs and carbon emissions while considering different energy sources for machine operation. We propose a bi-objective mixed-integer linear programming model to determine the optimal production strategy. Each machine can be powered by various energy sources with different costs and carbon emissions. We validate our model with an application to a manufacturer in Ulsan, Republic of Korea, and find that allocating non-identical parallel machines can minimize production costs and carbon emissions. We also observe a trade-off between energy sources and carbon emissions limits, where increasing the limit leads to a shift from natural gas to coal to reduce costs. We conduct a sensitivity analysis on electricity generation costs and energy source combinations, discovering that coal is more cost-effective and stable than natural gas during fluctuating energy costs. Furthermore, we identify the optimal combination of energy sources for different carbon emissions limits, aiming to minimize costs while meeting production and environmental constraints.