The production scheduling problem employing non-identical parallel machines with due dates considering carbon emissions and multiple types of energy sources

This paper addresses the production scheduling problem with non-identical parallel machines in a high-mix, lowvolume production environment with due dates, considering carbon emissions savings and diverse types of energy sources for machine operation. To this end, we present a bi-objective mixed-integer programming model that minimizes both the total production-related cost and the total carbon emissions in the production process to determine the optimal production strategy. For each machine, we consider various types of energy sources with different electricity generation costs and different amounts of carbon emissions. The proposed model is validated with an application to a manufacturer in Ulsan, the industrial capital of the Republic of Korea. Our results showcase the potential use of non-identical parallel machines to minimize the total cost and carbon emissions in green manufacturing. Furthermore, the results identify the trade-off between different energy sources and the total cost under different carbon emissions limits. Generally, as the carbon emissions limit increases, our proposed model tends to replace natural gas with coal to minimize the total cost. Also, we perform sensitivity analyses with respect to the energy price of different types of energy sources combined with nuclear and renewable energy sources. We find that coal provides more stability than natural gas in terms of the total cost, particularly when there are fluctuations in the price for coal and natural gas. Additionally, we determine the optimal combination of energy sources for various carbon emissions limits, aiming to minimize the total cost while simultaneously satisfying all production-related and environmental constraints.