Complex Multi-Stage Production Scheduling with Unrelated Parallel Machines in High-Mix Low Volume Environments Balancing Cost-Efficiency and Carbon Emissions

Abstract

This study investigates a complex production scheduling problem in high-mix low-volume (HMLV) manufacturing environments under carbon regulation, where multi-stage process dependencies and heterogeneous machine characteristics jointly shape cost and emission outcomes. We develop a multi- stage production scheduling framework that integrates sequential process dependencies with unrelated parallel machines, capturing heterogeneous processing times, operating costs, and carbon emission rates that substantially increase scheduling complexity. Within this framework, we formulate two mixed- integer linear programming models to represent alternative regulatory settings: a cost-carbon trade-off model and a carbon credit model. The cost-carbon trade-off model explicitly examines the trade-off between total production cost and carbon emissions under binding emission limits, whereas the carbon credit model minimizes total cost while allowing excess emissions to be offset through carbon credit purchases. The proposed models are validated using real-world data from a marine engine parts manufacturer in Ulsan, Republic of Korea. Numerical experiments reveal that, under strict emission limits, the cost-carbon trade-off model experiences severe shortages and high penalty costs, while relaxing the emission limit shifts production toward lower-cost, higher-emission machines and substantially reduces total cost. In contrast, the carbon credit model maintains production feasibility even under tight emission constraints by offsetting excess emissions through carbon credit purchases, resulting in only marginal changes in total cost as emission limits are relaxed. Sensitivity analyses further demonstrate how penalty costs, machine settings, and carbon credit prices reshape machine assignments, excess emissions, and cost structures. Overall, the proposed framework provides a unified decision-support tool for analyzing production scheduling decisions under alternative carbon regulation schemes and offers actionable insights for managing the cost-emission trade-off in environment- conscious HMLV manufacturing systems.