Two Multi-objective Optimization Approaches for Solving a Fuzzy Bi-objective Distributed Hybrid Flow Shop Scheduling Problem Under Uncertainty

Efficient production and distribution planning across a network of customers and producers is crucial in today’s world, especially given the growing focus on energy use and CO₂ emissions. This paper tackles the challenge by optimizing production scheduling at various production centers, followed by vehicle routing from these centers to customers and back. The model prioritizes two main objectives: minimizing the total flow time (i.e., cumulative delivery time) and reducing CO₂ emissions generated by both production machines and transport vehicles. Recognizing the uncertainties in real-world data, the model incorporates fuzzy logic to account for unknown processing and travel times. Fuzzy chance-constrained programming (FCCP) and expected value (EV) approaches are used to manage these uncertainties, converting the fuzzy model into a deterministic form. To solve the bi-objective problem, LP-metric and goal attainment (GA) approaches are employed. The model is validated through case studies, with both visual and quantitative results showing that the LP-metric approach outperforms the GA approach. When comparing the solutions using the TOPSIS (technique for order of preference by similarity to ideal solution) method, the LP-metric approach proves to be more effective, especially in balancing delivery efficiency with reduced energy consumption and CO₂ emissions. This research highlights the importance of integrating sustainability and efficiency into production and distribution planning, offering a robust model that addresses both operational and environmental goals.