Presenting a mathematical model for selecting the appropriate option to solve the lag problem, considering energy consumption

With the increasing complexity of supply chains and the growing need to reduce operational costs and energy consumption, the development of integrated models for production planning, distribution, and logistics has become increasingly important. This study proposes a comprehensive mathematical model for selecting an appropriate solution strategy for a four-echelon logistics problem while considering energy consumption. The proposed model integrates four supply chain levels, including suppliers, manufacturers, warehouses, and customers, and simultaneously addresses production planning, inventory management, facility location, heterogeneous vehicle routing, production and warehouse capacity, time windows, overtime scheduling, and supplier discount policies. Owing to the NP-hard nature of the problem, GAMS software was employed to solve small- and medium-sized instances, whereas the multi-objective metaheuristic algorithm NSGA-II was applied to large-scale problems. The results demonstrated that, for small-sized instances, the NSGA-II algorithm achieved solutions with less than 3% deviation from the optimal solutions obtained by GAMS, while producing identical results for the soft time-window objective function. For large-scale instances, NSGA-II significantly reduced computational time while maintaining high-quality and diverse Pareto-optimal solutions. Overall, the proposed model effectively improves production planning, distribution, and logistics performance by reducing total supply chain costs and energy consumption, providing an efficient decision-support tool for solving complex supply chain optimization problems.