A Lagrangian heuristic algorithm for sustainable supply chain network considering CO₂ emission

Manufacturing companies encounter pressure related to not only cost and service level but also certain limitations based on the constraints of energy saving and emission reduction. This study investigates production planning for a sustainable supply chain, for which factors such as the limits for CO₂ emission, stochastic demands, service level, and inventory capacities are considered. We build a mixed-integer programming model and propose a Lagrangian relaxation (LR) algorithm to solve the large-scale production planning problem in a cost-efficient way. Based on the historical data of HY Automobile Co. in China and 120 randomly generated instances, we find that the LR algorithm can generate near-optimal solutions with less than a 1% difference as compared to CPLEX solutions. The algorithm can find a solution within 5 min for a case with a large problem size, whereas CPLEX cannot find the solution in an hour. At the same service level, the cost decreases with the initial inventory capacity and CO₂ emission limit and increases with the demand and number of the types of products. The cost gap that is caused by increasing these parameters becomes larger when the service level is higher. This finding indicates that the parameters’ values are important to the company when a high service level is required.