A multi-objective lot sizing procurement model for multi-period cold chain management including supplier and carrier selection

The rapid expansion of the cold chain market is a key supply chain trend, but its high energy consumption conflicts with low-carbon goals. To address this, the paper proposes a multi-objective lot sizing procurement (LSP) model for managing the procurement of perishable products in the cold chain. This model, constrained by limited inventory and transportation capacity, aims to optimize multi-period procurement plans and order allocation and minimize total costs and carbon emissions. The proposed multi-objective LSP model adopts a posteriori mode, which contributes to enhancing the model's applicability, especially in countries where carbon tax and trading systems are not fully developed. To enhance decision makers’ decision efficiency and preserve the diversity of the original Pareto solutions as much as possible, the K-means++ algorithm is employed to prune the original Pareto solution set, providing decision-makers with three representative solutions (cost priority, balanced, and carbon priority solutions). In addition, the paper conducts sensitivity analysis, stability experiments, and compares the multi-objective LSP model with the benchmark model (relaxed carbon emission constraints). Experiments show that the multi-objective LSP model quickly and stably provides decision-makers with lot sizing purchasing plans for numerical examples of different scales and effectively controls the total carbon footprint of the entire cold chain at a low cost.