Lot Sizing Problem for Cold Supply Chain with Energy and Quality Considerations

Cold supply chains require coordinated inventory and storage decisions to preserve product quality while managing high energy consumption. This paper develops a joint economic lot-sizing model for a two-echelon cold supply chain that explicitly integrates time–temperature-dependent quality degradation with energy consumption in refrigerated warehouses. Unlike traditional approaches, energy is modeled as an endogenous function of warehouse filling level and warehouse temperature, allowing the interaction between inventory volume, energy efficiency, and quality preservation to be captured. The model is formulated under three coordination policies—Lot-for-Lot, traditional agreement, and consignment stock—and solved under joint decision making. Numerical results for chilled and frozen products show that neglecting energy and quality costs can lead to sub-optimal policies with total cost penalties exceeding 300% compared to the proposed integrated optimization. Results further indicate that a consignment stock agreement can reduce total system costs by up to 9% relative to traditional policies, while the optimal lot size is highly sensitive to energy prices, product value, and warehouse temperature. These findings highlight the critical role of jointly optimizing inventory, energy, and quality decisions in cold supply chains and provide actionable insights for designing more sustainable and energy-efficient production inventory systems.