A location-inventory problem with facility temperature selection and quality deterioration in fresh product supply chain

The storage environment in logistics activities, particularly temperature conditions, plays a crucial role in preserving the quality of fresh products. However, one of the key challenges for companies is finding a balance between reducing network costs and selecting the ideal storage temperature. Therefore, this paper investigates a location-inventory problem with multiple retailers in the fresh product supply chain. Due to uncertain customer demand, retailers employ risk-pooling measures to handle demand fluctuations and reduce inventory risk. Furthermore, considering the quality deterioration of fresh product, this paper examines ordering strategies and the selection of storage temperatures to meet customer demand and quality requirements. A mixed-integer nonlinear programming model is then established to minimize total costs, including construction costs, inventory costs, cooling costs of distribution centers, and transportation costs within the supply chain network. We analyze the nonlinearity of the model and prove that the nonlinear terms are submodular functions. Consequently, a polymatroid cutting-plane approach is proposed to solve the model. Finally, the validity of the model and the effectiveness of the algorithm are verified through numerical experiments of various sizes.