关键词: 冷链物流, 选址—分配问题, 需求和行程时间不确定, 分布鲁棒优化, 对偶理论

Abstract: With economic and living development, the demand for fresh products is increasing. However, due to the perishability, vulnerability, and time-sensitive nature of fresh products, a significant amount of them is lost through the existing distribution network before reaching consumers, resulting in significant losses for cold chain logistics companies. For example, fresh agricultural products in China can cause 300 billion RMB losses due to unreasonable logistics every year. In the United States, more than 40% of food, worth 218 billion USD, is wasted each year. The distribution center plays a crucial role in the cold chain logistics network as it connects suppliers to retailers. Scientifically locating distribution centers can improve distribution efficiency and reduce operational costs. Therefore, studying the problem of distribution center location-allocation is of great significance for optimizing the entire cold chain logistics network.
A cold chain logistics network typically consists of suppliers, distribution centers, and retailers, with the distribution center being a key link between suppliers and retailers, deciding the quality and efficiency of the entire cold chain logistics network. In order to save costs, cold chain logistics companies often rent existing candidate cold storage facilities as their distribution centers. Thus, the design problem of fresh logistics networks involves two decisions: (1)which cold storage facility is rented as the distribution center? and (2)what is the allocation plan from the distribution center to retailers? However, it is difficult to accurately predict consumer demand and travel time between network nodes, making the demand and travel time uncertain. Therefore, this paper focuses on the location-allocation problem of cold chain logistics distribution centers with uncertain demand and travel time.
Existing research generally solves the location-allocation problem of cold chain logistics with uncertain parameters using stochastic optimization and robust optimization methods. However, stochastic optimization methods assume exact knowledge of the distribution or scenarios of uncertain parameters, which is not feasible in practice. Robust optimization methods assume no knowledge of any distribution information about uncertain parameters and solve the uncertainty problem by optimizing the worst-case scenario, often leading to unnecessarily conservative decisions. Moreover, most existing research only considers uncertain demand, ignoring uncertain travel time. However, in reality, the traffic situation is complex, and neglecting uncertain travel time may lead to failed decisions on distribution center location and allocation, resulting in delayed delivery of fresh products to customers’ increased operating costs, and decreased customer satisfaction for the cold chain logistics company.
Considering factors such as the difficulty with accurately predicting retailer demand and the complex and variable road network traffic, a demand and travel time ambiguity set based on mean absolute deviation is constructed. This forms the foundation for the development of a cost-minimizing cold chain logistics distribution center location-allocation distributionally robust optimization (DRO) model. To make the model more tractable, auxiliary variables are introduced, and the DRO model is reformulated as a mixed integer programming model using dual theory. Finally, a comparison is made between the reformulated model and the stochastic programming (SP) model on both in-sample and out-sample data to evaluate their performance. The results demonstrate that the DRO model is more competitive in cold chain logistics distribution center location-allocation problems where it is difficult to obtain precise distributions of demand and travel time. Furthermore, it exhibits stronger resilience to extreme scenarios.

Key words: cold chain logistics, location-allocation problem, demand and travel time uncertainty, distributionally robust optimization, dual theory