Two-stage distributionally robust optimization model for warehousing-transportation problem under uncertain environment

In recent years, with the continuous development of people's income and consumption level, consumers have higher and higher requirements for goods and services. The traditional warehousing-transportation method may lead to the decline of customer satisfaction level due to insufficient supply. Assuming that the demands of customers are unknown, we propose a two-stage distributionally robust optimization model with chance constraints, in which the ambiguity set contains all the probability distribution with the same first and second moments. For the sake of computation, the proposed model is equivalently transformed into a mixed-integer semi-definite programming problem. Since the existing optimization solver is challenging to solve the proposed model, this paper presents a modified primal-dual Benders' decomposition algorithm and proves the convergence of the algorithm. The validity of the proposed model is validated through the study of the storage and transportation problems of a perishable food supply chain in Shanghai. Compared with the non-robust optimization model, the traditional robust optimization model, and the distributionally robust optimization model based on Kullback-Leibler divergence, we show that the customer satisfaction level obtained by our method is improved by 9.1-13.4% on average in the out-of-sample datasets.