Two-stage distributionally robust optimization model for a pharmaceutical cold supply chain network design problem

Pharmaceutical safety has received increasing attention from governments and corporations, and building a safe and effective pharmaceutical cold supply chain network has become an important issue. This paper proposes a two-stage pharmaceutical cold supply chain network design problem considering drug safety, in which the drug demand, transportation costs, and drug safety risk costs are assumed to be random variables. Due to the presence of uncertainty and the fact that information about the distribution of uncertain parameters is often only partially known, a distributionally robust optimization method is used to handle the uncertainty. A two-stage distributionally robust optimization model is constructed, in which the reliability of the estimation of the demand necessary to satisfy the entire cold chain network is ensured to be greater than a certain predetermined level by introducing an ambiguous joint chance constraint. The decision process for the problem can be divided into strategic and operational decisions with the goal of minimizing the total costs related to facility construction, the purchase of raw materials, drug production, transportation, and safety risks. By introducing an ambiguity set with mean and covariance information to describe the uncertain parameters, the two-stage model is eventually reformulated as a standard second-order cone program, thus making it computationally tractable. Finally, numerical experiments are presented to demonstrate the effectiveness of the proposed models and optimization methods.