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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. [ABSTRACT FROM AUTHOR]

• A new multi-period dynamic pre-positioning of emergency supplies problem is developed for disaster mitigation. • A distributionally robust optimization approach is proposed to deal with demand uncertainty. • The computationally tractable safe approximations of ambiguous chance constraints are reformulated. • A real-world numerical study is performed to illustrate our analytical results. The pre-positioning problem is an important part of emergency supply. Pre-positioning decisions must be made before disasters occur under high uncertainty and only limited distribution information. This study proposes a distributionally robust optimization model for the multi-period dynamic pre-positioning of emergency supplies with a static pre-disaster phase and a dynamic post-disaster phase. In the post-disaster phase, the uncertain demands are time varying and have partial distribution information that belongs to a given family of distributions. The family of distributions is described by a given perturbation set based on historical information. Therefore, the proposed model forms a semi-infinite programming problem with ambiguous chance constraints, which typically would be computationally intractable. We refine the bounded perturbation sets (box, box-ball and box-polyhedral) and develop computationally tractable safe approximations of the chance constraints. Finally, a realistic application to the Circum-Bohai Sea Region of China is presented to illustrate the effectiveness of the robust optimization model. [ABSTRACT FROM AUTHOR]

In this paper, we study an essential and more realistic variant of the hub location-routing problem in which third-party logistics (3PL) are incorporated into a self-built distribution hub network. A two-stage mixed-integer programming model is developed to address the proposed hub location-routing problem with mixed logistical strategies. In the strategic stage, the hub location and allocation decisions are made before the realization of uncertain demands to minimize the total construction and transportation costs. In the operational stage, the managers make vehicle routing decisions with and without the 3PL strategy, and route planning is considered for multiple owned and 3PL vehicles on the basis of simultaneous pickup and delivery. We investigate the effects of uncertain factors on the network design of this framework, as the node demands are often unobservable or difficult to obtain accurately in practice. To address the inherent uncertainty of the problem, we propose an adaptive distributionally robust model by limiting uncertain demands to a specified ambiguity set. Moreover, we reformulate the proposed model into tractable robust counterpart forms under the ambiguity set with information about the support, mean and upper bounds on the dispersion. We design a genetic algorithm with local search to solve the reformulated model on a large scale. Finally, we conduct a case study for a leading retail enterprise in the Beijing–Tianjin–Hebei region to demonstrate the effectiveness and applicability of our model. • A new model integrates third-party logistics into a hub location–routing problem with multiple vehicles. • The adaptive distributionally robust optimization is applied to characterize the uncertainties with partial information. • A tractable framework reformulates the two stage model into an MILP model. • A real-world chain of retail case study is perform ed to quantify our proposed method. [ABSTRACT FROM AUTHOR]