Multi-period dynamic distributionally robust pre-positioning of emergency supplies under demand uncertainty

Abstract

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.