A robust model for emergency supplies prepositioning and transportation considering road disruptions

Proper prepositioning of emergency supplies can dramatically improve the efficiency of emergency response work. However, the uncertainties of emergency demands and road conditions bring difficulties to the prepositioning of emergency supplies. This paper proposes a two-stage robust model to locate emergency supply points and preposition the corresponding storage amount of emergency supplies, in which we presented two budget sets to describe the uncertainties of demands and road conditions, respectively. The innovative use of variables in the model to limit road capacities addresses the representation of different road interruption scenarios. We proposed an algorithm based on Benders decomposition by transforming the second-stage model into a binary linear programming model. Computational experiments based on the Sioux Falls network demonstrate the validity of the model and algorithm. We conducted sensitivity analyses for some important parameters in the model, such as two uncertainty control parameters, unit transportation cost, budget for the construction of emergency supply points, etc. We find that the uncertainty of road disruptions has a greater impact on the model than the uncertainty of demands. In addition, when the control parameter of the road disruptions exceeds a certain threshold, its influence on the model remains essentially constant.