Stochastic network design for disaster preparedness

Abstract

This article introduces a risk-averse stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. The sizes and locations of the response facilities and the inventory levels of relief supplies at each facility are determined while guaranteeing a certain level of network reliability. A probabilistic constraint on the existence of a feasible flow is introduced to ensure that the demand for relief supplies across the network is satisfied with a specified high probability. Responsiveness is also accounted for by defining multiple regions in the network and introducing local probabilistic constraints on satisfying demand within each region. These local constraints ensure that each region is self-sufficient in terms of providing for its own needs with a large probability. In particular, the Gale–Hoffman inequalities are used to represent the conditions on the existence of a feasible network flow. The solution method rests on two pillars. A preprocessing algorithm is used to eliminate redundant Gale–Hoffman inequalities and then proposed models are formulated as computationally efficient mixed-integer linear programs by utilizing a method based on combinatorial patterns. Computational results for a case study and randomly generated problem instances demonstrate the effectiveness of the models and the solution method.