Applying robust optimization to the shelter location–allocation problem: a case study for Istanbul

In this study, we consider the shelter location and allocation problem under demand uncertainty. In particular, we seek to improve the disaster preparedness level of Turkey by developing a robust optimization approach for locating shelter areas required after a disastrous earthquake in Istanbul. Our robust modelling framework implements a demand prediction methodology which generates a number of ground shaking scenarios by incorporating the effect of uncertainties in seismic parameters as well as the exposure level of the urban vulnerability. We reformulate the deterministic mixed integer linear programming version of the problem as a robust model. This model leverages the robust nature of the model to account for the uncertainties of parameters within each individual scenario. Our numerical results for the small-scale Kartal district of Istanbul and the large-scale Anatolian side of Istanbul case studies show that the proposed formulation yields solutions that are socially more acceptable and preferable than those obtained by their deterministic and stochastic counterparts. Aiming to produce stable and proper solutions that perform consistently well for any possible occurrence of uncertain parameters, the recommended robust solutions lead to better results by reducing possible regret which cannot be compensated after an earthquake.