In order to model the emergency facility location-allocation problem with uncertain parameters, an uncertain multi-objective model is developed within the framework of uncertainty theory. The proposed model minimizes time penalty cost, distribution cost and carbon dioxide emissions. The equivalents of the model are discussed via operational laws of uncertainty distribution. By employing the goal attainment technique, a series of Pareto-optimal solutions are generated that can be used for decision-making. Finally, several numerical experiments are presented to verify the validity of the proposed model and to illustrate decision-making strategy.

The emergency facility location-allocation (EFLA) problem is a critical component of large-scale emergency logistics. Modeling such real-world problems often requires consideration of uncertainty. In humanitarian situations, both efficiency and fairness play significant roles in the effectiveness of emergency response decision-making. This paper focus on an EFLA problem in an uncertain environment, in which the distances, demands, and operation costs are described by uncertain variables. Consequently, a bi-objective emergency facility location-allocation (BEFLA) model that tries to optimize efficiency as well as fairness under uncertainty is formulated. Some essential results are discussed for equivalently converting the uncertain model into a crisp one. By employing a normalization method, the proposed uncertain bi-objective model is ultimately transformed into a single objective crisp location-allocation linear program. Finally, a real case study taken from the 20 April 2013 Ya'an Earthquake illustrates the practicality and validity of the model and the proposed methodology. Sensitivity and comparative analyses are also provided to demonstrate the superiorities of the model.