A probabilistic bi-objective model for a humanitarian location-routing problem under uncertain demand and road closure

Effective planning and execution of humanitarian aid logistics activities ensure that disaster-related losses are minimized. This study addresses a tactical-level pre-disaster humanitarian logistics problem where a decision-maker decides on cross-dock locations by taking potential vehicle routes into account. A decision support model is proposed for the location selection and distribution operations in humanitarian logistics with explicit fuel consumption estimation. In the addressed problem, the demand amount of each node depends on probabilistic disaster scenarios. Probabilities of whether each arc/road is open or closed and heterogeneous vehicle fleet in terms of vehicle sizes are also respected. The model is formulated as probabilistic bi-objective mixed integer linear programming, whose objectives are minimization of the total cost (i.e., fuel cost, vehicle fixed cost, and fixed opening cost) and total travel time. To the best of our knowledge, the proposed decision support model is unique in terms of the features considered simultaneously. The applicability of the model is demonstrated by the case study and subsequent numerical analyses of a possible earthquake in the Kartal district of Istanbul. The proposed model is shown to have the potential to support decision-makers in preparation for a disaster. A solution approach based on a clustering algorithm has been also proposed to solve larger instances of the problem. The effectiveness of this heuristic has been demonstrated through its application to larger-scale problems.