Bi-objective stochastic programming models for determining depot locations in disaster relief operations

This paper presents two-stage bi-objective stochastic programming models for disaster relief operations. We consider a problem that occurs in the aftermath of a natural disaster: a transportation system for supplying disaster victims with relief goods must be established. We propose bi-objective optimization models with a monetary objective and humanitarian objective. Uncertainty in the accessibility of the road network is modeled by a discrete set of scenarios. The key features of our model are the determination of locations for intermediate depots and acquisition of vehicles. Several model variants are considered. First, the operating budget can be fixed at the first stage for all possible scenarios or determined for each scenario at the second stage. Second, the assignment of vehicles to a depot can be either fixed or free. Third, we compare a heterogeneous vehicle fleet to a homogeneous fleet. We study the impact of the variants on the solutions. The set of Pareto-optimal solutions is computed by applying the adaptive Epsilon-constraint method. We solve the deterministic equivalents of the two-stage stochastic programs using the MIP-solver CPLEX.