  Multiple and usually conflicting objectives subject to data uncertainty are
main features in many real-world problems. Consequently, in practice,
decision-makers need to understand the trade-off between the objectives,
considering different levels of uncertainty in order to choose a suitable
solution. In this paper, we consider a two-stage bi-objective single source
capacitated model as a base formulation for designing a last-mile network in
disaster relief where one of the objectives is subject to demand uncertainty.
We analyze scenario-based two-stage risk-neutral stochastic programming,
adaptive (two-stage) robust optimization, and a two-stage risk-averse
stochastic approach using conditional value-at-risk (CVaR). To cope with the
bi-objective nature of the problem, we embed these concepts into two criterion
space search frameworks, the $\epsilon$-constraint method and the balanced box
method, to determine the Pareto frontier. Additionally, a matheuristic
technique is developed to obtain high-quality approximations of the Pareto
frontier for large-size instances. In an extensive computational experiment, we
evaluate and compare the performance of the applied approaches based on
real-world data from a Thies drought case, Senegal.
