Although there is a large body of literature on logistics optimisation in single-objective deterministic contexts, the real world is often stubbornly stochastic and multi-objective. While these aspects can be overlooked in some cases, there are also cases where taking stochasticity and multiple objectives into account while optimising can lead to better decision making. We investigate two logistics optimisation problems encountered in the context of disaster relief and service facility location. These problems are both stochastic and bi-objective in nature. We develop exact solution approaches based on integer and linear programming techniques. We also derive a heuristic method for tackling input data of meaningful size within realistic CPU budget constraints. Our solution approaches are validated through experiment.