This paper focuses on the design of a distribution network problem in a three-tiered supply chain under uncertainty. The objective is to determine the optimal number, locations and capacities of plants and warehouses to minimize the overall network costs over a variety of economic growth scenarios. For this purpose, a mixed integer linear programming model is extended in a robust optimization framework and then three heuristic approaches based on genetic and memetic algorithms and a mathematical programming approach are used to solve this problem. The effectiveness of the proposed heuristics and the trade-off between model robustness and solution robustness is investigated and directions for further researches are presented.