A supply chain distribution network design model is developed in this paper. The goal of the model is to select the optimum numbers, locations and capacity levels of plants and warehouses to deliver the products to the retailers at the least cost while satisfying the desired service level. Maximal covering approach is employed in statement of the service level. Different from the previous researches in this area, coverage functions which differ among the retailers according to their service standard requests are defined for the retailers. Additionally, to provide a more realistic model structure, decision maker’s imprecise aspiration levels for the goals, and demand uncertainties are incorporated into the model through fuzzy modeling approach. Realistic computational experiments are provided to confirm the viability of the model.