Bi-objective optimization of a multi-product multi-period three-echelon supply chain network consisting of manufacturing plants, distribution centers (DCs) each with uncertain services, and customer nodes is aimed in this paper. The two objectives are minimization of the total cost while maximizing the average number of products dispatched to customers. The decision variables are: (1) the number and the locations of reliable DCs in the network, (2) the optimum number of items produced by plants, (3) the optimum quantity of transported products, (4) the optimum inventory of products at DCs and plants, and (5) the optimum shortage quantity of the customer nodes. The problem is first formulated into the framework of a constrained bi-objective mixed integer linear programming model. Then, to solve the problem using the GAMS software, six multi-objective decision-making (MODM) methods are investigated in order to select the best in terms of total supply chain cost, total expected number of products dispatched to customers, and their required CPU time, simultaneously. At the end, some numerical illustrations are provided to show the applicability of the proposed methodology.