This study presents a metaheuristic based on a multiobjective evolutionary algorithm to solve a biobjective mixed-integer nonlinear programming model for supply chain design with location-inventory decisions and supplier selection. The supply chain has four echelons with suppliers, plants, distribution centers, and retailers. The decision variables are the opening of plants and distribution centers and the flow of materials between the different facilities, considering a continuous review inventory policy. The conflicting objectives are to minimize total costs on the entire chain, and to maximize a combined value of overall equipment effectiveness from suppliers. Small- and medium-sized scenarios are solved and compared with Pareto fronts obtained with commercial optimization software applying the epsilon-constraint method. The numerical results show the effectiveness of the proposed metaheuristic. The main contributions of this work are a new practical problem that has not been analyzed before, and the development of the evolutionary algorithm.