We consider a network design problem in a four tier supply chain consisting of suppliers, plants, distribution centers and customers. We suggest a cooperative coevolutionary algorithm(CCEA) to solve the problem. First, the problem is decomposed into three subproblems for each of which the chromosome population is created correspondingly. Each chromosome in a population is represented as an integer denoting a supply node. Then an algorithm generating a solution from a chromosome representation is suggested. Also an algorithm evaluating the performance of a solution is suggested. Finally we set the operator of selection, crossover, and mutation. An experimental study is carried out to compare the performance of the CCEA with that of a genetic algorithm. The results show that the CCEA tends to generate better solutions than genetic algorithms.