With the globalization of the supply chain and the change of demand environment, designing an effective logistic system in the sustainable development of the supply chain becomes more critical. This study proposes a location-routing problem to determine an efficient integration of single factory and multi-distribution centers and multi-customers in uncertain demands. This problem can be regarded as an optimization integrating location, distribution decision, and routing management. The objective function is to minimize the total cost and satisfy all the requirements, which is a highly complex NP-hard problem, so a hybrid algorithm of genetic algorithm (GA) and tabu search (TS) algorithm is proposed. A fuzzy c-means clustering algorithm is used to produce an initial solution. Fuzzy triangular number and confidence interval transformation are used to deal with fuzzy customer demand. The research findings concludes that (i) determine the numbers of facilities with locations that should be opened and (ii) minimize the total cost in supply chain. The experiments prove that the proposed hybrid algorithm of GA and TS algorithm overcomes the defect of local optimum in the literature viewpoint, and the optimization algorithms can effectively solve the location-routing problem.