When logistics services integrator integrates functional logistics service vendors, the determination of the number is critical. Considering the reliability of vendors, the paper formulates an integer non-linear programming model to solve the vendor selection problem. The objective function is to minimize the total cost. The constraint functions are to maximize the reliability and choose the appropriate vendors. The reliability of logistics service supply chain is studied. This paper constructs a combination algorithm based on sequential quadratic programming and branch and bound method. It can meet both non-linear programming and integer programming. By numerical simulation, the optimal solution and near optimal solution are given. The results show the suitable numbers of each kind of functional logistics service vendors, the minimum cost and the maximum reliability of logistics services supply chain.