In this work, a mixed-integer binary non-linear two-echelon inventory problem is formulated for a vendor-buyer supply chain network in which lead times are constant and the demands of buyers follow a normal distribution. In this formulation, the problem is a combination of an (r, Q) and periodic review policies based on which an order of size Q is placed by a buyer in each fixed period once his/her on hand inventory reaches the reorder point r in that period. The constraints are the vendors’ warehouse spaces, production restrictions, and total budget. The aim is to find the optimal order quantities of the buyers placed for each vendor in each period alongside the optimal placement of the vendors among the buyers such that the total supply chain cost is minimized. Due to the complexity of the problem, a Modified Genetic Algorithm (MGA) and a Particle Swarm Optimization (PSO) are used to find optimal and near-optimum solutions. In order to assess the quality of the solutions obtained by the algorithms, a mixed integer nonlinear program (MINLP) of the problem is coded in GAMS. A design of experiment approach named Taguchi is utilized to adjust the parameters of the algorithms. Finally, a wide range of numerical illustrations is generated and solved to evaluate the performances of the algorithms. The results show that the MGA outperforms the PSO in terms of the fitness function in most of the problems and also is faster than the PSO in terms of CPU time in all the numerical examples.