In this paper, we investigated an Inventory Routing Problem (IRP) with deterministic customer demand, in a two-tiered supply chain. The supply chain network consists of a supplier who uses a single vehicle with a given capacity to deliver a single type of product to many customers. We are interested in population-based algorithms to solve our problem. A Memetic Algorithm (MA) is developed based on Genetic Algorithm (GA) and Variable Neighborhood Search methods (VNS). The proposed metaheuristics are tested on small and large sizes referenced benchmarks. The results of MA are compared with those of classical GA and with the optimal solutions from the literature. The comparison showed the efficiency of the MA use and its ability to generate high quality solutions within a reasonable time.