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In this study, a vendor-managed inventory model is developed for a single-vendor multiple-retailer single-warehouse (SV-MR-SV) supply chain problem based on the economic order quantity in which demands are stochastic and follow a uniform probability distribution. In order to reduce holding costs and to help balanced on-hand inventory cost between the vendor and the retailers, it is assumed that all inventory is held at a central warehouse with the lowest cost among the parties. The capacity of the central warehouse is limited. The objective is to find the warehouse replenishment frequency, the vendor\'s replenishment frequency, the order points, and the order quantities of the retailers such that the total inventory cost of the integrated supply chain is minimized. The proposed model is a mixed integer nonlinear programming problem (MINLP); hence, a genetic algorithm (GA) is utilized to solve this NP-hard problem. The parameters of the GA are calibrated using the Taguchi method to find better solutions. Some numerical illustrations are solved at the end to demonstrate the applicability of the proposed methodology and to evaluate the performance of the solution method.