•We consider a single retailer, multiple suppliers, and price sensitive demand.•The objective is to maximize profit and determine order quantities for selected supplier.•A mixed integer nonlinear programming formulation of the problem is provided.•We determine sufficient conditions for the optimal selection of a single supplier.•We also investigate the impact of supplier's capacity on the optimal sourcing strategy. This article presents a mixed integer nonlinear programming model to find the optimal selling price and replenishment policy for a particular type of product in a supply chain defined by a single retailer and multiple potential suppliers. Each supplier offers all-unit quantity discounts as an incentive mechanism. Multiple orders are allowed to be submitted to the selected suppliers during a repeating order cycle. The demand rate is considered to be not constant but dependent upon the selling price. The model provides the optimal number of orders and corresponding order quantities for the selected suppliers, and the optimal demand rate and selling price that maximize the total profit per time unit under suppliers’ capacity and quality constraints. In addition, we provide sufficient conditions under which there exists an optimal solution where the retailer only orders from one supplier. We also apply the Karush–Kuhn–Tucker conditions to investigate the impact of supplier's capacity on the optimal sourcing strategy. The results show that, there may exist a range of capacity values for the dominating supplier, where the retailer's optimal sourcing strategy is to consider multiple suppliers without fully utilizing the dominating supplier's capacity. A numerical example is presented to illustrate the proposed model.