This paper introduces a variant of the vehicle routing problem where a group of retail stores are served from a distribution center using a fleet of vehicles. Moreover, products are distributed to consumers from some of these retail stores based on product availability at inventory and by means of the same fleet of vehicles. This variant of the vehicle routing problem can be found in omni-channel retail distribution systems. Retail distribution systems are considered omni- or multi-channel systems when consumers can either place orders online or physically visit the stores to buy the products. In this problem, the decisions of assigning consumers to retail stores based on inventory availability are combined with finding the routes of vehicles. The new problem can be considered a generalization of both capacitated vehicle routing problem and the pickup and delivery problem. The paper presents a mathematical formulation to describe this problem and proposes two solution approaches (two-phase heuristic and multi-ant colony algorithm). We also generate new benchmark problem instances to evaluate the performance of the proposed solution approaches.