Managing the distribution of goods is a vital operation for many companies. A successful distribution system requires an effective distribution strategy selection and optimum route planning at the right time and minimum cost. Furthermore, customer's demand and location can vary from order to order. In this situation, a mixed delivery system is a good solution for it and allows the use of different strategies together to decrease delivery costs. Although the "distribution strategy selection" is a critical issue for companies, there are only a few studies that focus on the mixed delivery network problem. There is a need to propose an efficient solution for the mixed delivery problem to guide researchers and practitioners. This paper develops a new "modified" savings-based genetic algorithm which is named "distribution strategy selection and vehicle routing hybrid algorithm (DSSVRHA)." Our new algorithm aims to contribute to the literature a new hybrid solution to solve a mixed delivery network problem that includes three delivery modes: "direct shipment," "milk run," and "cross-docking" efficiently. It decides the appropriate distribution strategy and also optimal routes using a heterogeneous fleet of vehicles at minimum cost. The results of the hybrid algorithm are compared with the results of the optimization model. And the performance of the hybrid algorithm is validated with statistical analysis. The computational results reveal that our developed algorithm provides a good solution for reducing the supply chain distribution costs and computational time.