The emergence of huge industries and mega economies has led to the creation of supply chains and the development of transportation systems. Supply chain management is used to direct raw materials and products through the supply chains, which were extended beyond the direct relation between the producer and customer. The vehicle routing problem (VRP) is concerned with one of the operational decisions in supply chain. The VRP is the class of problems in which the demand of customers should be fulfilled by a fleet of vehicles. This fleet of vehicles is starting from and returning to the depot while minimizing the total route cost such as travelled distance, time, etc. The VRP is considered a more sophisticated form of the famous TSP. In this thesis, VRP models arising in omni-channel retail distribution systems are introduced. Retail distribution systems are considered as omni-channel systems when consumers can either place orders online or visit the stores physically to buy the products. In case of online orders, the organizations are responsible for the products delivery. The resultant VRP models can be considered as new variants of the VRP. These models represent variety of scenarios adopted by different retail chain store organizations. Mathematical formulations are provided for these new variants of the VRP and solved to obtain optimum solutions for small problem instances. The VRP and its variants are NP-hard problems and difficult to solve in the case of large problem instances. Therefore, different heuristics and metaheuristics are proposed to obtain optimum (or near optimum) solutions for large problem instances. New bench mark problem instances are generated to test the proposed heuristics and metaheuristics performance. The average percentage deviation of the proposed metaheuristics with respect to the optimum solutions of small problem instances obtained from the mathematical models is less than 1%. It can be concluded that the proposed metaheuristics have good performance while succeeding to keep shorter calculation time.