Zakir Hussain Ahmed

Today, goods transportation is considered to be one of the most important activities of national economics. Logistics and supply chain play an important role in the industry and services, considering the needs of the people, while there is an increase in the population. In addition, the role of logistics in urban areas, especially in restaurants, grocery stores, etc., is clearly visible. Besides, the final price of the goods is the most important factor that is always considered in service and in production. Due to this important factor, transportation has been found to be one of the most significant and influential factors in determining the price of goods. For these reasons, the newest variant of the vehicle routing problem, called the line feeder vehicle routing problem (LFVRP), is considered in this paper, in which various types of vehicles (large and small vehicles) are used for providing services to customers. In this particular type of delivery issue, these vehicles must start from the warehouse, meet customers, and finally return to the depot. In fact, the issue of LFVRP is related to the fast customer service in urban areas because in this case, all that are considered to be of priority are to minimize transportation costs and overall distribution time for fast customer service, especially in urban areas. Due to the many applications of this problem in the real world, a general review of this problem is conducted, and the versions of this problem are described along with the algorithms for its solution in the paper.