Vehicle routing problems have received substantial attention in the field of delivery logistics as well as among the research community. The decisions regarding the assignment of cities or customers to vehicles, transporting goods by meeting the demands of customers, and the routing and sequencing of vehicles are all crucial in curbing the delivery costs involved in a network system. It is also to be noted that the traditional transportation sector has further expanded its horizons with the inclusion of autonomous vehicles like UAVs. With the application of new emerging technologies, our study focuses on optimizing vehicle routing problems in various contexts, a typical delivery network, an emergency relief-packet delivery system, and a solid waste management network. The proposed research addresses a multi-truck, multi-drone last-mile delivery system to minimize delivery time. We also develop a multi-objective location routing problem to strategically plan the locations of distribution centers to distribute relief packages to communities in the event of a disaster, coordinating ground vehicles and drones. Our research also manages to optimize the transportation network in a municipal solid waste management system in a city to minimize the total fixed and operational costs involved. The cases discussed, and the models developed promise substantial savings in terms of cost and time, thereby guaranteeing efficient delivery systems.