After Dantzig and Rasmer introduced Vehicle Routing Problem in 1959, this field has been studied with numerous approaches so far. Classical Vehicle Routing Problem can be described as a problem of multiple number of homogeneous vehicles sharing a same starting node and having their own routes to meet the needs of demand nodes. After satisfying all the needs, they go back to the starting node. In order to apply the real world problem, this problem had been developed with additional constraints and pick up & delivery model is one of them. To enhance the effectiveness of pick up & delivery, hub became a popular concept, which often helps reducing the overall cost and improving the quality of service. Lots of studies have suggested heuristic methods to realize this problem because it often becomes a NP-hard problem. However, because of this characteristic, there are not many studies solving this problem optimally. If the problem can be solved in polynomial time, optimal solution is the best option. Therefore, this study proposes a new mathematical model to solve this problem optimally, verified by a real world problem. The main improvements of this study compared to real world case are firstly, make drivers visit every nodes once except hub, secondly, make drivers visit every nodes at the right time, and thirdly, make drivers start and end their journey at their own homes.

An efficient heuristic for two-vehicle-one-depot problems is developed in this research. Vehicle moving speeds are various along hour based time intervals due to traffic jams of rush hours. Two different heuristics are examined. One is that the delivery area assignment is made using Sweep algorithm for two vehicles by splitting the whole area in half to equally divide all delivery points. The other is using common area by leaving unassigned area between the assigned for two vehicles. The common area is reassigned by two stages to balance the completion time of two vehicle's delivery. The heuristic with common area performed better than the other due to various vehicle moving speeds and traffic jams.

A sweep-based heuristic using common area is developed for multi-vehicle VRPs under time various and unsymmetric forward and backward vehicle moving speed. One depot and 2 delivery vehicle are assumed in this research to make the problem solving strategy simple. A common area is held to make adjustment of possible unbalance of between two vehicle delivery completion times. The 4 time zone heuristic is used to solve for efficient delivery route for each vehicle. The current size of common area needs to be studied for better results, but the suggested problem solving procedures can be expanded for any number of vehicles.

The growing logistics strategy of a company is to optimize their vehicle route scheduling in their supply chain system. It is very important to analyze for continuous pickups and delivery vehicle scheduling. This paper is a computational study to investigate the effectiveness of continuous pickups and delivery vehicle routing problems. These scheduling problems have 3 subproblems; Inbound Vehicle Routing Problem with Makespan and Pickup, Line-haul Network Problem, and Outbound Vehicle Routing Problem with Delivery. In this paper, we propose 5 heuristic Algorithms; Selecting Routing Node, Routing Scheduling, Determining Vehicle Type with Number and Quantity, and Modification Selecting Routing Node. We apply these Algorithms to S vehicle company. The results of computational experiments demonstrate that proposed methods perform well and have better solutions than other methods considering the basic time and due-date.

Many research papers on transportation studies have focused on the Vehicle Routing Problem (VRP) and Vehicle Scheduling Problem (VSP). However in the real world, it is known that it takes long time to build vehicle scheduling in the process of transporting the amount of orders from the logistics center to the vendors due to the realistic constraints. This paper presents a framework design for each process enabling delivery planning automatically using heuristic algorithm. In addition, an interactive automatic delivery planning system is implemented utilizing the proposed algorithm.