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.

In this paper, we consider a two-machine re-entrant permutation flowshop scheduling problem with the objective of minimizing total flowtime, and suggest branch and bound algorithms for the scheduling problem. In this scheduling problem, each job must be p

This paper dealt with a kind of heterogeneous vehicle routing problem with known demand and time deadline of customers. The customers are supposed to have one of tight deadline and loose deadline. The demand of customers with tight deadline must be fulfil