AN EXACT SOLUTION FOR REAL-LIFE TRANSSHIPMENT PATH PROBLEM

In industrial engineering, transportation planning, vehicle routing problem, warehousing, inventory management, and customer service are logistics problems. Graph theory algorithms provide solutions to logistics problems such as the shortest path, minimum spanning tree, and vehicle routing problems. In a logistics company system with branches and transfer centers to which the branches are affiliated, if the sorting process is carried out in the transfer centers, the deliveries collected from the branches must be transported to a transfer center. Thus, there are situations where delivery is transferred in the sending branch, the sending transfer center, the receiving transfer center, and the receiving branch, respectively. In this flow, transferring with a single transfer center without visiting two transfer centers reduces the total cost. While moving from the sender transfer center to the receiver transfer center, stopping by some branches on the way allows us to complete the transfer process with a single transfer center and eliminates the necessity of leaving the vehicle from the receiver transfer center to these branches again. Thus, the number of vehicles that need to go from the receiver transfer center to the branches is reduced. The mentioned logistics structure is defined as a graph that is considered a network design problem. Given the sender transfer center S, the receiver transfer center T, the set of branches A connected to S, and the set of branches C that are not connected to S or T, a counting algorithm that gives the minimum value route among all combinations are designed in order to find the optimal route from the source node s ∈ A∪{S}, to the target node t=T. The algorithm has been implemented in Python and Gams and tested by the different number of elements of the set A and the set C.